ORIGINAL_ARTICLE
Vibration Analysis of Magneto-Electro-Elastic Timoshenko Micro Beam Using Surface Stress Effect and Modified Strain Gradient Theory under Moving Nano-Particle
In this article, the free vibration analysis of magneto-electro-elastic (MEE) Timoshenko micro beam model based on surface stress effect and modified strain gradient theory (MSGT) under moving nano-particle is presented. The governing equations of motion using Hamilton’s principle are derived and these equations are solved using differential quadrature method (DQM). The effects of dimensionless electric potential, dimensionless magnetic parameter, material length scale parameter, external electric voltage, external magnetic parameter, slenderness ratio, temperature change, surface stress effect, two parameters of elastic foundation on the dimensionless natural frequency are investigated. It is shown that the effect of electric potential and magnetic parameter simultaneously increases the dimensionless natural frequency. On the other hands, with considering two parameters, the stiffness of MEE Timoshenko micro beam model increases. It can be seen that the dimensionless natural frequency of micro structure increases by MSGT more than modified couple stress theory (MCST) and classical theory (CT). It is found that by increasing the mass of nano-particle, the dimensionless natural frequency of system decreases. The results of this study can be employed to design and manufacture micro-devices to prevent resonance phenomenon or as a sensor to control the dynamic stability of micro structures.
http://jsm.iau-arak.ac.ir/article_539690_d2d55706e7c6eb2c9b05057419af21b5.pdf
2018-03-01T11:23:20
2019-10-22T11:23:20
1
22
Vibration analysis
Moving nano-particle
Timoshenko micro beam model
Surface stress effect, MSGT
Magneto-electro-elastic loadings
DQM
M
Mohammadimehr
mmohammadimehr@kashanu.ac.ir
true
1
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
LEAD_AUTHOR
H
Mohammadi Hooyeh
true
2
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
AUTHOR
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2
[3] Priya S., Islam R., Dong S., Viehland D., 2007, Recent advancements in magneto-electric particulate and laminate composites, Journal of Electroceramics 19: 149-166.
3
[4] Zhai J., Xing Z., Dong S., Li J., Viehland D., 2008, Magnetoelectric laminate composites: an overview, Journal of the American Ceramic Society 91: 351-358.
4
[5] Nan C.W., Bichurin M., Dong S., Viehland D., Srinivasan G., 2008, Multiferroic magnetoelectric composites: historical perspective, status, and future directions, Journal of Applied Physics 103: 031101.
5
[6] Bhangale R.K., Ganesan N., 2006, Free vibration of functionally graded non-homogeneous magneto-electro-elastic cylindrical shell, International Journal for Computational Methods in Engineering Science and Mechanics 7: 191-200.
6
[7] Lang Z., Xuewu L., 2013, Buckling and vibration analysis of functionally graded magneto-electro-thermo-elastic circular cylindrical shells, Applied Mathematical Modelling 37: 2279-2292.
7
[8] Razavi S., Shooshtari A., 2015, Nonlinear free vibration of magneto-electro-elastic rectangular plates, Composite Structures 119: 377-384.
8
[9] Ke L.L., Wang Y.S., Yang J., Kitipornchai S., 2014, Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory, Acta Mechanica Sinica 30: 516-525.
9
[10] Li Y.S., Cai Z.Y., Shi S.Y., 2014, Buckling and free vibration of magneto-electro-elastic nanoplate based on nonlocal theory, Composite Structures 111: 522-529.
10
[11] Shooshtari A., Razavi S., 2015, Linear and nonlinear free vibration of a multilayered magneto-electro-elastic doubly-curved shell on elastic foundation, Composite Part B 78: 95-108.
11
[12] Shooshtari A., Razavi S., 2015, Large amplitude free vibration of symmetrically laminated magneto-electro-elastic rectangular plates on Pasternak type foundation, Mechanics Research Communications 69: 103-113.
12
[13] Mohammadimehr M., Rostami R., Arefi M., 2016, Electro-elastic analysis of a sandwich thick plate considering FG core and composite piezoelectric layers on Pasternak foundation using TSDT, Steel and Composite Structures 20: 513-543.
13
[14] Ansari R., Gholami R., Rouhi H., 2015, Size-dependent nonlinear forced vibration analysis of magneto-electro-thermo-elastic Timoshenko Nano beams based upon the nonlocal elasticity theory, Composite Structures 126: 216-226.
14
[15] Xin L., Hu Z., 2015, Free vibration of layered magneto-electro-elastic beams by SS-DSC approach, Composite Structures 125: 96-103.
15
[16] Xin L., Hu Z., 2015, Free vibration of simply supported and multilayered magneto-electro-elastic plates, Composite Structures 121: 344-350.
16
[17] Mohammadimehr M., Monajemi A.A., Moradi M., 2015, Vibration analysis of viscoelastic tapered micro-rod based on strain gradient theory resting on visco-Pasternak foundation using DQM, Journal of Mechanical Science and Technology 29 (6): 2297-2305.
17
[18] Rahmati A.H., Mohammadimehr M., 2014, Vibration analysis of non-uniform and non-homogeneous boron nitride nanorods embedded in an elastic medium under combined loadings using DQM, Physica B: Condensed Matter 440: 88-98.
18
[19] Ke L.L., Wang Y.S., 2014, Free vibration of size-dependent magneto-electro-elastic Nano beams based on the nonlocal theory, Phisyca E 63: 52-61.
19
[20] Wang Y., Xu R., Ding H., 2011, Axisymmetric bending of functionally graded circular magneto-electro-elastic plates, European Journal of Mechanics-A/Solid 30: 999-1011.
20
[21] Rao M.N., Schmidt R., Schröder K.U., 2015, Geometrically nonlinear static FE-simulation of multilayered magneto-electro-elastic, Composite Structures 127: 120-131.
21
[22] Mohammadimehr M., Rousta Navi B., Ghorbanpour Arani A., 2015, Free vibration of viscoelastic double-bonded polymeric nanocomposite plates reinforced by FG-SWCNTs using MSGT, sinusoidal shear deformation theory and meshless method, Composite Structures 131: 654-671.
22
[23] Mohammadimehr M., Rousta Navi B., Ghorbanpour Arani A., 2016, Modified strain gradient Reddy rectangular plate model for biaxial buckling and bending analysis of double-coupled piezoelectric polymeric nanocomposite reinforced by FG-SWNT, Composite Part B: Engineering 87: 132-148.
23
[24] Kattimani S.C., Ray M.C., 2015, Control of geometrically nonlinear vibrations of functionally graded magneto-electro-elastic plates, International Journal of Mechanical Sciences 99: 154-167.
24
[25] Liu Y., Han Q., Li C., Liu X., Wu B., 2015, Guided wave propagation and mode differentiation in the layered magneto-electro-elastic hollow cylinder, Composite Structures 132: 558-566.
25
[26] Sedighi H. M., Farjam N., 2016, A modified model for dynamic instability of CNT based actuators by considering rippling deformation, tip-charge concentration and Casimir attraction, Microsystem Technologies 23: 2175-2191.
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[27] Zare J., 2015, Pull-in behavior analysis of vibrating functionally graded micro-cantilevers under suddenly DC voltage, Journal of Applied and Computational Mechanics 1(1): 17-25.
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[28] Sedighi H. M., 2014, The influence of small scale on the pull-in behavior of nonlocal nano bridges considering surface effect, Casimir and van der Waals attractions, International Journal of Applied Mechanics 6(3): 1450030.
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[29] Fleck N. A., Hutchinson J. W., 1993, Phenomenological theory for strain gradient effects in plasticity, Journal of the Mechanics and Physics of Solids 41(12): 1825-1857.
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[30] Fleck N. A., Hutchinson J. W., 1997, Strain gradient plasticity, Advances in Applied Mechanics 33: 296-358.
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[31] Fleck N. A., Hutchinson J. W., 2001, A reformulation of strain gradient plasticity, Journal of the Mechanics and Physics of Solids 49(10): 2245- 2271.
31
[32] Lam D.D.C., Yang F., Chong A.C.M., Wang J., Tong P., 2003, Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics Solids 51: 1477-1508.
32
[33] Akgöz B., Civalek Ö., 2013, A size-dependent shear deformation beam model based on the strain gradient elasticity theory, International Journal of Engineering Science 70: 1-14.
33
[34] Mohammadimehr M., Salemi M., Rousta Navi B., 2016, Bending, buckling, and free vibration analysis of MSGT microcomposite Reddy plate reinforced by FG-SWCNTs with temperature- dependent material properties under hydro-thermo-mechanical loadings using DQM, Composite Structures 138: 361-380.
34
[35] Gurtin M., Ian Murdoch A., 1975, A continuum theory of elastic material surfaces, Archive for Rational Mechanics and Analysis 57: 291-323.
35
[36] Gurtin M., Ian Murdoch A., 1987, Surface stress in solids, International Journal of Solids and Structures 14: 431-440.
36
[37] Mohammadimehr M., Rousta Navi B., Ghorbanpour Arani A., 2015, Surface stress effect on the nonlocal biaxial buckling and bending analysis of polymeric piezoelectric Nano plate reinforced by CNT using Eshelby-Mori-Tanaka approach, Journal of Solid Mechanics 7( 2): 173-190.
37
[38] Karimi M., Shokrani M. H., Shahidi A. R., 2015, Size-dependent free vibration analysis of rectangular nanoplates with the consideration of surface effects using finite difference method, Journal of Applied and Computational Mechanics 1(3): 122-133.
38
[39] Ghorbanpour Arani A., Kolahchi R., Mosayebi M., Jamali M., 2016, Pulsating fluid induced dynamic instability of visco-double-walled carbon nano-tubes based on sinusoidal strain gradient theory using DQM and Bolotin method, International Journal of Mechanics and Materials in Design 12(1): 17-38.
39
[40] Ansari R., Gholami R., Sahmani S., 2011, Free vibration analysis of size-dependent functionally graded microbeams based on the strain gradient Timoshenko beam theory, Composite Structures 94 : 221-228.
40
[41] Şimşek M., Kocatürk T., Akbaş Ş.D., 2013, Static bending of a functionally graded microscale Timoshenko beam based on the modified couple stress theory, Composite Structures 95: 740-747.
41
[42] Li Y.S., Feng W.J., Cai Z.Y., 2014, Bending and free vibration of functionally graded piezoelectric beam based on modified strain gradient theory, Composite Structures 115: 41-50.
42
[43] Ghorbanpour Arani A., Abdollahian M., Kolahchi R., 2015, Nonlinear vibration of a Nano beam elastically bonded with a piezoelectric Nano beam via strain gradient theory, International Journal of Mechanical Sciences 100: 32-40.
43
[44] Ansari R., Mohammadi V., Faghih Shojaei M., Gholami R., Rouhi H., 2013, Nonlinear vibration analysis of Timoshenko Nano beams based on surface stress elasticity theory, European Journal of Mechanics-A/Solid 45 :143-152.
44
[45] Ke L.L., Wang Y.S., Wang Z.D., 2012, Nonlinear vibration of the piezoelectric Nano beams based on the nonlocal theory, Composite Structures 94: 2038-2047.
45
[46] Şimşek M., 2011, Nonlocal effects in the forced vibration of an elastically connected double-carbon nanotube system under a moving nanoparticle, Computational Materials Science 50: 2112-2123.
46
[47] Ghorbanpour Arani A., Mortazavi S.A., Kolahchi R., Ghorbanpour Arani A.H., 2015, Vibration response of an elastically connected double-Smart Nano beam-system based nano-electro-mechanical sensor, Journal of Solid Mechanics 7: 121-130.
47
[48] Ghorbanpour Arani A., Atabakhshian V., Loghman A., Shajari A.R., Amir S., 2012, Nonlinear vibration of embedded SWBNNTs based on nonlocal Timoshenko beam theory using DQ method, Phisyca B 407: 2549-2555.
48
[49] Murmu T., Pradhan S.C., 2009, Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM, Phisyca E 41: 1232-1239.
49
[50] Civalek O., 2006, Harmonic differential quadrature-finite differences coupled approaches for geometrically nonlinear static and dynamic analysis of rectangular plates on elastic foundation, Journal of Sound and Vibrations 294: 966-980.
50
[51] Akgoz B., Civalek O., 2011, Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams, International Journal of Engineering Science 49: 1268-1280.
51
[52] Zhang B., He Y., Liu D., Gan Z., Shen L., 2014, Non - classical Timoshenko beam element based on the strain gradient elasticity theory, Finite Element in Analysis and Design 79: 22-39.
52
[53] Ansari R., Gholami R., Darabi M.A., 2012, A non-linear Timoshenko beam formulation based on strain gradient theory, Journal of Mechanics of Materials and Structures 7: 195-211.
53
[54] Ghorbanpour Arani A., Kolahchi R., Zarei M.Sh., 2015, Visco-surface-nonlocal piezo-elasticity effects on nonlinear dynamic stability of graphene sheets integrated with ZnO sensors and actuators using refined zigzag theory, Composite Structures 132: 506-526.
54
ORIGINAL_ARTICLE
A Nonlocal First Order Shear Deformation Theory for Vibration Analysis of Size Dependent Functionally Graded Nano beam with Attached Tip Mass: an Exact Solution
In this article, transverse vibration of a cantilever nano- beam with functionally graded materials and carrying a concentrated mass at the free end is studied. Material properties of FG beam are supposed to vary through thickness direction of the constituents according to power-law distribution (P-FGM). The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived based on Timoshenko beam theory in order to consider the effect of shear deformation and rotary inertia. Hamilton’s principle is applied to obtain the governing differential equation of motion and boundary conditions and they are solved applying analytical solution. The purpose is to study the effects of parameters such as tip mass, small scale, beam thickness, power-law exponent and slenderness on the natural frequencies of FG cantilever nano beam with a point mass at the free end. It is explicitly shown that the vibration behavior of a FG Nano beam is significantly influenced by these effects. The response of Timoshenko Nano beams obtained using an exact solution in a special case is compared with those obtained in the literature and is found to be in good agreement. Numerical results are presented to serve as benchmarks for future analyses of FGM cantilever Nano beams with tip mass.
http://jsm.iau-arak.ac.ir/article_539691_977b620996b5f81f455edb5c3f0c474b.pdf
2018-03-01T11:23:20
2019-10-22T11:23:20
23
37
Timoshenko Beam Theory
Free vibration
Functionally graded Nano beam
Nonlocal elasticity theory
Tip mass
M
Ghadiri
ghadiri@eng.ikiu.ac.ir
true
1
Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
LEAD_AUTHOR
A
Jafari
true
2
Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
AUTHOR
[1] Iijima S., 1991, Helical microtubules of graphitic carbon, Nature 354: 56-58.
1
[2] Zhang Y. Q., Liu G. R., Wang J. S., 2004, Small-scale effects on buckling of multi walled carbon nanotubes under axial compression, Physical Review B 70(20): 205430.
2
[3] Eringen A. C., 1972, Nonlocal polar elastic continua, International Journal of Engineering Science 10(1): 1-16.
3
[4] Eringen A. C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54(9): 4703-4710.
4
[5] Peddieson J., George R. B., Richard P. M., 2003, Application of nonlocal continuum models to nanotechnology, International Journal of Engineering Science 41(3): 305-312.
5
[6] Aydogdu M., 2009, A general nonlocal beam theory: its application to Nano beam bending, buckling and vibration, Physica E: Low-Dimensional Systems and Nanostructures 41(9): 1651-1655.
6
[7] Phadikar J. K., Pradhan S. C., 2010, Variational formulation and finite element analysis for nonlocal elastic Nano beams and Nano plates, Computational Materials Science 49(3): 492-499.
7
[8] Pradhan S. C., Murmu T., 2010, Application of nonlocal elasticity and DQM in the flap wise bending vibration of a rotating Nano cantilever, Physica E: Low-Dimensional Systems and Nanostructures 42(7): 1944-1949.
8
[9] Ghorbanpour Arani A., Kolahchi R., Rahimi pour H., Ghaytani M., Vossough H., 2012, Surface stress effects on the bending wave propagation of Nano beams resting on a pasternak foundation, International Conference on Modern Application of Nanotechnology, Belarus.
9
[10] Ansari R., Gholami R., Sahmani S., 2011, Free vibration analysis of size-dependent functionally graded
10
microbeams based on the strain gradient Timoshenko beam theory, Composite Structures 94(1): 221-228.
11
[11] Ebrahimi F., Salari E., 2015, Thermo-mechanical vibration analysis of nonlocal temperature-dependent FG Nano beams with various boundary conditions, Composites Part B: Engineering 78: 272-290.
12
[12] Srinath L. S., Das Y. C., 1967, Vibration of beams carrying mass , Journal of Applied Mechanics 34(3): 784-785.
13
Goel R. P., 1976, Free vibrations of a beam mass system with elastically restrained ends, Journal of Sound and Vibration 47: 9-14.
14
[13] Saito H., Otomi K., 1979, Vibration and stability of elastically supported beams carrying an attached mass axial and tangential loads, Journal of Sound and Vibration 62: 257-266.
15
[14] Lau J. H., 1981, Fundamental frequency of a constrained beam , Journal of Sound and Vibration 78: 154-157.
16
[15] Lauara P. A. A., Filipich C., Cortinez V. H., 1987, Vibration of beams and plates carrying concentrated masses, Journal of Sound and Vibration 117: 459-465.
17
[16] Liu W. H., Yeh F. H., 1987, Free vibration of a restrained-uniform beam with intermediate masses, Journal of Sound and Vibration 117: 555-570.
18
[17] Maurizi M. J., Belles P. M., 1991, Natural frequencies of the beam-mass system: comparison of the two fundamental theories of beam vibrations, Journal of Sound and Vibration 150: 330-334.
19
[18] Maurizi M. J., Belles P. M., 1991, Natural frequencies of the beam-mass system: comparison of the two fundamental theories of beam vibrations, Journal of Sound and Vibration 150: 330-334.
20
[19] Bapat C.N., Bapat C., 1987, Natural frequencies of a beam with non-classical boundary conditions and concentrated masses, Journal of Sound and Vibration 112: 177-182.
21
[20] Oz H. R., 2000, Calculation of the natural frequencies of a beam-mass system using finite element method, Mathematical and Computational Applications 5: 67-75.
22
[21] Low K.H.,1991, A comprehensive approach for the Eigen problem of beams with arbitrary boundary conditions, Computers & Structures 39: 671-678.
23
[22] Kosmatka J.B., 1995, An improved two-node finite element for stability and natural frequencies of axial-loaded Timoshenko beams, Computers & Structures 57:141-149.
24
[23] Lin H.P., Chang S.C.,2005, Free vibration analysis of multi-span beams with intermediate flexible constraints, Journal of Sound and Vibration 281: 155-169.
25
[24] Ferreira A.J.M., Fasshauer G.E., 2006, Computation of natural frequencies of shear deformable beams and plates by an RBF-pseudospectral method, Computer Methods in Applied Mechanics and Engineering 196:134-146.
26
[25] Ruta P., 2006, The application of Chebyshev polynomials to the solution of the nonprismatic Timoshenko beam vibration problem, Journal of Sound and Vibration 296: 243-263.
27
[26] Laura P.A.A., Pombo J.A., Susemihl E.A., 1974, A note on the vibration of a clamped-free beam with a mass at the free end, Journal of Sound and Vibration 37: 161-168.
28
[27] Goel R.P., 1976, Free vibrations of a beam-mass system with elastically restrained ends, Journal of Sound and Vibration 47: 9-14.
29
[28] Parnell L.A., Cobble M.H., 1976, Lateral displacements of a vibrating cantilever beam with a concentrated mass, Journal of Sound and Vibration 44: 499-511.
30
[29] To C.W.S., 1982, Vibration of a cantilever beam with a base excitation and tip mass, Journal of Sound and Vibration 83: 445-460.
31
[30] Grant D.A., 1978, The effect of rotary inertia and shear deformation on the frequency and normal mode equations of uniform beams carrying a concentrated mass, Journal of Sound and Vibration 57: 357-365.
32
[31] Brunch Jr J.C., Mitchell T.P., 1987, Vibrations of a mass-loaded clamped-free Timoshenko beam, Journal of Sound and Vibration 114: 341-345.
33
[32] Abramovich H., Hamburger O., 1991, Vibration of a cantilever Timoshenko beam with a tip mass, Journal of Sound and Vibration 148: 162-170.
34
[33] Abramovich H., Hamburger O., 1992,Vibration of a uniform cantilever Timoshenko beam with translational and rotational springs and with a tip mass, Journal of Sound and Vibration 154: 67-80.
35
[34] Rossi R.E., Laura P.A.A., Avalos D.R., Larrondo H., 1993, Free vibrations of Timoshenko beams carrying elastically mounted concentrated masses, Journal of Sound and Vibration 165: 209-223.
36
[35] Salarieh H., Ghorashi M., 2006, Free vibration of Timoshenko beam with finite mass rigid tip load and flexural-torsional coupling, International Journal of Mechanical Sciences 48:763-779.
37
[36] Wu J.S., Hsu S.H., 2007, The discrete methods for free vibration analyses of an immersed beam carrying an eccentric tip mass with rotary inertia, Ocean Engineering 34: 54-68.
38
[37] Lin H.Y., Tsai Y.C., 2007, Free vibration analysis of a uniform multi-span carrying multiple spring-mass systems, Journal of Sound and Vibration 302: 442-456.
39
[38] Necla T., 2016, Nonlinear vibration of nanobeam with attached mass at the free end via nonlocal elasticity theory, Microsystem Technologies 22(9): 2349-2359.
40
[39] Simsek M., 2010, Fundamental frequency of functionally graded beams by using different higher order beam theories, Nuclear Engineering and Design 240(4): 697-705.
41
[40] Pradhan K.k., Chakraverty S., 2014, Effects of different shear deformation theories on free vibration of functionally graded beams, International Journal of Mechanical Science 82:149-160.
42
ORIGINAL_ARTICLE
Non Uniform Rational B Spline (NURBS) Based Non-Linear Analysis of Straight Beams with Mixed Formulations
Displacement finite element models of various beam theories have been developed traditionally using conventional finite element basis functions (i.e., cubic Hermite, equi-spaced Lagrange interpolation functions, or spectral/hp Legendre functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, total rotation , and/or shear strain , as well as the variational method used (e.g., collocation, weak form Galerkin, or least-squares). When nonlinear shear deformation theories are used, the displacement finite element models experience membrane and shear locking. The present study is concerned with development of alternative beam finite elements using both uniform and non-uniform rational b-splines (NURBS) to eliminate shear and membrane locking in an hpk finite element setting for both the Euler-Bernoulli beam and Timoshenko beam theories. Both linear and non-linear analysis are performed using mixed finite element models of the beam theories studied. Results obtained are compared with analytical (series) solutions and non-linear finite element and spectral/hp solutions available in the literature, and excellent agreement is found for all cases.
http://jsm.iau-arak.ac.ir/article_539692_7de7e45c949e258c87bffbd8a599183e.pdf
2018-03-01T11:23:20
2019-10-22T11:23:20
38
56
NURBS basis
Euler-Bernoulli beam theory
Timoshenko Beam Theory
B-splines
Mixed formulation
R
Ranjan
ranrakesh@gmail.com
true
1
School of Aerospace and Mechanical Engineering, 865 Asp Avenue, Norman, OK, 73019, USA
School of Aerospace and Mechanical Engineering, 865 Asp Avenue, Norman, OK, 73019, USA
School of Aerospace and Mechanical Engineering, 865 Asp Avenue, Norman, OK, 73019, USA
LEAD_AUTHOR
J.N
Reddy
true
2
Department of Mechanical Engineering, 3123 TAMU, College Station, TX, USA
Department of Mechanical Engineering, 3123 TAMU, College Station, TX, USA
Department of Mechanical Engineering, 3123 TAMU, College Station, TX, USA
AUTHOR
[1] Reddy J.N., Wang C., Lee K., 1997, Relationships between bending solutions of classical and shear deformation beam theories, International Journal of Solids and Structures 34(26): 3373-3384.
1
[2] Reddy J.N., 2014, An Introduction to Nonlinear Finite Element Analysis: with Applications to Heat Transfer Fluid Mechanics, and Solid Mechanics, OUP Oxford.
2
[3] Reddy J.N., Wang C., Lam K., 1997, Unified finite elements based on the classical and shear deformation theories of beams and axisymmetric circular plates, Communications in Numerical Methods in Engineering 13(6): 495-510.
3
[4] Severn R., 1970, Inclusion of shear deflection in the stiffness matrix for a beam element, The Journal of Strain Analysis for Engineering Design 5(4): 239-241.
4
[5] Reddy J.N., 1997, On locking-free shear deformable beam finite elements, Computer Methods in Applied Mechanics and Engineering 149(1): 113-132.
5
[6] Oden J.T., Reddy J.N., 2012, Variational Methods in Theoretical Mechanics, Springer Science & Business Media.
6
[7] Arciniega R., Reddy J.N., 2007, Large deformation analysis of functionally graded shells, International Journal of Solids and Structures 44(6): 2036-2052.
7
[8] Karniadakis G., Sherwin S., 2013, Spectral/hp Element Methods for Computational Fluid Dynamics, Oxford University Press.
8
[9] Melenk J.M., 2002, On condition numbers in hp-fem with gauss-Lobatto-based shape functions, Journal of Computational and Applied Mathematics 139(1): 21-48.
9
[10] Ranjan R., Feng Y., Chronopolous A., 2016, Augmented stabilized and Galerkin least squares formulations, Journal of Mathematics Research 8 (6): 1-12.
10
[11] Ranjan R., Chronopolous A., Feng Y., 2016, Computational algorithms for solving spectral/hp stabilized incompressible flow problems, Journal of Mathematics Research 8(4): 1-19.
11
[12] Ranjan R., Reddy J.N., 2009, Hp-spectral finite element analysis of shear deformable beams and plates, Journal of Solid Mechanics 1(3): 245-259.
12
[13] Ranjan R., 2011, Nonlinear finite element analysis of bending of straight beams using hp-spectral approximations, Journal of Solid Mechanics 3(1): 96-113.
13
[14] Da Veiga L.B., Lovadina C., Reali A., 2012, Avoiding shear locking for the timoshenko beam problem via isogeometric collocation methods, Computer Methods in Applied Mechanics and Engineering 241: 38-51.
14
[15] Tran L.V., Ferreira A., Nguyen-Xuan H., 2013, Isogeometric analysis of functionally graded plates using higher-order shear deformation theory, Composites Part B: Engineering 51: 368-383.
15
[16] Ranjan R., 2010, Hp-spectral Methods for Structural Mechanics and Fluid Dynamics Problems, Texas A&M University, Ph.D. Thesis.
16
[17] Cottrell J.A., Hughes T.J., Bazilevs Y., 2009, Isogeometric Analysis: Toward Integration of CAD and FEA, John Wiley & Sons.
17
[18] Reali A., Gomez H., 2015, An isogeometric collocation approach for Bernoulli Euler beams and Kirchhoff plates, Computer Methods in Applied Mechanics and Engineering 284: 623-636.
18
[19] Weeger O., Wever U., Simeon B., 2013, Isogeometric analysis of nonlinear Euler-Bernoulli beam vibrations, Nonlinear Dynamics 72(4): 813-835.
19
[20] Thai C.H., Nguyen-Xuan H., Bordas S., Nguyen-Thanh N., Rabczuk T., 2015, Isogeometric analysis of laminated composite plates using the higher-order shear deformation theory, Mechanics of Advanced Materials and Structures 22(6): 451-469.
20
[21] Kapoor H., Kapania R., 2012, Geometrically nonlinear nurbs isogeometric finite element analysis of laminated composite plates, Composite Structures 94(12): 3434-3447.
21
[22] Reddy J.N., 2006, Theory and Analysis of Elastic Plates and Shells, CRC press.
22
ORIGINAL_ARTICLE
Reflection From Free Surface of a Rotating Generalized Thermo-Piezoelectric Solid Half Space
The analysis of rotational effect on the characteristics of plane waves propagating in a half space of generalized thermo-piezoelectric medium is presented in context of linear theory of thermo-piezoelectricity including Coriolis and centrifugal forces. The governing equations for a rotating generalized thermo-piezoelectric medium are formulated and solved for plane wave solutions to show the propagation of three quasi plane waves in the medium. A problem on the reflection of these plane waves is considered from a thermally insulated/isothermal boundary of a rotating generalized thermo-piezoelectric solid half space. The expressions for reflection coefficients of three reflected waves are obtained in explicit from. For experimental data of LiNbO3 and BaTiO3, the speeds of various plane waves are computed. The reflection coefficients of various reflected waves are also obtained numerically by using the data of BaTiO3. The dependence of speeds of plane waves and reflection coefficients of various reflected waves is shown graphically on the rotation parameter at each angle of incidence.
http://jsm.iau-arak.ac.ir/article_539693_1d90610775405560eac8b64d31e01f9d.pdf
2018-03-01T11:23:20
2019-10-22T11:23:20
57
66
Thermo-piezoelectric
Plane waves
Reflection
Rotation
Reflection coefficients
Baljeet
Singh
bsinghgc11@gmail.com
true
1
Department of Mathematics, Post Graduate Government College, Sector-11, Chandigarh, 160011,India
Department of Mathematics, Post Graduate Government College, Sector-11, Chandigarh, 160011,India
Department of Mathematics, Post Graduate Government College, Sector-11, Chandigarh, 160011,India
LEAD_AUTHOR
B
Singh
true
2
Department of Applied Sciences, Rayat Bahra Institute of Engineering and Nano Technology, Hoshiarpur, 146001, Punjab, India
Department of Applied Sciences, Rayat Bahra Institute of Engineering and Nano Technology, Hoshiarpur, 146001, Punjab, India
Department of Applied Sciences, Rayat Bahra Institute of Engineering and Nano Technology, Hoshiarpur, 146001, Punjab, India
AUTHOR
[1] Abd-alla A.N., Alsheikh F.A., 2009, Reflection and refraction of plane quasi longitudinal waves at an interface of two piezoelectric media under initial stresses, Archive of Applied Mechanics 79(9): 843-857.
1
[2] Abd-alla A.N., Hamdan A.M., Giorgio I., Vescova D.D., 2014, The mathematical model of reflection and refraction of longitudinal waves in thermo-piezoelectric materials, Archive of Applied Mechanics 84(9): 1229-1248.
2
[3] Alshit V.I., Lothe J., Lyubimov V.N., 1984, The phase shift for reflection of elastic waves in hexagonal piezoelectric crystals, Wave Motion 6: 259-264.
3
[4] Alshits V.I., Shuvalov A.L., 1995, Resonance reflection and transmission of shear elastic waves in multilayered piezoelectric structures, Journal of Applied Physics 77(6): 2659-2665.
4
[5] Auld B.A., 1981, Wave propagation and resonance in piezoelectric materials, Journal of Acoustical Society of America 70(6): 1577-1585.
5
[6] Burkov S.I., Sorokin B.P., Aleksandrov K.S., Karpovich A.A., 2009, Reflection and refraction of bulk acoustic waves in piezo electrics under uniaxial stress, Acoustical Physics 55(2): 178-185.
6
[7] Cady W.G., 1946, Piezoelectricity, McGraw-Hill, New York.
7
[8] Chandrasekharaih D.S., 1984, A temperature rate dependent theory of piezoelectricity, Journal of Thermal Stresses 7: 293-306.
8
[9] Chen J.Y., Chen H.L., Pan E., 2008, Reflection and transmission coefficients of plane waves in magneto-electro-elastic layered structures, Journal of Vibration and Acoustics 130: 031002.
9
[10] Clezio E.L., Shuvalov A., 2004, Transmission of acoustic waves through piezoelectric plates: Modeling and Experiment, IEEE Ultrasonics Symposium 1: 553-556.
10
[11] Darinskii A.N., Clezio E.L., Feuillard G., 2008, The role of electromagnetic waves in the reflection of acoustic waves in piezoelectric crystals, Wave Motion 45(1): 428-444.
11
[12] Dunn M. L., 1993, Micromechanics of coupled electro-elastic composites: effective thermal expansion and pyroelectric coefficients, Journal of Applied Physics 73: 5131-5140.
12
[13] Eringen A.C., Maugin G.A., 1990, Electrodynamics of Continua: I Foundations and Solid Media, Springer Verlag, New York.
13
[14] Every A.G., Neiman V.I., 1992, Reflection of electroacoustic waves in piezoelectric solids: Mode conversion into four bulk waves, Journal of Applied Physics 71(12): 6018-6024.
14
[15] Green A.E., Lindsay K.A., 1972, Thermoelasticity, Journal of Elasticity 2: 1-7.
15
[16] Ikeda T., 1996, Fundamentals of Piezoelectricity, Oxford Science Publications, Oxford University Press.
16
[17] Kuang Z.B., Yuan X.G., 2011, Reflection and transmission of waves in pyroelectric and piezoelectric materials, Journal of Sound and Vibration 330(6): 1111-1120.
17
[18] Kaung Z. B., 2013, Theory of Electroelasticity, Springer.
18
[19] Lord H., Shulman Y., 1967, A generalised dynamical theory of thermoelasticity, Journal of Mechanics and Physics of the Solids 15: 299-309.
19
[20] Lothe J., Barnett D.M., 1976, Integral formalism for surface waves in piezoelectric crystals: Existence considerations, Journal of Applied Physics 47: 1799-1807.
20
[21] Maugin G.A., 1988, Continuum Mechanics of Electromagnetic Solids, Elsevier Science Publishers, Amsterdam, New York, Oxford.
21
[22] Mindlin R.D., 1972, High frequency vibrations of piezoelectric crystal plates, International Journal of Solids and Structures 8(7): 895-906.
22
[23] Mindlin R.D., 1974, Equations of high frequency vibrations of thermo-piezoelectric crystal plates, International Journal of Solids and Structures 10(6): 625-637.
23
[24] Nayfeh A.H, Chien H.T., 1992, The influence of piezoelectricity on free and reflected waves from fluid loaded anisotropic plates, Journal of Acoustical Society of America 91(3): 1250 -1261.
24
[25] Noorbehesht B., Wade G., 1980, Reflection and transmission of plane elastic waves at the boundary between piezoelectric materials and water, Journal of Acoustical Society of America 67(6): 1947-1953.
25
[26] Nowacki W., 1978, Some general theorems of thermo-piezo-electricity, Journal of Thermal Stresses 1: 171-182.
26
[27] Pal A.K., 1979, Surface wave in a thermo-piezoelectric medium of monoclinic symmetry, Czechslovak Journal of physics 29: 1271-1281.
27
[28] Pang Y., Wang Y.S., Liu J.X., Fang D.N., 2008, Reflection and refraction of plane waves at the interface between piezoelectric and piezo magnetic media, International Journal of Engineering Science 46(11): 1098-1110.
28
[29] Parton V.Z., Kudryavtsev B.A., 1988, Electromagnetoelasticity: Piezo electrics and Electrically conductive Solids, Gordon and Beach, New York.
29
[30] Ponnusamy P., 2016, Elastic waves in generalized thermo-piezoelectric transversely isotropic circular bar immersed in fluid, Advances in Applied Mathematics and Mechanics 8(1): 82-103.
30
[31] Rosenbaum J.F., 1988, Bulk Acoustic Wave Theory and Devices, Artech House, Boston.
31
[32] Schoenberg M., Censor D., 1973, Elastic waves in rotating media, Quarterly of Applied Mathematics 31: 115-125.
32
[33] Sharma J.N., Kumar M., 2000, Plane harmonic waves in piezothermoelastic materials, Indian Journal of Engineering and Material Sciences 7: 434-442.
33
[34] Sharma J.N., Walia V., 2007, Effect of rotation on Rayleigh waves in piezothermoelastic half-space, International Journal of Solids and Structures 44: 1060-1072.
34
[35] Shuvalov A.L., Clezio E.L., 2010, Low-frequency dispersion of fundamental waves in anisotropic piezoelectric plates, International Journal of Solids and Structures 47: 3377-3388.
35
[36] Singh B., 2005, On the theory of generalized thermoelasticity for piezoelectric materials, Applied Mathematics and Computation 171: 398-405.
36
[37] Singh B., 2010, Wave propagation in a pre-stressed piezoelectric half-space, Acta Mechanica 211: 337-344.
37
[38] Singh B., 2013, Propagation of shear waves in a piezoelectric medium, Mechanics of Advanced Materials and Structures 20: 434-440.
38
[39] Tiersten H.F., 1969, Linear Piezoelectric Plate Vibrations, Plenum, New York.
39
[40] Toupin R.A., 1956, The elastic dielectric, Archive for Rational Mechanics and Analysis 5: 849-915.
40
[41] Voigt W., 1910, Lehrbuch der Krystallphysik, Mathematischen Wissenschaften, band XXXIV, Leipzig und Berlin, B.G. Teubner.
41
[42] Weis R.S., Gaylord T.K., 1985, Summary of physical properties and crystal structure, Applied Physics A 37: 191-203.
42
[43] Yang J., 2005, An Introduction to the Theory of Piezoelectricity, Springer, New York.
43
[44] Zhang Q.M., Geng X., Yuan J., 1996, Reflection of plane waves at medium composite interfaces and input acoustic impedance of laminated piezo ceramic polymer composites, Journal of Applied Physics 80(9): 5503-5505.
44
ORIGINAL_ARTICLE
Two New Non-AFR Criteria for Depicting Strength Differential Effect (SDE) in Anisotropic Sheet Metals
The issue of pressure sensitivity of anisotropic sheet metals is investigated with introducing two new non-AFR criteria which are called here linear and non-Linear pressure sensitive criteria. The yield and plastic potential functions of these criteria are calibrated with directional tensile/compressive yield stresses and directional tensile Lankford coefficients, respectively. To determine unknown coefficients of yield and plastic potential functions of these criteria two error functions are presented which are minimized by Downhill Simplex Method. Three anisotropic materials are considered as case studies such as Al 2008-T4 (BCC), Al 2090-T3 (FCC) and AZ31 (HCP). It is shown that the non-Linear pressure sensitive criterion is more accurate than the linear one and other existed criteria compared to experimental results in calculating the directional mechanical properties of anisotropic sheet metals.
http://jsm.iau-arak.ac.ir/article_539694_542f46d7fb2f38092ec7f84eb015acb6.pdf
2018-03-01T11:23:20
2019-10-22T11:23:20
67
85
Linear pressure sensitive criterion
Non-linear pressure sensitive criterion
Asymmetric anisotropic sheet metals
Non-AFR
Tensile/compressive yield stresses
Lankford coefficients
F
Moayyedian
farzad.moayyedian@eqbal.ac.ir
true
1
Department of Mechanical Engineering, Eqbal Lahoori Institute of Higher Education, Mashhad, Iran
Department of Mechanical Engineering, Eqbal Lahoori Institute of Higher Education, Mashhad, Iran
Department of Mechanical Engineering, Eqbal Lahoori Institute of Higher Education, Mashhad, Iran
LEAD_AUTHOR
M
Kadkhodayan
kadkhoda@um.ac.ir
true
2
Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
AUTHOR
[1] Spitzig W.A., Richmond O., 1984, The effect of pressure on the flow stress of metals, Acta Metallurgic 32)3(: 457-463.
1
[2] Liu C., Huang Y., Stout M.G., 1997, On the asymmetric yield surface of plastically orthotropic materials: a phenomenological study, Acta Metallurgica 45(6): 2397-2406.
2
[3] Barlat F., Brem J.C., Yoon J.W., Chung K., Dick R.E., Lege D.J., Pourboghrat F., Choi S.H., Chu E., 2003, Plane stress yield function for aluminum alloy sheets-part 1: theory, International Journal of Plasticity 19: 1297-1319.
3
[4] Stoughton T.B., Yoon J.W., 2004,A pressure-sensitive yield criterion under a non-associated flow rule for sheet metal forming, International Journal of Plasticity 20: 705-731.
4
[5] Hu W., Wang Z.R., 2009,Construction of a constitutive model in calculations of pressure-dependent material, Computational Material Sciences 46: 893-901.
5
[6] Hu W., 2005, An orthotropic criterion in a 3-D general stress state, International Journal of Plasticity 21: 1771-1796.
6
[7] Aretz H., 2009, A non-quadratic plane stress yield function for orthotropic sheet metals, Journal of Materials Processing Technology 36: 246-251.
7
[8] Lee M.G., Wagoner R.H., Lee J.K., Chung K., H.Y. Kim, 2008,Constitutive modeling for anisotropic/asymmetric hardening behavior of magnesium alloy sheets, International Journal of Plasticity 24: 545-582.
8
[9] Stoughton T.B., Yoon J.W., 2009,Anisotropic hardening and non-associated flow in proportional loading of sheet metals, International Journal of Plasticity 25: 1777-1817.
9
[10] Hu W., Wang Z.R., 2005, Multiple-factor dependence of the yielding behavior to isotropic ductile materials, Computational Materials Science 32: 31-46.
10
[11] Huh H., Lou Y., Bae G., Lee C., 2010, Accuracy analysis of anisotropic yield functions based on the root-mean square error, AIP Conference Proceeding of the NUMIFORM, Pohang, Republic of Korea.
11
[12] Moayyedian F., Kadkhodayan M., 2013,A general solution for implicit time stepping scheme in rate-dependant plasticity, International Journal of Engineering 26(6): 641-652.
12
[13] Lou Y., Huh H., Yoon J.W., 2013,Consideration of strength differential effect in sheet metals with symmetric yield functions, International Journal of Mechanical Sciences 66: 214-223.
13
[14] SafaeiM., Lee M.G., Zang S.L., WaeleW.D., 2014, An evolutionary anisotropic model for sheet metals based on non-associated flow rule approach, Computational Materials Science 81:15-29.
14
[15] Yoon J.W., Lou Y., Yoon J., Glazoff M.V., 2014, Asymmetric yield function based on the stress invariants for pressure sensitive metals, International Journal of Plasticity 56: 184-202.
15
[16] Safaei M., Yoon J.W., Waele W.D., 2014, Study on the definition of equivalent plastic strain under non-associated flow rule for finite element formulation, International Journal of Plasticity 58: 219-238.
16
[17] Moayyedian F., Kadkhodayan M., 2014,A study on combination of von Mises and Tresca yield loci in non-associated viscoplasticity, International Journal of Engineering 27: 537-545.
17
[18] Oya T., Yanagimoto J., Ito K., Uemura G., Mori N., 2014, Material model based on non-associated flow rule with higher-order yield function for anisotropic metals, Procedia Engineering 81: 1210-1215.
18
[19] Moayyedian F., Kadkhodayan M., 2015,Combination of modified Yld2000-2d and Yld2000-2d in anisotropic pressure dependent sheet metals, Latin American Journal of Solids and Structures 12(1): 92-114.
19
[20] Moayyedian F., Kadkhodayan M., 2015, Modified Burzynski criterion with non-associated flow rule for anisotropic asymmetric metals in plane stress problems, Applied Mathematics and Mechanics 36(3): 303-318.
20
[21] Ghaei A., Taherizadeh A., 2015, A two-surface hardening plasticity model based on non-associated flow rule for anisotropic metals subjected to cyclic loading, International Journal of Mechanical Sciences 92: 24-34.
21
ORIGINAL_ARTICLE
Influence of Notch Depth-to-Width Ratios on J-Integral and Critical Failure Load of Single-Edge Notched Tensile Aluminium 8011 Alloy Specimens
In this paper, the influence of notch depth-to-width ratios on J-integral and critical load of Aluminium 8011 alloy specimens with U-notch under Mode I loading are studied. Using experiments, for a set of specimens having different notch depth–to–width ratios, J-integral was found and the same was verified using analytical methods. Further, using the results obtained from the experiments, failure assessment diagrams (FAD) were plotted for the same ratios, to determine the safe or critical load and the type of failure mechanism was also studied. The results show that, for both shallow and deep notch depths, the J-integral values obtained from the experimental method, are in very close agreement with the analytical values. J-integral values decrease with increase in notch depth and increase with increase in applied load. Furthermore, from FAD, the safe load decreases when the notch depth-to-width ratio increases and it was found that, all the tested specimens failed due to elastic plastic deformation mechanism.
http://jsm.iau-arak.ac.ir/article_539695_2b358a90e04e0a68c39aca4cb501763f.pdf
2018-03-01T11:23:20
2019-10-22T11:23:20
86
97
Aluminium 8011 alloy
Notch depth
J-integral
fracture toughness
Critical failure load
C.S
Sumesh
cs_sumesh@cb.amrita.edu
true
1
Department of Mechanical Engineering, Amrita School of Engineering, Coimbatore Amrita Vishwa Vidyapeetham, India
Department of Mechanical Engineering, Amrita School of Engineering, Coimbatore Amrita Vishwa Vidyapeetham, India
Department of Mechanical Engineering, Amrita School of Engineering, Coimbatore Amrita Vishwa Vidyapeetham, India
LEAD_AUTHOR
P.J
Arun Narayanan
true
2
Department of Mechanical Engineering, Amrita School of Engineering, Coimbatore Amrita Vishwa Vidyapeetham, India
Department of Mechanical Engineering, Amrita School of Engineering, Coimbatore Amrita Vishwa Vidyapeetham, India
Department of Mechanical Engineering, Amrita School of Engineering, Coimbatore Amrita Vishwa Vidyapeetham, India
AUTHOR
[1] Mohan Kumar S., Pramod R., Shashi Kumar M.E., Govindaraju H.K., 2014, Evaluation of fracture toughness and mechanical properties of Aluminum alloy 7075, T6 with Nickel coating, Procedia Engineering 97: 178-185.
1
[2] Shih C.F., Hutchinson J.W., 1976, Fully plastic solutions and large-scale yielding estimates for plane stress crack problems, Journal of Engineering Materials and Technology 98: 289-295.
2
[3] Vijayan V.J., Arun A., Bhowmik Sh., Abraham M.C., Ajeesh G.B., Pitchan M. Kb., 2016, Development of lightweight high-performance polymeric composites with functionalized nanotubes, Journal of Applied Polymer Science 133: 43471.
3
[4] Kumar V., German M.D., Shih C.F., 1981, An Engineering Approach for Elastic-Plastic Fracture Analysis, Electric Power Research Institute, Calofornia.
4
[5] Shimakawa T., Asada Y., Kitagawa M. , Kodaira T., Wada Y., Asayama T., 1992, Analytical evaluation method of J-integral in creep-fatigue fracture for type 304 stainless steel, Nuclear Engineering and Design 133: 361-367.
5
[6] Rice J.R., 1968, A path independent integral and the approximate analysis of strain concentration by notches and cracks, Journal of Applied Mechanics 35: 379-386.
6
[7] Alan T., Zehnder A., Rosakis J., Krishnaswamy S., 1990, Dynamic measurement of the j-integral in ductile metals, Comparison of Experimental and Numerical Techniques International Journal of Fracture 42: 209-230.
7
[8] Begley J. A., Landes J. D., 1972, The J- integral as a fracture criterion, ASTM 1972: 1-20.
8
[9] Montgomery S.S. R., 1976, J-Integral measurements on various types of specimens in AISI 304, Commission of the European Communities Nuclear Science and Technology 2008: 2-28.
9
[10] Aldo F., 1984, Experimental measurement of the J-integral engineering fracture mechanics, Engineering Failure Analysis 19(4): 1105-1137.
10
[11] Madrazo V., Cicero S., García T., 2014, Assessment of notched structural steel components using failure assessment diagrams and the theory of critical distances, Engineering Failure Analysis 36: 104-120.
11
[12] Tipple C., Thorwald G., 2012, Using the failure assessment diagram method with fatigue crack growth to determine leak-before-rupture, SIMULIA Customer Conference.
12
[13] Akhurst K.N., Milne I., 1984, Failure assessment diagrams and J-estimates: validation for an austenitic steel, Application of Fracture Mechanics to Materials and Structures 1984: 401-413.
13
[14] Hasanaj A., Gjeta A., Kullolli M., 2014, Analyzing defects with failure assessment diagrams of gas pipelines, World Academy of Science, Engineering and Technology International Journal of Mechanical and Mechatronics Engineering 8(5): 1045-1047.
14
[15] Marcos A., Bergant A., Yawny A., Juan E., Perez I., 2015, Failure assessment diagram in structural integrity analysis of steam generator tubes, International Congress of Science and Technology of Metallurgy and Materials 8: 128-138.
15
[16] Xudong Q., 2013, Failure assessment diagrams for circular hollow section X- and K-joints, International Journal of Pressure Vessels and Piping 104: 43-56.
16
[17] Matvienko Y. G., 2013, Notch Fracture Mechanics Approaches in an Analysis of Notch-like Defects, ECF.
17
[18] Matvienko Y., 2013, Safety factors in structural integrity assessment of components with defects, International Journal of Structural Integrity 4(4): 457-476.
18
[19] Mostafa S., Elsaadany M., Younan Y.A., Hany F.A., 2014, Determination of shakedown boundary and failure-assessment-diagrams of cracked pipe bends, Journal of Pressure Vessel Technology 136: 011209-1-9.
19
[20] Anthony H., Mikhail T., Hertele S., 2015, Failure prediction of curved wide plates using the strain- based failure assessment diagram with correction for constraint and notch radius, Journal of Pressure Vessel Technology 137: 021208-1-10.
20
[21] Luis F.S., Parise C. R., Noel P., Dowd O’., 2015, Fully-plastic strain-based J-estimation scheme for circumferential surface cracks in pipes subjected to reeling, Journal of Pressure Vessel Technology 137: 041204-1-8.
21
[22] Giorgio D., Candida P., 2010, A failure assessment diagram for components subjected to rolling contact loading, International Journal of Fatigue 32(2): 256-268.
22
[23] Lie S.T., Li T., 2014, Failure pressure prediction of a cracked compressed natural gas (CNG) cylinder using failure assessment diagram, Journal of Natural Gas Science and Engineering 18: 474-483.
23
ORIGINAL_ARTICLE
Improving Power Density of Piezoelectric Vibration-Based Energy Scavengers
Vibration energy harvesting with piezoelectric materials currently generate up to 300 microwatts per cm2, using it to be mooted as an appropriate method of energy harvesting for powering low-power electronics. One of the important problems in bimorph piezoelectric energy harvesting is the generation of the highest power with the lowest weight. In this paper the effect of the shape and geometry of a bimorph piezoelectric cantilever beam harvester on the electromechanical efficiency of the system is studied. An analytic model has been presented using Rayleigh cantilever beam approximations for piezoelectric harvesters with tapered bimorph piezoelectric cantilever beam. In order to study the effect of a cantilever beam length and geometry on the generated voltage, finite element simulation has been performed using ABAQUS. Design optimization has been used to obtain the maximum output power and tapered beams are observed to lead to more uniform distribution of strain in the piezoelectric layer, thus increasing efficiency.
http://jsm.iau-arak.ac.ir/article_539696_79670b78c8fb31c02ab4753916b77fc4.pdf
2018-03-01T11:23:20
2019-10-22T11:23:20
98
109
Vibration energy harvesting
Piezoelectric
Power scavenger
Natural frequency
Design optimization
R
Hosseini
r.hosseini.mech@gmail.com
true
1
Young Researchers and Elite Club, South Tehran Branch, Islamic Azad University, Tehran, Iran
Young Researchers and Elite Club, South Tehran Branch, Islamic Azad University, Tehran, Iran
Young Researchers and Elite Club, South Tehran Branch, Islamic Azad University, Tehran, Iran
LEAD_AUTHOR
O
Zargar
true
2
School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran
School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran
School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran
AUTHOR
M
Hamedi
mhamedi@ut.ac.ir
true
3
Department of Mechanical Engineering, Faculty of Engineering, University of Tehran, Iran
Department of Mechanical Engineering, Faculty of Engineering, University of Tehran, Iran
Department of Mechanical Engineering, Faculty of Engineering, University of Tehran, Iran
AUTHOR
[1] Beeby S.P., Tudor M.J., White N., 2006, Energy harvesting vibration sources for microsystems applications, Measurement Science and Technology 17: R175.
1
[2] Erturk A., Inman D.J., 2011, Piezoelectric Energy Harvesting, John Wiley & Sons.
2
[3] Jagtap S.N., Paily R., 2011, Geometry optimization of a MEMS-based energy harvesting device, Students' Technology Symposium (TechSym) 2011: 265-269.
3
[4] Patel R., McWilliam S., Popov A.A., 2011, A geometric parameter study of piezoelectric coverage on a rectangular cantilever energy harvester, Smart Materials and Structures 20: 085004.
4
[5] Zhu M., Worthington E., Tiwari A., 2010, Design study of piezoelectric energy-harvesting devices for generation of higher electrical power using a coupled piezoelectric-circuit finite element method, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 57: 427-437.
5
[6] Ayed S.B., Najar F., Abdelkefi A., 2009, Shape improvement for piezoelectric energy harvesting applications, 3rd International Conference, IEEE 2009: 1-6.
6
[7] Roundy S., Leland E.S., Baker J., Carleton E., Reilly E., Lai E., Otis B., Rabaey J.M., Wright P.K., Sundararajan V., 2005, Improving power output for vibration-based energy scavengers, IEEE Pervasive Computing 4: 28-36.
7
[8] Hosseini R., Hamedi M., 2016, An investigation into resonant frequency of trapezoidal V-shaped cantilever piezoelectric energy harvester, Microsystem Technologies 22: 1127-1134.
8
[9] Yang B., Yun K.-S., 2011, Efficient energy harvesting from human motion using wearable piezoelectric shell structures, 16th International Solid-State Sensors, Actuators and Microsystems Conference, IEEE 2011: 2646-2649.
9
[10] Hu H., Xue H., Hu Y., 2007, A spiral-shaped harvester with an improved harvesting element and an adaptive storage circuit, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 54: 1177-1187.
10
[11] Karami M.A., Inman D.J., 2012, Parametric study of zigzag microstructure for vibrational energy harvesting, Journal of Microelectromechanical Systems 21: 145-160.
11
[12] Thomson W., 1996, Theory of Vibration with Applications, CRC Press.
12
[13] Rao S.S., 2007, Vibration of Continuous Systems, John Wiley & Sons.
13
[14] Muthalif A.G., Nordin N.D., 2015, Optimal piezoelectric beam shape for single and broadband vibration energy harvesting: Modeling, simulation and experimental results, Mechanical Systems and Signal Processing 54: 417-426.
14
[15] Hosseini R., Hamedi M., 2015, Improvements in energy harvesting capabilities by using different shapes of piezoelectric bimorphs, Journal of Micromechanics and Microengineering 25:125008.
15
[16] Hosseini R., Hamedi M., 2015, Study of the resonant frequency of unimorph triangular V-shaped piezoelectric cantilever energy harvester, International Journal of Advanced Design and Manufacturing Technology 8: 75-82.
16
[17] Hosseini R., Hamedi M., 2016, An investigation into resonant frequency of triangular V-shaped cantilever piezoelectric vibration energy harvester, Journal of Solid Mechanics 8: 560-567.
17
[18] Hosseini R., Hamedi M., 2016, Resonant frequency of bimorph triangular V-shaped piezoelectric cantilever energy harvester, Journal of Computational and Applied Research in Mechanical Engineering 6: 65-73.
18
[19] Yang K., Li Z., Jing Y., Chen D., Ye T., 2009, Research on the resonant frequency formula of V-shaped cantilevers, 4th IEEE International Conference on Nano/Micro Engineered and Molecular Systems.
19
[20] Fakhzan M., Muthalif A.G., 2013, Harvesting vibration energy using piezoelectric material: Modeling, simulation and experimental verifications, Mechatronics 23: 61-66.
20
[21] Ambrosio R., Gonzalez H., Moreno M., Torres A., Martinez R., Robles E., Sauceda A., Hurtado A., Heredia A., 2014, Study of cantilever structures based on piezoelectric materials for energy harvesting at low frequency of vibration, Advanced Materials Research 2014: 159-163.
21
ORIGINAL_ARTICLE
Nonlinear Dynamic Analysis of Cracked Micro-Beams Below and at the Onset of Dynamic Pull-In Instability
In this paper, the effect of the crack on dynamic behavior of cracked micro-beam in the presence of DC and AC loads are investigated. By applying the residual axial stress and fringing field stress, a nonlinear analytical model of cracked micro-beam is presented and crack is modeled by a massless rotational spring. The governing equation of the system is solved using Galerkin procedure and shooting method. The equilibria curve and dynamic response of cracked cantilever and clamped-clamped micro-beam are extracted below and at the onset of the dynamic pull-in instability. The results show that the behavior of cracked micro-beam is different from ordinary cracked beam due to nonlinear effects. For a fixed relative crack location, increasing the crack depth causes increasing in the resonance amplitude and reduction in the resonance frequency below dynamic pull-in instability. Also, in cracked cantilever micro-beams, by approaching the crack to fixed end, the resonance frequency reduces and the resonance amplitude increases. In cracked clamped-clamped micro-beam, trend of variations of resonance frequency and resonance amplitude against the crack location is not regular. At the onset pull-in instability, the presence of the crack causes cyclic-fold bifurcation points to appear at the lower frequency. Therefore, it causes early pull-in phenomenon or unwanted abrupt change at the micro-beam behavior. The achievement of this study is simulation of the response of the faulty low-voltage switch and MEMS resonators for different severity of crack at the onset of dynamic pull-in phenomenon.
http://jsm.iau-arak.ac.ir/article_539697_20af6913b602e12a32ca272bc4531793.pdf
2018-03-01T11:23:20
2019-10-22T11:23:20
110
123
Micro-electromechanical systems
Crack
Pull-in phenomenon
Nonlinear dynamics
Bellow and at the onset of pull-in instability
R
Hassannejad
hassannejhad@tabrizu.ac.ir
true
1
Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran
Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran
Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran
LEAD_AUTHOR
Sh
Amiri Jahed
true
2
Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran
Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran
Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran
AUTHOR
[1] Vardan V. M., Vinoy K. J., Jose K. A., 2003, RF MEMS and their Applications, Wiley, New York.
1
[2] Younis M. I., Nayfeh A. H., 2009, A study of the nonlinear response of a resonant micro-beam to an electric actuation, Nonlinear Dynamic 3(1): 91-117.
2
[3] Rezazadeh G., Tahmasebi A., Ziaei-rad S., 2009, Nonlinear electrostatic behavior for two elastic parallel fixed-fixed and cantilever micro-beams, Mechatronics 19: 840-846.
3
[4] Valilou S., Jalilpour M., 2012, Frequency response analysis of a capacitive micro-beam resonator considering residual and axial stresses and temperature changes effects, Journal of Solid Mechanics 4(4): 416-425.
4
[5] Osterberg P. M., Senturia S. D., 1997, M-TEST: A test chip for MEMS material property measurement using electrostatically actuated test structures, Micro-Electromechanical Systems 6(2): 107-118.
5
[6] Zhang Y., Zhao Y., 2006, Numerical and analytical study on the pull-in instability of micro-structure under electrostatic loading, Sensor Actuator A 127: 366-380.
6
[7] Rezazadeh G., Tahmasebi A., Ziaei-rad S., 2009, Nonlinear electrostatic behavior for two elastic parallel fixed-fixed and cantilever micro-beams, Mechatronics 19: 840-846.
7
[8] Mojahedi M., Moghimi zand M., Ahmadian M.T, 2010, Static pull-in analysis of electrostatically actuated microbeams using homotopy perturbation method, Applied Mathematical Modeling 34: 1032-104.
8
[9] Wang Y.G., Lin W.H., Feng Z. J., Li X. M., 2012, Characterization of extensional multi-layer microbeams in pull-in phenomenon and vibrations, Mechanical Sciences 54: 225-233.
9
[10] Mohammad T. F., Ouakad H. M., 2016, Static, eigenvalue problem and bifurcation analysis of MEMS arches actuated by electrostatic fringing-fields, Microsystem Technologies 22: 193-206.
10
[11] Younis M.I., 2015, Analytical expressions for the electrostatically actuated curled beam problem, Microsystem Technologies 21: 1709-1717.
11
[12] Mohammad-Alasti B., Rezazadeh G., Abbasgholipour M., 2012, Effect of temperature changes on dynamic pull-in phenomenon in a functionally graded capacitive micro-beam, Journal of Solid Mechanics 4(3): 277-295.
12
[13] Nayfeh A.H., Younis M.I., Abdel-Rahman E.M., 2007, Dynamic pull-in phenomenon in MEMS resonators, Nonlinear Dynamic 48: 153-163.
13
[14] Rezazadeh G., Fathalilou M., Sadeghi M., 2011, Pull-in voltage of electrostatically-actuated micro-beams in terms of lumped model pull-in voltage using novel design corrective coefficients, Sensing and Imaging 12: 117-131.
14
[15] Sedighi H.M., Shirazi K.H., Changizian M., 2015, Effect of the amplitude of vibrations on the pull-in instability of doubled-sided actuated microswitch resonators, Applied Mechanics and Technical Physics 56(2): 304-312.
15
[16] Muhlstein C., Brown S., 1997, Reliability and fatigue testing of MEMs, Tribology Issues and Opportunities in MEMS 1997: 519-528.
16
[17] Motallebi A., Fathalilou M., Rezazadeh G., 2012, Effect of the open crack on the pull-in instability of an electrostatically actuated Micro-beam, Acta Mechanica Solidica Sinica 25(6): 627-637.
17
[18] Zhou H., Zhang W. M., Peng Z. K., Meng G., 2015, Dynamic characteristics of electrostatically actuated micro-beams with slant crack, Mathematical Problems in Engineering 2015: 1-13.
18
[19] Sourki R., Hoseini S.A.H., 2016, Free vibration analysis of size-dependent cracked microbeam based on the modified couple stress theory, Applied Physics A 122: 1-11.
19
[20] Younis M.I., Abdel-Rahman E.M., Nayfeh A.H., 2002, Static and dynamic behavior of an electrically excited resonant microbeam, Proceedings of the 43rd Conference on AIAA Structures, Structural Dynamics, and Materials, Denver, Colorado.
20
[21] Abdel-Rahman E.M., Younis M.I., Nayfeh A.H. 2002, Characterization of the mechanical behavior of an electrically actuated micro-beam, Micromechanical and Microengineering 12: 795-766.
21
[22] Lin H. P., Chang S. C., Wu J. D., 2002, Beam vibrations with an arbitrary number of cracks, Sound and Vibration 258(5): 987-999.
22
[23] Younis M.I., 2010, MEMS Linear and Nonlinear Statics and Dynamics, Ph.D. thesis, State University of New York.
23
ORIGINAL_ARTICLE
Preparation and Mechanical Properties of Compositionally Graded Polyethylene/Clay Nanocomposites
This paper presents the preparation and mechanical properties of compatibilized compositionally graded Polyethylene/ low density polyethylene (LDPE)/ modified montmorillonite (MMT) nanocomposites prepared by solution and melt mixing techniques. Use of polyethylene glycol as compatibilizer improves compatibility of modified montmorillonite and low density polyethylene. Comparisons between two techniques show that the melt mixing technique is the preferred method for preparation the Polyethylene/Clay nanocomposites for uniform and compositionally graded distributions. It is observed, the addition of Nano clay improves the mechanical properties like tensile strength. Also, it is noticed the mechanical properties of compositionally graded Polyethylene/Clay nanocomposites are improved rather than the uniform distribution of Polyethylene/Clay nanocomposites. The morphology of nanocomposites cross section samples is studied by Scanning Electron Microscopy (SEM) and finally the comparison are made between two techniques and then between compositionally graded polyethylene/clay nanocomposites with uniform ones. Its show that when the compatibilizer was added for melt mixing technique, the density and the size of the aggregates decreased, which indicates that the dispersion of nano clays within the polymer matrix is much better.
http://jsm.iau-arak.ac.ir/article_539699_013e2a350ca5083367892447f830bbc0.pdf
2018-03-01T11:23:20
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124
129
Compositionally graded
Polyethylene
montmorillonite
Solution technique
Melt mixing technique
M.H
Yas
yas@razi.ac.ir
true
1
Department of Mechanical Engineering, Engineering Faculty, Razi University, Kermanshah, Iran
Department of Mechanical Engineering, Engineering Faculty, Razi University, Kermanshah, Iran
Department of Mechanical Engineering, Engineering Faculty, Razi University, Kermanshah, Iran
LEAD_AUTHOR
M
Karami Khorramabadi
mehdi_karami2001@yahoo.com
true
2
Department of Mechanical Engineering, Engineering Faculty, Razi University, Kermanshah, Iran
Department of Mechanical Engineering, Engineering Faculty, Razi University, Kermanshah, Iran
Department of Mechanical Engineering, Engineering Faculty, Razi University, Kermanshah, Iran
AUTHOR
[1] Rado R., Zelenak P., 1992, Cross linking of polyethylene , International Polymer Science and Technology 19(6): 33-47.
1
[2] Thorburn B., 1994, Cross linking techniques for electrical jacketing materials, Proceedings of ANTEC 94 Conference, San Francisco.
2
[3] Roberts B.E., Verne S., 1984, Applications of different methods of cross linking polyethylene, Plastic and Rubber Processing and Applications 4(2): 135-139.
3
[4] Kawasumi M., Hasegawa N., Kato M., Usuki A., Okada A., 1997, Preparation and mechanical properties of polypropylene-clay hybrids, Macromolecules 30(20): 6333-6338.
4
[5] Tan H., Yang W., 1998, Toughening mechanisms of nano-composite ceramics, Mechanics of Materials 30(2): 111-123.
5
[6] Han Y., Wang Z., Li X., Fu J., Cheng Z., 2001, Polymer-layered silicate nanocomposites: synthesis, characterization, properties and applications, Current Trends in Polymer Science 6(1): 1-16.
6
[7] Kornmann X., Lindberg H., Berglund L.A., 2001, Synthesis of epoxy-clay nanocomposites: inluence of the nature of the clay on structure, Polymer 42(4): 1303-1310.
7
[8] Utracki L.A., Kamal M.R., 2002, Clay-containing polymeric nanocomposites, Arabian Journal for Science and Engineering 27(1): 43-67.
8
[9] Hotta S., Paul D.R., 2004, Nanocomposites formed from linear low density polyethylene and organoclays, Polymer 45(22): 7639-7654.
9
[10] Zhao K., He K., 2006, Dielectric relaxation of suspensions of nanoscale particles surrounded by a thick electric double layer, Physical Review B 74(20): 1-10.
10
[11] Awaji H., Nishimura Y., Choi S., Takahashi Y., Goto T., Hashimoto S., 2009, Toughening mechanism and frontal process zone size of ceramics, Journal of the Ceramic Society of Japan 117(65): 623-629.
11
[12] Chen L., Chen G., 2009, Relaxation behavior study of silicone rubber cross linked network under static and dynamic compression by electric response, Polymer Composites 30(1): 101-106.
12
[13] Kim P.N., Doss M., Tillotson J.P., 2009, High energy density nanocomposites based on surface-modified BaTiO3 and a ferroelectric polymer, ACS Nano 3(9): 2581-2592.
13
[14] Zhao C., Qin H., Gong F., Feng M., Zhang S., Yang M., 2005, Mechanical, thermal and flammability properties of polyethylene/clay nanocomposites, Polymer Degradation and Stability 87(1): 183-189.
14
[15] Huang G., Zhu B., Shi H., 2011, Effect of organics-modified montmorillonite with intumescent flame retardants on thermal stability and ire behavior of polyethylene nanocomposites, Journal of Applied Polymer Science 121(3): 1285-1291.
15
[16] Meneghetti P., Qutubuddin S., 2006, Synthesis, thermal properties and applications of polymer-clay nanocomposites, Hermo Chimica Acta 442(1): 74-77.
16
ORIGINAL_ARTICLE
Magneto-Electro-Thermo-Mechanical Response of a Multiferroic Doubly-Curved Nano-Shell
Free vibration of a simply-supported magneto-electro-elastic doubly-curved nano-shell is studied based on the first-order shear deformation theory in the presence of the rotary inertia effect. To model the electric and magnetic behaviors of the nano-shell, Gauss’s laws for electrostatics and magneto statics are used. By using Navier’s method, the partial differential equations of motion are reduced to a single ordinary differential equation. Then, an analytical relation is obtained for the natural frequency of magneto-electro-elastic doubly-curved nano-shell. Some examples are presented to validate the proposed model. Moreover, the effects of the electric and magnetic potentials, temperature rise, nonlocal parameter, parameters of Pasternak foundation, and the geometry of the nano-shell on the natural frequencies of magneto-electro-elastic doubly-curved nano-shells are investigated. It is found that natural frequency of magneto-electro-elastic doubly-curved nano-shell decreases with increasing the temperature, increasing the electric potential, or decreasing the magnetic potential.
http://jsm.iau-arak.ac.ir/article_539700_0d46779d43e8a55531d9f90425aaf696.pdf
2018-03-01T11:23:20
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130
141
Magneto-electro-elastic
Nano-shell
Doubly-curved
First-order theory
S
Razavi
soheilrazavi@outlook.com
true
1
Young Researchers and Elite Club, Tabriz Branch, Islamic Azad University, Tabriz, Iran
Young Researchers and Elite Club, Tabriz Branch, Islamic Azad University, Tabriz, Iran
Young Researchers and Elite Club, Tabriz Branch, Islamic Azad University, Tabriz, Iran
LEAD_AUTHOR
[1] Arash B., Wang Q., 2012, A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes, Computational Materials Science 51: 303-313.
1
[2] Pradhan S.C., Kumar A., 2010, Vibration analysis of orthotropic graphene sheets embedded in Pasternak elastic medium using nonlocal elasticity theory and differential quadrature method, Computational Materials Science 50: 239-245.
2
[3] Babaei H., Shahidi A.R., 2013, Free vibration analysis of quadrilateral Nano plates based on nonlocal continuum models using the Galerkin method: the effects of small scale, Meccanica 48(4): 971-982.
3
[4] Alibeigloo A., 2011, Free vibration analysis of nano-plate using three-dimensional theory of elasticity, Acta Mechanica 222: 149-159.
4
[5] Hosseini-Hashemi S., Zare M., Nazemnezhad R., 2013, An exact analytical approach for free vibration of Mindlin rectangular nano-plates via nonlocal elasticity, Composite Structures 100: 290-299.
5
[6] Daneshmehr A., Rajabpoor A., Hadi A., 2015, Size dependent free vibration analysis of Nano plates made of functionally graded materials based on nonlocal elasticity theory with high order theories, International Journal of Engineering Science 95: 23-35.
6
[7] Malekzadeh P., Shojaee M., 2013, Free vibration of Nano plates based on a nonlocal two-variable refined plate theory, Composite Structures 95: 443-452.
7
[8] Analooei H.R., Azhari M., Heidarpour A., 2013, Elastic buckling and vibration analyses of orthotropic Nano plates using nonlocal continuum mechanics and spline finite strip method, Applied Mathematical Modelling 37(10-11): 6703-6717.
8
[9] Aksencer T., Aydogdu M., 2011, Levy type solution method for vibration and buckling of Nano plates using nonlocal elasticity theory, Physica E 43: 954-959.
9
[10] Tadi Beni Y., Mehralian F., Razavi H., 2015, Free vibration analysis of size-dependent shear deformable functionally graded cylindrical shell on the basis of modified couple stress theory, Composite Structures 120: 65-78.
10
[11] Rouhi H., Ansari R., Darvizeh M., 2016, Size-dependent free vibration analysis of Nano shells based on the surface stress elasticity, Applied Mathematical Modelling 40: 3128-3140.
11
[12] Pouresmaeeli S., Ghavanloo E., Fazelzadeh S.A., 2013, Vibration analysis of viscoelastic orthotropic Nano plates resting on viscoelastic medium, Composite Structures 96: 405-410.
12
[13] Ghorbanpour Arani A., Khoddami Maraghi Z., Khani Arani H., 2016, Orthotropic patterns of Pasternak foundation in smart vibration analysis of magnetostrictive Nano plate, Proceedings of the Institution of Mechanical Engineers, Part C: Mechanical Engineering Science 230(4): 559-572.
13
[14] Ghorbanpour Arani A, Haghparast E, Rarani MH, Maraghi ZK, 2015, Strain gradient shell model for nonlinear vibration analysis of visco-elastically coupled Boron Nitride nano-tube reinforced composite micro-tubes conveying viscous fluid, Computational Materials Science 96: 448-458.
14
[15] Liu C., Ke L.L., Wang Y.S., Yang J., Kitipornchai S., 2013, Thermo-electro-mechanical vibration of piezoelectric nanoplates based on the nonlocal theory, Composite Structures 106: 167-174.
15
[16] Ke L.L., Liu C., Wang Y.S., 2015, Free vibration of nonlocal piezoelectric Nano plates under various boundary conditions, Physica E 66: 93-106.
16
[17] Ke L.L., Wang Y.S., Reddy J.N., 2014, Thermo-electro-mechanical vibration of size-dependent piezoelectric cylindrical nanoshells under various boundary conditions, Composite Structures 116: 626-636.
17
[18] Vaezi M., Moory Shirbany M., Hajnayeb A., 2016, Free vibration analysis of magneto-electro-elastic micro beams subjected to magneto-electric loads, Physica E 75: 280-286.
18
[19] Amiri A., Pournaki I.J., Jafarzadeh E., Shabani R., Rezazadeh G., 2016, Vibration and instability of fluid‑conveyed smart micro‑tubes based on magneto‑electro‑elasticity beam model, Micro Fluids Nano Fluids 20: 38-48.
19
[20] Ebrahimi F., Barati M.R., 2016, A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures, International Journal of Engineering Science 107: 183-196.
20
[21] Li Y.S., Ma P., Wang W., 2016, Bending, buckling, and free vibration of magnetoelectroelastic nanobeam based on nonlocal theory, Journal of Intelligent Material Systems and Structures 27(9): 1139-1149.
21
[22] Ansari R., Hasrati E., Gholami R., Sadeghi F., 2015, Nonlinear analysis of forced vibration of nonlocal third-order shear deformable beam model of magneto-electro-thermo elastic nanobeams, Composites Part B 83: 226-241.
22
[23] Ansari R., Gholami R., Rouhi H., 2015, Size-dependent nonlinear forced vibration analysis of magneto-electro-thermo-elastic Timoshenko Nano beams based upon the nonlocal elasticity theory, Composite Structures 126: 216-226.
23
[24] Ke L.L., Wang Y.S., 2014, Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory, Physica E 63: 52-61.
24
[25] Ke L.L., Wang Y.S., Yang J., Kitipornchai S., 2014, Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory, Acta Mechanica Sinica 30(4): 516-525.
25
[26] Wang W., Li P., Jin F., 2016, Two-dimensional linear elasticity theory of magneto-electro-elastic plates considering surface and nonlocal effects for nanoscale device applications, Smart Materials and Structures 25: 095026-095041.
26
[27] Li Y.S., Cai Z.Y., Shi S.Y., 2014, Buckling and free vibration of magnetoelectroelastic Nano plate based on nonlocal theory, Composite Structures 111: 552-529.
27
[28] Pan E., Waksmanski N., 2016, Deformation of a layered magnetoelectroelastic simply-supported plate with nonlocal effect, an analytical three-dimensional solution, Smart Materials and Structures 25: 095013-095030.
28
[29] Ansari R., Gholami R., 2016, Nonlocal free vibration in the pre- and post-buckled states of magneto-electro-thermo elastic rectangular Nano plates with various edge conditions, Smart Materials and Structures 25: 095033-095050.
29
[30] Farajpour A., Hairi Yazdi M.R., Rastgoo A., Loghmani M., Mohammadi M., 2016, Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic Nano plates, Composite Structures 140: 323-336.
30
[31] Ke L.L., Wang Y.S., Yang J., Kitipornchai S., 2014, The size-dependent vibration of embedded magneto-electro-elastic cylindrical Nano shells, Smart Materials and Structures 23: 125036-125053.
31
[32] Ghadiri M., Safarpour H., 2016, Free vibration analysis of embedded magneto-electro-thermo-elastic cylindrical Nano shell based on the modified couple stress theory, Applied Physics A 122: 833-844.
32
[33] Mohammadimehr M., Okhravi S.V., Akhavan Alavi S.M., 2016, Free vibration analysis of magneto-electro-elastic cylindrical composite panel reinforced by various distributions of CNTs with considering open and closed circuits boundary conditions based on FSDT, Journal of Vibration and Control 24: 1551-1569.
33
[34] Reddy J.N., 2004, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press.
34
[35] Hosseini-Hashemi S., Atashipour S.R., Fadaee M., Girhammar U.A., 2012, An exact closed-form procedure for free vibration analysis of laminated spherical shell panels based on Sanders theory, Archive of Applied Mechanics 82: 985-1002.
35
[36] Fadaee M., Atashipour S.R., Hosseini-Hashemi S., 2013, Free vibration analysis of Lévy-type functionally graded spherical shell panel using a new exact closed-form solution, International Journal of Mechanical Sciences 77: 227-238.
36
[37] Khare R.K., Kant T., Garg A.K., 2004, Free vibration of composite and sandwich laminates with a higher-order facet shell element, Composite Structures 65: 405-418.
37
[38] Chern Y.C., Chao C.C., 2000, Comparison of natural frequencies of laminates by 3D theory-part II: curved panels, Journal of Sound and Vibration 230: 1009-1030.
38
[39] Pouresmaeeli S., Fazelzadeh S.A., Ghavanloo E., 2012, Exact solution for nonlocal vibration of double-orthotropic Nano plates embedded in elastic medium, Composites Part B 43: 3384-3390.
39
ORIGINAL_ARTICLE
Mathematical Modeling of Thermoelastic State of a Thick Hollow Cylinder with Nonhomogeneous Material Properties
The object of the present paper is to study heat conduction and thermal stresses in a hollow cylinder with nonhomogeneous material properties. The cylinder is subjected to sectional heating at the curved surface. All the material properties except for Poisson’s ratio and density are assumed to be given by a simple power law in the axial direction. A solution of the two-dimensional heat conduction equation is obtained in the transient state. The solutions are obtained in the form of Bessel’s and trigonometric functions. For theoretical treatment, all the physical and mechanical quantities are taken as dimensional, whereas we have considered non-dimensional parameters, for numerical analysis. The influence of inhomogeneity on the thermal and mechanical behaviour is examined. The transient state temperature field and its associated thermal stresses are discussed for a mixture of copper and tin metals in the ratio 70:30 respectively. Numerical calculations are carried out for both homogeneous and nonhomogeneous cylinders and are represented graphically.
http://jsm.iau-arak.ac.ir/article_539715_76a9f43b0cd1d8e44502c55f211a3057.pdf
2018-03-01T11:23:20
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142
156
Hollow cylinder
Heat conduction
Thermal stresses
Inhomogeneity
Shear modulus
V. R
Manthena
vkmanthena@gmail.com
true
1
Department of Mathematics, RTM Nagpur University, Nagpur, India
Department of Mathematics, RTM Nagpur University, Nagpur, India
Department of Mathematics, RTM Nagpur University, Nagpur, India
LEAD_AUTHOR
N.K
Lamba
true
2
Department of Mathematics, Shri Lemdeo Patil Mahavidyalaya, Nagpur, India
Department of Mathematics, Shri Lemdeo Patil Mahavidyalaya, Nagpur, India
Department of Mathematics, Shri Lemdeo Patil Mahavidyalaya, Nagpur, India
AUTHOR
G.D
Kedar
true
3
Department of Mathematics, RTM Nagpur University, Nagpur, India
Department of Mathematics, RTM Nagpur University, Nagpur, India
Department of Mathematics, RTM Nagpur University, Nagpur, India
AUTHOR
[1] Al-Hajri M., Kalla S.L., 2004, On an integral transform involving Bessel functions, Proceedings of the International Conference on Mathematics and its Applications.
1
[2] Arefi M., Rahimi G. H., 2011, General formulation for the thermoelastic analysis of an arbitrary structure made of functionally graded piezoelectric materials, based on the energy method, Mechanical Engineering 62: 221-235.
2
[3] Birkoff G., Rota G. C., 1989, Ordinary Differential Equations, Wiley, New York.
3
[4] Cho H., Kardomateas G.A., Valle C.S., 1998, Elastodynamic solution for the thermal shock stresses in an orthotropic thick cylindrical shell, Transactions of the ASME 65: 184-193.
4
[5] Deshmukh K.C., Khandait M.V., Kumar R., 2005, Thermal Stresses in a circular plate by a moving heat source, Material Physics and Mechanics 22: 86-93.
5
[6] Deshmukh K.C., Quazi Y.I., Warbhe S.D., Kulkarni V.S., 2011, Thermal stresses induced by a point heat source in a circular plate by quasi-static approach, Theoretical and Applied Mechanics Letters 1: 031007.
6
[7] Edited by the Japan Society of Mechanical Engineers, 1980, Elastic Coefficient of Metallic Materials, Japan Society of Mechanical Engineers.
7
[8] Ghasemi A.R, Kazemian A., Moradi M., 2014, Analytical and numerical investigation of FGM pressure vessel reinforced by laminated composite materials, Journal of Solid Mechanics 6: 43-53.
8
[9] Ghorbanpour A. A., Arefi M., Khoshgoftar M. J., 2009, Thermoelastic analysis of a thick walled cylinder made of functionally graded piezoelectric material, Smart Materials and Structures 18: 115007.
9
[10] Ghorbanpour A. A., Haghparast E., Zahra K. M., Amir S., 2014, Static stress analysis of carbon nano-tube reinforced composite (CNTRC) cylinder under non-axisymmetric thermo-mechanical loads and uniform electro-magnetic fields, Composites Part B: Engineering 68: 136-145.
10
[11] Hata T., 1982, Thermal stresses in a non-homogeneous thick plate under steady distribution of temperature, Journal of Thermal Stresses 5: 1-11.
11
[12] Hosseini S.M., Akhlaghi M., 2009, Analytical solution in transient thermoelasticity of functionally graded thick hollow cylinders, Mathematical Methods in the Applied Sciences 32: 2019-2034.
12
[13] Jabbari M., Aghdam M.B., 2015, Asymmetric thermal stresses of hollow FGM cylinders with piezoelectric internal and external layers, Journal of Solid Mechanics 7: 327-343.
13
[14] Kassir K., 1972, Boussinesq Problems for Non-homogeneous Solid, Proceedings of the American Society of Civil Engineers,Journal of the Engineering Mechanics Division 98: 457-470.
14
[15] Kaur J., Thakur P., Singh S.B., 2016, Steady thermal stresses in a thin rotating disc of finitesimal deformation with mechanical load, Journal of Solid Mechanics 8: 204-211.
15
[16] Kim K.S., Noda N., 2002, Green's function approach to unsteady thermal stresses in an infinite hollow cylinder of functionally graded material, Acta Mechanica 156: 145-161.
16
[17] Morishita H., Tanigawa Y., 1998, Formulation of three dimensional elastic problem for nonhomogeneous medium and its analytical development for semi-infinite body, The Japan Society of Mechanical Engineers 97: 97-104.
17
[18] Noda N., Hetnarski R. B., Tanigawa Y., 2003, Thermal Stresses, Taylor & Francis, New York.
18
[19] Noda N., Ootao Y., Tanigawa Y., 2012, Transient thermoelastic analysis for a functionally graded circular disk with piecewise power law, Journal of Theoretical and Applied Mechanics 50: 831-839.
19
[20] Ootao Y., Tanigawa Y., 1994, Three-dimensional transient thermal stress analysis of a nonhomogeneous hollow sphere with respect to rotating heat source, Transactions of the Japan Society of Mechanical Engineering 60: 2273-2279.
20
[21] Ootao Y., Akai T., Tanigawa Y., 1995, Three-dimensional transient thermal stress analysis of a nonhomogeneous hollow circular cylinder due to a moving heat source in the axial direction, Journal of Thermal Stresses 18: 497-512.
21
[22] Ootao Y., Tanigawa Y., 2005, Transient thermoelastic analysis for a functionally graded hollow cylinder, Journal of Thermal Stresses 29: 1031-1046.
22
[23] Ootao Y., 2010, Transient thermoelastic analysis for a multilayered hollow cylinder with piecewise power law nonhomogenity, Journal of Solid Mechanics and Materials Engineering 4: 1167-1177.
23
[24] Ootao Y., Tanigawa Y., 2012, Transient thermoelastic analysis for a functionally graded hollow circular disk with piecewise power law nonhomogenity, Journal of Thermal Stresses 35: 75-90.
24
[25] Rezaei R., Shaterzadeh A.R., Abolghasemi S., 2015, Buckling analysis of rectangular functionally graded plates with an elliptic hole under thermal loads, Journal of Solid Mechanics 7: 41-57.
25
[26] Sugano Y., 1987, Transient thermal stresses in a non-homogeneous doubly connected region, The Japan Society of Mechanical Engineers 53: 941-946.
26
[27] Sugano Y., 1987, An expression for transient thermal stress in a nonhomogeneous plate with temperature variation through thickness, Ingenieur-Archiv 57: 147-156.
27
[28] Sugano Y., 1988, Transient thermal stresses in a nonhomogeneous doubly connected region, JSME International Journal Series 31: 520-526.
28
[29] Sugano Y., Akashi K., 1989, An analytical solution of unaxisymmetric transient thermal stresses in a nonhomogeneous hollow circular plate, Transactions of the Japan Society of Mechanical Engineers Part A 55: 89-95.
29
[30] Tanigawa Y., Jeon S.P., Hata T., 1997, Analytical development of axisymmetrical elastic problem for semi-infinite body with Kasser’s nonhomogeneous material property, The Japan Society of Mechanical Engineers 96:86-93.
30
[31] Tanigawa Y., Kawamura R., Ishida S., 2002, Derivation of fundamental equation systems of plane isothermal and thermoelastic problems for in-homogeneous solids and its applications to semi-infinite body and slab, Theoretical and Applied Mechanics 51: 267-279.
31
[32] Vimal J., Srivastava R.K., Bhatt A.D., Sharma A.K., 2015, Free vibration analysis of moderately thick functionally graded plates with multiple circular and square cutouts using finite element method, Journal of Solid Mechanics 7: 83-95.
32
[33] Wang Xi., 1993, The elastodynamic solution for a solid sphere and dynamic stress focusing phenomenon, Applied Mathematics and Mechanics 14: 777-785.
33
[34] Zamani N. M., Rastgoo A., Hadi A., 2014, Effect of exponentially-varying properties on displacements and stresses in pressurized functionally graded thick spherical shells with using iterative technique, Journal of Solid Mechanics 6: 366-377.
34
ORIGINAL_ARTICLE
Global Optimization of Stacking Sequence in a Laminated Cylindrical Shell Using Differential Quadrature Method
Based on 3-D elasticity approach, differential quadrature method (DQM) in axial direction is adopted along with Globalized Nelder–Mead (GNM) algorithm to optimize the stacking sequence of a laminated cylindrical shell. The anisotropic cylindrical shell has finite length with simply supported boundary conditions. The elasticity approach, combining the state space method and DQM is used to obtain a relatively accurate objective function. Shell thickness is fixed and orientations of layers change in a set of angles. The partial differential equations are reduced to ordinary differential equations with variable coefficients by applying DQM to the equations, then, the equations with variables at discrete points are obtained. Natural frequencies are attained by solving the Eigen-frequency equation, which appears by incorporating boundary conditions into the state equation. A GNM algorithm is devised for optimizing composite lamination. This algorithm is implemented for maximizing the lowest natural frequency of cylindrical shell. The results are presented for stacking sequence optimization of two to five-layered cylindrical shells. Accuracy and convergence of developed formulation is verified by comparing the natural frequencies with the results obtained in the literature. Finally, the effects of mid-radius to thickness ratio, length to mid-radius ratio and number of layers on vibration behavior of optimized shell are investigated. Results are compared with those of Genetic Algorithm (GA) method, showing faster and more accurate convergence.
http://jsm.iau-arak.ac.ir/article_539716_2f43cf8cbcc601fb10152cb6c9498487.pdf
2018-03-01T11:23:20
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157
174
Stacking sequence optimization
Globalized Nelder–Mead
Laminated cylinder
Vibration analysis
Diﬀerential quadrature method
M.R
Saviz
saviz@azaruniv.ac.ir
true
1
Mechanical Engineering Department, Azarbaijan Shahid Madani University, Tabriz, Iran
Mechanical Engineering Department, Azarbaijan Shahid Madani University, Tabriz, Iran
Mechanical Engineering Department, Azarbaijan Shahid Madani University, Tabriz, Iran
LEAD_AUTHOR
A
Ziaei Asl
true
2
Mechanical Engineering Department, Azarbaijan Shahid Madani University, Tabriz, Iran
Mechanical Engineering Department, Azarbaijan Shahid Madani University, Tabriz, Iran
Mechanical Engineering Department, Azarbaijan Shahid Madani University, Tabriz, Iran
AUTHOR
[1] Schmit L.A.,1979, Optimum design of laminated fiber composite plates, International Journal for Numerical Methods in Engineering 11: 623-640.
1
[2] Haftka R.T., Walsh J.L., 1992, Stacking sequence optimization for buckling of laminated plates by integer programming, AIAA Journal 30: 814-819.
2
[3] Nagendra S., Haftka R.T., Gurdal Z., 1992, Stacking sequence of simply supported laminated with stability and strain constraints, AIAA Journal 30: 2132-2137.
3
[4] Kam T.Y., Lai F.M., 1995, Design of laminated composite plates for optimal dynamic characteristics using a constrained global optimization technique, Computer Methods in Applied Mechanics and Engineering 20(3-4): 384-402.
4
[5] Narita Y., Zhao X., 1998, An optimal design for the maximum fundamental frequency of laminated shallow shells, International Journal of Solids and Structures 35(20): 2571-2583.
5
[6] Narita Y., Zhao X., 1997, Maximization of fundamental frequency for generally laminated rectangular plates by the complex method, Transaction of the Japan Society of Mechanical Engineers Part C 63: 364-370.
6
[7] Tsau L.R., Chang Y.H., Tsao F.L., 1995, The design of optimal stacking sequence for laminated FRP plates with inplane loading, Computers & Structures 55(4): 565-580.
7
[8] Spendley W., Hext G.R., Himsworth F.R., 1962, Sequential application of simplex designs in optimization and evolutionary operation, Techno Metrics 4: 441-461.
8
[9] Nelder J.A., Mead R., 1965, A simplex for function minimization, The Computer Journal 7: 308-313.
9
[10] Lagarias J.C., Reeds J.A., Wright M.H., Wright P.E., 1999, Convergence behavior of the Nelder–Mead simplex algorithm in low dimensions, The SIAM Journal on Optimization 9: 112-147.
10
[11] Abouhamze M., Shakeri M., 2007, Multi-objective stacking sequence optimization of laminated cylindrical panels using a genetic algorithm and neural networks, Composite Structures 81: 253-263.
11
[12] Margarida F.C., Salcedo R.L., 1996, The simplex-simulated annealing approach to continuous non-linear optimization, Computers & Chemical Engineering 20(9): 1065-1080.
12
[13] Chelouah R., Siarry P., 2003, Genetic and Nelder–Mead algorithms hybridized for a more accurate global optimization of continuous multiminima functions, The European Journal of Operational Research 148: 335-348.
13
[14] Chelouah R., Siarry P., 2005, A hybrid method combining continuous tabu search and Nelder–Mead simplex algorithms for the global optimization of multiminima functions, The European Journal of Operational Research 161: 636-654.
14
[15] Luersen M.A., Riche R.L., 2004, Globalized Nelder–Mead method for engineering optimization, Computers & Structures 82: 2251-2260.
15
[16] Siarry P., Chelouah R., 2005, A hybrid method combining continuous Tabu search and Nelder-Mead simplex algorithms for the global optimization of multiminima functions, The European Journal of Operational Research 161: 634-654.
16
[17] Bert C.W., Malik M., 1997, Differential quadrature method: a powerful new technique for analysis of composite structures, Composite Structures 39: 179-189.
17
[18] Malekzadeh P., Farid M., Zahedinejad P., 2008, A three-dimensional layer wise differential quadrature free vibration analysis of laminated cylindrical shells, International Journal of Pressure Vessels and Piping 85: 450-458.
18
[19] Malekzadeh P., Fiouz A.R., Razi H., 2009, Three-dimensional dynamic analysis of laminated composite plates subjected to moving load, Composite Structures 90: 105-114.
19
[20] Li H., Lam K.Y., 1998, Frequency characteristics of a thin rotating cylindrical shell using the generalized differential quadrature method, International Journal of Mechanical Sciences 40(5): 443-459.
20
[21] Li H., Lam K.Y., 2001, Orthotropic influence on frequency characteristics of a rotating composite laminated conical shell by the generalized differential quadrature method, International Journal of Solids and Structures 38: 3995-4015.
21
[22] Wu C.P., Lee C.Y., 2001, Differential quadrature solution for the free vibration analysis of laminated conical shells with variable stiffness, International Journal of Mechanical Sciences 43(8): 1853-1869.
22
[23] Chen W.Q., Lv C.F., Bian Z.G., 2003, Elasticity solution for free vibration of laminated beams, Composite Structures 62: 75-82.
23
[24] Soong T.V., 1970, A subdivisional method for linear system, AIAA/ASME Structures 1970: 211-223.
24
[25] Duda O.R., Hart P.E., Strol D.G., 2001, Pattern Classification, New York, John Wiley & Sons.
25
[26] Gilli M., Winker P., 2003, A global optimization heuristic for estimating agent based models, Computational Statistics and Data Analysis 42: 299-312.
26
[27] Luersen M.A., Riche R.L., 2004, Globalized Nelder–Mead method for engineering optimization, Computers & Structures 82: 2251-2260.
27
[28] Shu C., Richards B.E., 1992, Application of generalized differential quadrature to solve two-dimensional incompressible Navier–Stoaks equations, International Journal for Numerical Methods in Fluids 15: 791-798.
28
[29] Chen W.Q., Lu C.F., 2005, 3D free vibration analysis of cross-ply laminated plates with one pair of opposite edges simply supported, Composite Structures 69: 77-87.
29
[30] Lam K.Y., Loy C.T., 1995, Analysis of rotating laminated cylindrical shells by different thin shell theories, Journal of Sound and Vibration 1995: 23-35.
30
[31] Zhang X.M., 2001, Vibration analysis of cross-ply laminated composite cylindrical shells using the wave propagation approach, Applied Acoustics 62: 1221-1228.
31
[32] Khalili S.M.R., Davar A., Malekzadeh Fard K., 2012, Free vibration analysis of homogeneous isotropic circular cylindrical shells based on a new three-dimensional reﬁned higher-order theory, International Journal of Mechanical Sciences 56: 1-25.
32
[33] Shakeri M., Yas M.H., Ghasemi G.M., 2005, Optimal stacking sequence of laminated cylindrical shells using genetic algorithm, Mechanics of Advanced Materials and Structures 12: 305-312.
33
ORIGINAL_ARTICLE
Rayleigh Surface Wave Propagation in Transversely Isotropic Medium with Three-Phase-Lag Model
The present paper is dealing with the propagation of Rayleigh surface waves in a homogeneous transversely isotropic medium .This thermo-dynamical analysis is carried out in the context of three-phase-lags thermoelasticity model. Three phase lag model is very much useful in the problems of nuclear boiling, exothermic catalytic reactions, phonon-electron interactions, phonon scattering etc. The normal mode analysis is employed to obtain the exact expressions of the considered variables. The frequency equations for thermally insulated and isothermal surface in the closed form are derived. Some special cases of frequency equation are also discussed. In order to illustrate the analytical developments, the numerical solution is carried out and the computer simulated results in respect of phase velocity and attenuation coefficient are presented graphically. It is found that the results obtained in the present problem agree with that of the existing results obtained by various researchers. This study may find its applications in the design of surface acoustic waves (SAW) devices, structural health monitoring and damage characterization of materials.
http://jsm.iau-arak.ac.ir/article_539717_522d0bce3f86e1528332d3ec9fe9f092.pdf
2018-03-01T11:23:20
2019-10-22T11:23:20
175
185
Rayleigh waves
Transversely isotropic material
Three-phase-lag model, Frequency equation
S
Biswas
siddharthabsws957@gmail.com
true
1
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, India
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, India
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, India
LEAD_AUTHOR
B
Mukhopadhyay
true
2
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, India
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, India
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, India
AUTHOR
[1] Rayleigh W.S., 1887, On waves propagating along the plane surface of an elastic solid, Proceedings of the London Mathematical Society 17: 4-11.
1
[2] Hetnarski R.B., Ignaczak J., 2000, Nonclassical dynamical thermoelasticity, International Journal of Solids and Structures 37: 215-224.
2
[3] Lord H. W., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15: 299-309.
3
[4] Green A. E., Lindsay K. A., 1972, Thermoelasticity, Journal of Elasticity 2: 1-7.
4
[5] Hetnarski R. B., Ignaczak J., 1996, Soliton like waves in a low temperature non-linear thermoelastic solid, International Journal of Engineering Science 34: 1767-1787.
5
[6] Green A.E., Naghdi P. M., 1993, Thermoelasticity without energy dissipation, Journal of Elasticity 31: 189-208.
6
[7] Tzou D. Y., 1995, A unique field approach for heat conduction from macro to micro scales, Journal of Heat Transfer 117: 8-16.
7
[8] Roychoudhuri S. K., 2007, On thermoelastic three phase lag model, Journal of Thermal Stresses 30: 231-238.
8
[9] Abd-Alla A. M., Abo-Dahab S.M., Hammad H.A.H., 2011, Propagation of Rayleigh waves in generalized magneto-thermoelastic orthotropic material under initial stress and gravity field, Applied Mathematical Modeling 35: 2981-3000.
9
[10] Sharma J. N., Kumar S., Sharma Y.D., 2009, Effect of micro polarity, micro stretch and relaxation times on Rayleigh surface waves in thermoelastic solids, International Journal of Applied Mathematics and Mechanics 5(2): 17-38.
10
[11] Kumar R., Chawla V., I. A. Abbas, 2012, Effect of viscosity in anisotropic thermoelastic medium with three phase lag model, Journal of Theoretical and Applied Mechanics 39(4): 313-341.
11
[12] Sharma J. N., Singh H., 1985, Thermoelastic surface waves in a transversely isotropic half space with thermal relaxations, Indian Journal of Pure and Applied Mathematics 16(10): 1202-1212.
12
[13] Singh B., Kumari S., Singh J., 2014, Propagation of Rayleigh waves in transversely isotropic dual phase lag thermoelasticity, International Journal of Applied Mathematics and Mechanics 10(3): 1-14.
13
[14] Shaw S., Mukhopadhyay B., 2015, Analysis of Rayleigh surface wave propagation in isotropic micro polar solid under three phase lag model of thermoelasticity, European Journal of Computational Mechanics 24(2): 64-78.
14
[15] Othman M. I. A., Hasona W. M., Mansour N. T., 2015, The influence of gravitational field on generalized thermoelasticity with two-temperature under three-phase-lag model, Computers, Materials & Continua 45(3): 203-219.
15
[16] Othman M. I. A., Hasona W. M., Abd-Elaziz E.M., 2015, Effect of rotation and initial stress on generalized micro-polar thermoelastic medium with three-phase-lag, Computational and Theoretical Nanoscience 12(9): 2030-2040.
16
[17] Othman M. I. A., Zidan M. E. M., 2015, The effect of two temperature and gravity on the 2-D problem of thermoviscoelastic material under three-phase-lag model, Computational and Theoretical Nanoscience 12(8): 1687-1697.
17
[18] Othman M. I. A., Said S. M., 2014, 2-D problem of magneto-thermoelasticity fiber-reinforced medium under temperature-dependent properties with three-phase-lag theory, Meccanica 49(5): 1225-1243.
18
[19] Biswas S., Mukhopadhyay B., Shaw S., 2017, Rayleigh surface wave propagation in orthotropic thermoelastic solids under three-phase-lag model, Journal of Thermal Stresses 40: 403-419.
19
[20] Nowinski J. L., 1978, Theory of Thermoelasticity with Applications, Mechanics of Surface Structures, Sijthoff and Noordhoff International Publishing, Alphen aan den Rijn, Netherlands.
20
ORIGINAL_ARTICLE
A New Eight Nodes Brick Finite Element Based on the Strain Approach
In this paper, a new three dimensional brick finite element based on the strain approach is presented with the purpose of identifying the most effective to analyze linear thick and thin plate bending problems. The developed element which has the three essential external degrees of freedom (U, V and W) at each of the eight corner nodes, is used with a modified elasticity matrix in order to satisfy the basic hypotheses of the theory of plates. The displacements field of the developed element is based on assumed functions for the various strains satisfying the compatibility and the equilibrium equations. New and efficient formulations of this element is discussed in detail, and the results of several examples related to thick and thin plate bending in linear analysis are used to demonstrate the effectiveness of the proposed element. The linear analyses using this developed element exhibit an excellent performance over a set of problems.
http://jsm.iau-arak.ac.ir/article_539718_981b69b160e797c70051b2a471b55881.pdf
2018-03-01T11:23:20
2019-10-22T11:23:20
186
199
Strain approach
Plate bending
Brick element
Finite Element
Kh
Guerraiche
guer.khelifa@yahoo.com
true
1
Department of Mechanical Engineering, Djelfa University, Batna, Algeria
Department of Mechanical Engineering, Djelfa University, Batna, Algeria
Department of Mechanical Engineering, Djelfa University, Batna, Algeria
LEAD_AUTHOR
L
Belounar
true
2
NMISSI Laboratory, Biskra University, Biskra, Algeria
NMISSI Laboratory, Biskra University, Biskra, Algeria
NMISSI Laboratory, Biskra University, Biskra, Algeria
AUTHOR
L
Bouzidi
true
3
NMISSI Laboratory, Biskra University, Biskra, Algeria
NMISSI Laboratory, Biskra University, Biskra, Algeria
NMISSI Laboratory, Biskra University, Biskra, Algeria
AUTHOR
[1] Ait-Ali L., 1984, Développement d’ Eléments Finis de Coque Pour le Calcul des Ouvrages d’Art, Thèse de Doctorat, Ecole Nationale Des Ponts Chaussées Paris Tech.
1
[2] Ashwell D.G., Sabir A.B., Roberts T.M., 1971, Further studies in the application of curved finite elements to circular arches, International Journal of Mechanical Sciences 13(6): 507-517.
2
[3] Ayad R., Batoz J.L., Dhatt G., 1995, Un élément quadrilatéral de plaque basé sur une formulation mixte-hybride avec projection en cisaillement, Revue Européenne des Eléments Finis 4(4): 415-440.
3
[4] Bassayya K., Shrinivasa U., 2000, A 14-node brick element, PN5X1, for plates and shells, Computers & Structures 74(2): 176 -178.
4
[5] Bassayya k., Bahattacharya K., Shrinivasa U., 2000, Eight –Node brick, PN340, represents constant stress fields exactly, Computers & Structures 74(4): 441-460.
5
[6] Bathe K.J., Dvorkin E.N., 1985, A four‐node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation, International Journal for Numerical Methods in Engineering 21(2): 367-383.
6
[7] Belarbi M.T., Charif A., 1998, Nouvel élément secteur basé sur le modèle de déformation avec rotation Dans le plan, Revue Européenne des Eléments Finis 7(4): 439-458.
7
[8] Belarbi M.T., Charif A., 1999, Développement d'un nouvel élément hexaédrique simple basé sur le modèle en déformation pour l'étude des plaques minces et épaisses, Revue Européenne des Eléments Finis 8(2): 135-157.
8
[9] Belarbi M.T., Maalem T., 2005, On improved rectangular finite element for plane linear elasticity analysis, Revue Européenne des Elements Finis 14(8): 985-997.
9
[10] Belarbi M.T., Bourezane M., 2005, On improved Sabir triangular element with drilling rotation, Revue Européenne de Génie Civil 9(9-10): 1151-117.
10
[11] Belounar L., Guenfoud M., 2005, A new rectangular finite element based on the strain approach for plate bending, Thin-Walled Structures 43(1): 47-63.
11
[12] Belounar L., Guerraiche K., 2014, Anew strain based brick element for plate bending, Alexandria Engineering Journal 53(1): 95-105.
12
[13] Bull J.W., 1984, The Strain approach to the development of thin cylindrical shell finite element, Thin-Walled Structures 2(3): 195-205.
13
[14] Charhabi A., 1990, Calcul des Plaques Minces et Epaisses à L'aide des Eléments Finis Tridimensionnels, Annales de l'ITBTP.
14
[15] Chen Y.I., Wu G.Y., 2004, A mixed 8-node hexahedral element based on the Hu-Washizu principle and the field extrapolation technique, Structural Engineering and Mechanics 17(1): 113-140.
15
[16] Djoudi M.S., Bahai H., 2003, A shallow shell finite element for the linear and non-linear analysis of cylindrical shells, Engineering Structures 25(6): 769-778.
16
[17] De Rosa M.A., Franciosi C., 1990, Plate bending analysis by the cell method: numerical comparisons with finite element methods, Computers & Structures 37(5): 731-735.
17
[18] Djoudi M. S., Bahai H., 2004, Strain based finite element for the vibration of cylindrical panels with opening, Thin-Walled Structures 42(4): 575-588.
18
[19] Fredriksson M., Ottosen N.S., 2007, Accurate eight-node hexahedral element, International Journal for Numerical Methods and Engineering 72(6): 631-657.
19
[20] Gallagher R.H., 1976, Introduction aux Eléments Finis, Edition Pluralise.
20
[21] Himeur M., Guenfoud M., 2011, Bending triangular finite element with a fictitious fourth node based on the strain approach, European Journal of Computational Mechanics 20(7-8): 455-485.
21
[22] Himeur M., Benmarce A., Guenfoud M., 2014, A new finite element based on the strain approach with transverse shear effect, Structural Engineering and Mechanics 49(6): 793-810.
22
[23] Himeur M., Zergua A., Guenfoud M., 2015, A Finite Element Based on the Strain Approach Using Airy’s Function, Arabian Journal for Science and Engineering 40(3): 719-733.
23
[24] Hamadi D., Ayoub A., Toufik M., 2016, A new strain-based finite element for plane elasticity problems, Engineering Computations 33(2): 562-579.
24
[25] Jirousek J., Wroblewski A., Qin Q., He X., 1995, A family of quadrilateral hybrid –Trefftz p-elements for thick plate analysis, Computer Methods in Applied Mechanics Engineering 127(1-4): 315-344.
25
[26] Lemosse D., 2000, Eléments Finis Isoparamétriques Tridimensionnels Pour L’étude des Structures Minces, Thèse de Doctorat, Ecole Doctorale SPMI/INSA-Rouen.
26
[27] Li H.G., Cen S., Cen Z.Z., 2008, Hexahedral volume coordinate method (HVCM) and improvements on 3D Wilson hexahedral element, Computer Methods in Applied Mechanics and Engineering 197(51-52): 4531-4548.
27
[28] Lo S.H., Ling C., 2000, Improvement on the 10-node tetrahedral element for three-dimensional problems, Computer Methods in Applied Mechanics and Engineering 189(3): 961-974.
28
[29] MacNeal R.H., Harder R. L., 1985, A Proposed Standard Set of Problems to Test Finite Element Accuracy, Finite Element in Analysis and Design 1(1): 3-20.
29
[30] Mindlin R.D., 1951, Influence of rotary inertia and shear on flexural motions of isotropic elastic plates, Journal of Applied Mechanics 18: 31-38.
30
[31] Ooi E.T., Rajendran S., Yeo J.H., 2004, A 20-node hexahedron element with enhanced distortion tolerance, International Journal for Numerical Methods in Engineering 60(15): 2501-2530.
31
[32] Reissner E., 1945, The effect of transverse shear deformation on the bending of elastic plates, Journal of Applied Mechanics ASME 12: 69-77.
32
[33] Sabir A.B., Lock A.C.,1972, Curved Cylindrical Shell Finite element, International Journal of Mechanical Sciences 14(2): 125-135.
33
[34] Sabir A.B., 1983, A new class of finite elements for plane elasticity problems, CAFEM7, 7th International Conference on Structural Mechanics in Reactor Technology, Chicago.
34
[35] Sabir A.B., Sfendji A., 1995, Triangular and rectangular plane elasticity finite elements, Thin-Walled Structures 21(3): 225-232.
35
[36] Sabir A.B., Moussa A.I., 1997, Analysis of fluted conical shell roofs using the finite element method, Computers & Structures 64(1-4): 239-251.
36
[37] Smith I.M., Grifﬁth D.V., 1988, Programming the Finite Element Method, John Wiley & Sons, UK.
37
[38] Smith I.M., Grifﬁth D.V., 2004, Programming the Finite Element Method, John Wiley & Sons, UK.
38
[39] Sze K.Y., Chan W.K., 2001, A six-node pentagonal assumed natural strain solid-shell element, Finite Elements in Analysis and Design 37(8): 639-655.
39
[40] Timoshenko S., Woinowsky-Krieger S., 1959, Theory of Plates and Shells, London, McGraw-Hill.
40
[41] Timoshenko S., Goodier J. N., 1951, Theory of Elasticity, McGraw-Hill.
41
[42] Trinh V.D., 2009, Formulation, Développement et Validation d’Eléments Finis de Type Coques Volumiques Sous Intégrés Stabilisés Utilisables Pour des Problèmes a Cinématique et Comportement Non Linéaires, Thèse de Doctorat, Ecole Doctorale, ENSAM-Paris.
42
[43] Trinh V.D., Abed-Meraim F., A. Combescure, 2011, Assumed strain solid–shell formulation “SHB6” for the six-node prismatic, Journal of Mechanical Science and Technology 25(9): 2345-2364.
43
[44] Venkatesh D.N., Shrinivasa U., 1996, Plate bending with hexahedral with PN elements, Computers & Structures 60(4): 635-641.
44
[45] Yuan F., Miller R.E., 1988, A rectangular finite element for moderately thick flat plates, Computers & Structures 30(6): 1375-1387.
45
[46] Zienkiewicz O.C., Taylor R.L., 1977, The Finite Element Method, McGraw-Hill.
46
[47] Zienkiewicz O.C., Taylor R.L., 1989, The Finite Element Method, McGraw–Hill.
47
[48] Zienkiewicz O.C., Taylor R.L., 2000, The Finite Element Method, Butterworth-Heinemann.
48
ORIGINAL_ARTICLE
Thermoelastic Analysis of a Rectangular Plate with Nonhomogeneous Material Properties and Internal Heat Source
This article deals with the determination of temperature distribution, displacement and thermal stresses of a rectangular plate having nonhomogeneous material properties with internal heat generation. The plate is subjected to sectional heating. All the material properties except Poisson’s ratio and density are assumed to be given by a simple power law along x direction. Solution of the two-dimensional heat conduction equation is obtained in the transient state. Integral transform method is used to solve the system of fundamental equation of heat conduction. The effects of inhomogeneity on temperature and thermal stress distributions are examined. For theoretical treatment, all the physical and mechanical quantities are taken as dimensional, whereas for numerical computations we have considered non-dimensional parameters. The transient state temperature field and its associated thermal stresses are discussed for a mixture of copper and zinc metals in the ratio 70:30 respectively. Numerical calculations are carried out for both homogeneous and nonhomogeneous cases and are represented graphically.
http://jsm.iau-arak.ac.ir/article_539719_89990b6ee5e44f20691aec7be32a4c22.pdf
2018-03-01T11:23:20
2019-10-22T11:23:20
200
215
Stresses
Inhomogeneity
Heat source
Shear modulus
Simple power law
V. R
Manthena
vkmanthena@gmail.com
true
1
Department of Mathematics, RTM Nagpur University, Nagpur, India
Department of Mathematics, RTM Nagpur University, Nagpur, India
Department of Mathematics, RTM Nagpur University, Nagpur, India
LEAD_AUTHOR
N.K
Lamba
true
2
Department of Mathematics, Shri Lemdeo Patil Mahavidyalaya, Nagpur, India
Department of Mathematics, Shri Lemdeo Patil Mahavidyalaya, Nagpur, India
Department of Mathematics, Shri Lemdeo Patil Mahavidyalaya, Nagpur, India
AUTHOR
G.D
Kedar
true
3
Department of Mathematics, RTM Nagpur University, Nagpur, India
Department of Mathematics, RTM Nagpur University, Nagpur, India
Department of Mathematics, RTM Nagpur University, Nagpur, India
AUTHOR
[1] Al-Hajri M., Kalla S.L., 2004, On an integral transform involving Bessel functions, Proceedings of the International Conference on Mathematics and its Applications.
1
[2] Birkoff G., Rota G. C., 1989, Ordinary Differential Equations, Wiley, New York.
2
[3] Churchill R.V., 1972, Operational Mathematics, Mc-Graw Hill.
3
[4] Ding S.H., Li X., 2015, Thermoelastic analysis of nonhomogeneous structural materials with an interface crack under uniform heat flow, Applied Mathematics and Computation Archive 271: 22-33.
4
[5] Edited by the Japan Society of Mechanical Engineers, 1980, Elastic Coefficient of Metallic Materials, Japan Society of Mechanical Engineers.
5
[6] Gupta A.K., Singhal P., 2010, Thermal effect on free vibration of non-homogeneous orthotropic visco-elastic rectangular plate of parabolically varying thickness, Applied Mathematics 1: 456-463.
6
[7] Gupta A.K., Saini M., Singh S., Kumar R., 2014, Forced vibrations of non-homogeneous rectangular plate of linearly varying thickness, Journal of Vibration Control 20: 876-884.
7
[8] Hata T., 1983, Thermal stresses in a nonhomogeneous thick plate with surface radiation under steady distribution of temperature, The Japan Society of Mechanical Engineers 49: 1515-1521.
8
[9] Kassir M.K., 1972, Boussinesq problems for nonhomogeneous solid, Proceedings of the American Society of Civil Engineers,Journal of the Engineering Mechanics Division 98: 457-470.
9
[10] Kawamura R., Huang D., Tanigawa Y., 2001, Thermoelastic deformation and stress analyses of an orthotropic nonhomogeneous rectangular plate, Proceedings of the Fourth International Congress on Thermal Stresses.
10
[11] Kumar Y., 2012, Free vibrations of simply supported nonhomogeneous isotropic rectangular plates of bilinearly varying thickness and elastically restrained edges against rotation using Rayleigh-Ritz method, Earthquake Engineering and Engineering Vibration 11: 273-280.
11
[12] Lal R., Kumar Y., 2013, Transverse vibrations of nonhomogeneous rectangular plates with variable thickness, Mechanics of Advanced Materials and Structures 20: 264-275.
12
[13] Manthena V.R., Lamba N.K., Kedar G.D., 2016, Transient thermoelastic problem of a nonhomogeneous rectangular plate, Journal of Thermal Stresses 40: 627-640.
13
[14] Martynyak R.M., Dmytriv M.I., 2010, Finite-element investigation of the stress-strain state of an inhomogeneous rectangular plate, Journal of Mathematical Sciences 168: 633-642.
14
[15] Morishita H., Tanigawa Y., 1998, Formulation of three dimensional elastic problem for nonhomogeneous medium and its analytical development for semi-infinite body, The Japan Society of Mechanical Engineers 97: 97-104.
15
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ORIGINAL_ARTICLE
Calculation of Natural Frequencies of Bi-Layered Rotating Functionally Graded Cylindrical Shells
In this paper, an exact analytical solution for free vibration of rotating bi-layered cylindrical shell composed of two independent functionally graded layers was presented. The thicknesses of the shell layers were assumed to be equal and constant. The material properties of the constituents of bi-layered FGM cylindrical shell were graded in the thickness direction of the layers of the shell according to a volume fraction power-law distribution. In order to derive the equations of motion, the Sanders’ thin shell theory and Rayleigh-Ritz method were used. Also the results were extracted by considering Coriolis, centrifugal and initial hoop tension effects. Effects of rotating speed, geometrical parameters, and material distribution in the two functionally graded layers of the shell, circumferential and longitudinal wave number on the forward and backward natural frequencies were investigated. A comparison of the results was made with those available in the literature for the validity and accuracy of the present methodology.
http://jsm.iau-arak.ac.ir/article_539720_1840b8742de2a284ee65d63068456218.pdf
2018-03-01T11:23:20
2019-10-22T11:23:20
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231
Functionally graded material (FGM)
Free vibration
Natural frequency
Bi-layered FGM cylindrical shell
I
Fakhari Golpayegani
fakhari@gut.ac.ir
true
1
Department of Mechanical Engineering, Golpayegan University of Technology, Golpayegan, Iran
Department of Mechanical Engineering, Golpayegan University of Technology, Golpayegan, Iran
Department of Mechanical Engineering, Golpayegan University of Technology, Golpayegan, Iran
LEAD_AUTHOR
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