ORIGINAL_ARTICLE
A Problem of Axisymmetric Vibration of Nonlocal Microstretch Thermoelastic Circular Plate with Thermomechanical Sources
In the present manuscript, we investigated a two dimensional axisymmetric problem of nonlocal microstretch thermoelastic circular plate subjected to thermomechanical sources. An eigenvalue approach is proposed to analyze the problem. Laplace and Hankel transforms are used to obtain the transformed solutions for the displacements, microrotation, microstretch, temperature distribution and stresses. The results are obtained in the physical domain by applying the numerical inversion technique of transforms. The results of the physical quantities have been obtained numerically and illustrated graphically. The results show the effect of nonlocal in the cases of Lord Shulman (LS), Green Lindsay (GL) and coupled thermoelasticity (CT) on all the physical quantities.
http://jsm.iau-arak.ac.ir/article_664213_77b256d640d75f4c41ee056225009cad.pdf
2019-03-30
1
13
10.22034/jsm.2019.664213
Nonlocal microstretch
Thermoelasticity
Laplace and Hankeltransforms
Eigenvalue approach
Circular plate
R
Kumar
rajneesh_kuk@rediffmail.com
1
Department of Mathematices, Kurukshetra University, Kurukshetra, Haryana, India
LEAD_AUTHOR
R
Rani
2
Department of Mathematices, Choudhary Devilal University, Sirsa, Haryana, India
AUTHOR
A
Miglani
3
Department of Mathematices, Choudhary Devilal University, Sirsa, Haryana, India
AUTHOR
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[2] Eringen A. C., 1972, Nonlocal polar elastic continua, International Journal of Engineering Science 10: 1-16.
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[5] Edelen D. G. B., Green A. E., Laws N., 1971, Nonlocal continuum mechanics, Rational Mechanics and Analysis 43: 36-44.
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[6] Eringen A. C., Edelen D. G. B., 1972, On nonlocal elasticity, International Journal of Engineering Science 10: 233-248.
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[12] Gao J., 1999, An asymmetric theory of nonlocal elasticity, International Journal of Solids and Structures 36: 2959-2971.
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[14] Paola M. D., Faillla G., Zingales M., 2010, The mechanically based approach to 3D nonlocal linear elasticity theory: Longe-range central interactions, International Journal of Solids and Structures 47: 2347-2358.
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[17] Sumelka W., Zaera R., Fernandez-Saez J., 2015, A theoretical analysis of the free axial vibration of nonlocal rods with fractional continuum mechanics, Meccanica 50: 2309-2323.
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[28] Eringen A. C., 1984, Plane waves in nonlocal micropolar elasticity, International Journal of Engineering Science 22: 1113-1121.
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36
ORIGINAL_ARTICLE
Size-Dependent Green’s Function for Bending of Circular Micro Plates Under Eccentric Load
In this paper, a Green’s function is developed for bending analysis of micro plates under an asymmetric load. In order to consider the length scale effect, the modified couple stress theory is used. This theory can accurately predict the behavior of micro structures. A thin micro plate is considered and therefore the classical plate theory is utilized. The size dependent governing equilibrium equation of a circular micro plate under an eccentric load is obtained by using the minimum total potential energy principle. This equation is a partial differential equation and it is hard to solve it for an arbitrary loading. A transformation of the coordinate system is introduced to obtain the asymmetric exact solution for deflection of circular micro-plates. By using the obtained size dependent Green’s function, the bending behavior of microplates under arbitrary loads can be easily defined. The results are presented for different asymmetric loads. Also, it is concluded that the length scale has a significant effect on bending of micro plates.
http://jsm.iau-arak.ac.ir/article_664212_755559e9217f228cc090f1d527bf5d27.pdf
2019-03-30
14
25
10.22034/jsm.2019.664212
Green’s function
Micro plate
Length scale effect
M
Shahrokhi
1
Faculty of Mechanical and Material Engineering, Graduate University of Advanced Technology, Kerman, Iran
AUTHOR
E
Jomehzadeh
2
Faculty of Mechanical and Material Engineering, Graduate University of Advanced Technology, Kerman, Iran
AUTHOR
M
Rezaeizadeh
m.rezaeizadeh@kgut.ac.ir
3
Faculty of Mechanical and Material Engineering, Graduate University of Advanced Technology, Kerman, Iran
LEAD_AUTHOR
[1] Lam D.C.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 of Solids 51: 1477-1508.
1
[2] Yang F., Chong A.C.M., Lam D.C.C., Tong P., 2002, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures 39: 2731-2743.
2
[3] Mindlin R.D., 1965, Second gradient of strain and surface tension in linear elasticity, International Journal of Solids and Structures 1: 417-438.
3
[4] Jomehzadeh E., Noori H.R., Saidi A.R., 2011, The size-dependent vibration analysis of micro-plates based on a modiﬁed couple stress theory, Journal of Physica E 43: 877-883.
4
[5] Reddy J.N., Berry J., 2012, Nonlinear theories of axisymmetric bending of functionally graded circular plates with modiﬁed couple stress, Composite Structures 94: 3664-3668.
5
[6] Kumar R., Devi Sh., Sharma V., 2017, Axisymmetric problem of thick circular plate with heat sources in modified couple stress theory, Journal of Solid Mechanics 9: 157-171.
6
[7] Gholami R., Darvizeh A., Ansari R., Pourashraf T., 2017, Analytical treatment of the size-dependent nonlinear post-buckling of functionally graded circular cylindrical micro-/ nano-Shells, Iranian Journal of Science and Technology Transactions of Mechanical Engineering 42: 85-97.
7
[8] Ansari R., Gholami R., 2016 , Surface effect on the large amplitude periodic forced vibration of first-order shear deformable rectangular nanoplates with various edge supports, Acta Astronautica 118: 72-89.
8
[9] Gholami R., Ansari R., Darvizeh A., Sahmani S., 2015, Axial buckling and dynamic stability of functionally graded microshells based on the modified couple stress theory, International Journal of Structural Stability and Dynamics 15(04): 1450070.
9
[10] Ansari R., Gholami R., 2016, Nonlocal free vibration in the pre- and post- buckled states of magneto-electro-thermo elastic rectangular nanoplates with various edge conditions, Smart Materials and Structures 25: 5095033.
10
[11] Wang Y., Lin W., Zhou C., 2013, Nonlinear bending of size-dependent circular microplates based on the modiﬁed couple stress theory, Archive of Applied Mechanics 84: 391-400.
11
[12] Stolken J.S., Evans A.G., 1998, A microbend test method for measuring the plasticity length scale, Acta Metallurgica et Materialia 46: 5109-5115.
12
[13] Saidi A. R., Naderi A., Jomehzadeh E., 2009, A closed form solution for bending/stretching analysis of functionally graded circular plates under as symmetric loading using the Green function, IMECHE Part C Journal of Mechanical Engineering Science 1: 1-3.
13
[14] Liang K., Yang J., Kitipornchai S., Bradford M.A., 2012, Bending, buckling and vibration of size-dependent functionally graded annular micro-plates, Composite Structures 94: 3250-3257.
14
[15] Zhang B., He Y., Liu D., Shen L., Lei J., 2015, An efﬁcient size-dependent plate theory for bending, buckling and free vibration analyses of functionally graded microplates resting on elastic foundation, Mathematical Modelling 39: 3814-3845.
15
[16] Ansari R., Hasrati E., Faghih Shojaei M., Gholami R., Mohammadi V., Shahabodini A., 2016, Size-dependent bending, buckling and free vibration analyses of microscale functionally graded Mindlin plates based on the strain gradient elasticity theory, Latin American Journal of Solids and Structures 13(4): 632-664.
16
[17] Park S.K., Gao X.L., 2006, Bernoulli-Euler beam model based on a modified couple stress theory, Journal of Micromechanics and Microengineering 16: 2355-2359.
17
[18] Kong S., Zhou S., Nie, Z., Wang K., 2008, The size-dependent natural frequency of Bernoulli-Euler micro-beams, International Journal of Engineering Science 46: 427-437.
18
[19] Simsek M., Kocat¨urk T., Akbas S.D., 2013, Static bending of a functionally graded microscale Timoshenko beam based on the modified couple stress theory, Composite Structures 95: 740-747.
19
[20] Nateghi A., Salamat-talab M., Rezapour J., Daneshian B., 2012, Size dependent buckling analysis of functionally graded micro beams based on modified couple stress theory, Applied Mathematical Modelling 36: 4971-4987.
20
[21] Roque C.M.C., Fidalgo D.S., Ferreira A.J.M., Reddy J.N., 2013, A study of a microstructure-dependent composite laminated Timoshenko beam using a modified couple stress theory and a meshless method, Composite Structures 96: 532-537.
21
[22] Ke L.L., Wang Y., Yang J., Kitipornchai S., 2012, Nonlinear free vibration of size-dependent functionally graded micro-beams, International Journal of Engineering Science 50: 256-267.
22
[23] Ansari R., Gholami R., Faghih Shojaei M., Mohammadi V., Sahmani S., 2014, Bending, buckling and free vibration analysis of size-dependent functionally graded circular/annular micro-plates based on the modified strain gradient elasticity theory, European Journal of Mechanics 49: 251-267.
23
[24] Baghani M., MohammadSalehi M., Dabaghian P.H., 2016, Analytical couple-stress solution for size-dependent large-amplitude vibrations of FG tapered-nanobeams, Latin American Journal of Solids and Structures 13(1): 95-118.
24
[25] Karimipour I., Tadi Beni Y., Taheri N., 2017, Influence of electrical double-layer dispersion forces and size dependency on pull-in instability of clamped microplate immersed in ionic liquid electrolytes, Indian Journal of Physics 91(10): 1179-1195.
25
[26] Karimipour I., Tadi Beni Y., Zeighampour H., 2017, Nonlinear size-dependent pull-in instability and stress analysis of thin plate actuator based on enhanced continuum theories including nonlinear effects and surface energy, Microsystem Technologies 24: 1811-1839.
26
ORIGINAL_ARTICLE
Bending Behavior of Sandwich Plates with Aggregated CNT-Reinforced Face Sheets
The main aim of this paper is to investigate bending behavior in sandwich plates with functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets with considering the effects of carbon nanotube (CNT) aggregation. The sandwich plates are assumed resting on Winkler-Pasternak elastic foundation and a mesh-free method based on first order shear deformation theory (FSDT) is developed to analyze the deflection of sandwich plates. In the face sheets, volume fraction of CNTs and their clusters are considered to be changed along the thickness. To estimate the material properties of the nanocomposite, Eshelby-Mori-Tanaka approach is applied. In the mesh-free analysis, moving least squares (MLS) shape functions are employed to approximate the displacement field and transformation method is used for imposition of essential boundary conditions. The effects of CNT volume fraction, distribution and degree of aggregation, and also boundary conditions and geometric dimensions are investigated on the bending behavior of the sandwich plates. It is observed that in the same value of cluster volume, FG distribution of clusters leads to less deflection in these structures.
http://jsm.iau-arak.ac.ir/article_664214_ffde374ff33e440f13237b4aee54e77d.pdf
2019-03-30
26
38
10.22034/jsm.2019.664214
Bending
Aggregated carbon nanotube
Sandwich plates
Elastic foundation, Mesh-free method
M
Mirzaalian
1
Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran
AUTHOR
F
Aghadavoudi
davoodi@iaukhsh.ac.ir
2
Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran
LEAD_AUTHOR
R
Moradi-Dastjerdi
3
Young Researchers and Elite Club, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran
AUTHOR
[1] Iijima S., Ichihashi T., 1993, Single-shell carbon nanotubes of 1-nm diameter, Nature 363: 603-605.
1
[2] Thai H., Choi D., 2011, A refined plate theory for functionally graded plates resting on elastic foundation, Composites Science and Technology 71(16): 1850-1858.
2
[3] Shen H., 2009, Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments, Composite Structures 91(1): 9-19.
3
[4] Alibeigloo A., 2013, Static analysis of functionally graded carbon nanotube-reinforced composite plate embedded in piezoelectric layers by using theory of elasticity, Composite Structures 95: 612-622.
4
[5] Shariyat M., Darabi E., 2013, A variational iteration solution for elastic – plastic impact of polymer / clay nanocomposite plates with or without global lateral deflection , employing an enhanced contact law, International Journal of Mechanical Sciences 67: 14-27.
5
[6] Pourasghar A., Kamarian S., 2013,Three-dimensional solution for the vibration analysis of functionally graded multiwalled carbon nanotubes/phenolic nanocomposite cylindrical panels on elastic foundation, Polymer Composites 34(12): 2040-2048.
6
[7] Malekzadeh P., Zarei A. R., 2014, Free vibration of quadrilateral laminated plates with carbon nanotube reinforced composite layers, Thin Walled Structures 82: 221-232.
7
[8] Kundalwal S. I., Meguid S. A., 2015, Effect of carbon nanotube waviness on active damping of laminated hybrid composite shells, Acta Mechanica 226: 2035-2052.
8
[9] Mohammadimehr M., Navi B. R., 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, Composites Part B 87: 132-148.
9
[10] Ghorbanpour Arani A., Mosayyebi M., Kolahdouzan F., Kolahchi R., Jamali M., 2017, Refined zigzag theory for vibration analysis of viscoelastic functionally graded carbon nanotube reinforced composite microplates integrated with piezoelectric layers, Proceedings of the Institution of Mechanical Engineers Part G, Journal of Aerospace Engineering 231(13): 2464-2478.
10
[11] Ghorbanpour Arani A., Jafari G. S., 2015, Nonlinear vibration analysis of laminated composite Mindlin micro/nano-plates resting on orthotropic Pasternak medium using DQM, Applied Mathematics and Mechanics 36(8): 1033-1044.
11
[12] Ghorbanpour Arani A., Haghparast E., Ghorbanpour Arani A. H., 2016, Size‐dependent vibration of double‐bonded carbon nanotube‐reinforced composite microtubes conveying fluid under longitudinal magnetic field, Polymer Composites 37(5): 1375-1383.
12
[13] Pourasghar A., Yas M., Kamarian S., 2013, Local aggregation effect of CNT on the vibrational behavior of four-parameter continuous grading nanotube-reinforced cylindrical panels, Polymer Composites 34: 707-721.
13
[14] Aragh B. S., Hedayati H., 2012, Eshelby-Mori-Tanaka approach for vibrational behavior of continuously graded carbon nanotube-reinforced cylindrical panels, Composites Part B 43(4): 1943-1954.
14
[15] Tahouneh V., Yas M. H., 2014, Influence of equivalent continuum model based on the Eshelby-Mori-Tanaka scheme on the vibrational response of elastically supported thick continuously graded carbon nanotube-reinforced annular plates, Polymer Composites 35: 1644-1661.
15
[16] Moradi-Dastjerdi R., Payganeh G., Malek-Mohammadi H., 2015, Free vibration analyses of functionally graded CNT reinforced nanocomposite sandwich plates resting on elastic foundation, Journal of Solid Mechanics 7(2): 158-172.
16
[17] Moradi-Dastjerdi R., Malek-Mohammadi H., 2017, Biaxial buckling analysis of functionally graded nanocomposite sandwich plates reinforced by aggregated carbon nanotube using improved high-order theory, Journal of Sandwich Structures & Materials 19(6): 736-769.
17
[18] Moradi-Dastjerdi R., Malek-Mohammadi H., Momeni-Khabisi H., 2017, Free vibration analysis of nanocomposite sandwich plates reinforced with CNT aggregates, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematikund Mechanik 97(11): 1418-1435.
18
[19] Moradi-Dastjerdi R., Malek-Mohammadi H., 2017, Free vibration and buckling analyses of functionally graded nanocomposite plates reinforced by carbon nanotube, Mechanics of Advanced Materials and Structures 4(1): 59-73.
19
[20] Lei Z. X., Liew K. M., Yu J. L., 2013, Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp -Ritz method, Composite Structures 98: 160-168.
20
[21] Moradi-Dastjerdi R., Sheikhi M. M., Shamsolhoseinian H. R., 2014, Stress distribution in functionally graded nanocomposite cylinders reinforced by wavy carbon nanotube, International Journal of Advanced Manufacturing Technology 7(4): 43-54.
21
[22] Sheikhi M. M., Shamsolhoseinian H. R., Moradi-Dastjerdi R., 2016, Investigation on stress distribution in functionally graded nanocomposite cylinders reinforced by carbon nanotubes in thermal environment, International Journal of Advanced Manufacturing Technology 9(2): 81-93.
22
[23] Moradi-Dastjerdi R., Pourasghar A., 2016, Dynamic analysis of functionally graded nanocomposite cylinders reinforced by wavy carbon nanotube under an impact load, Journal of Vibration and Control 22: 1062-1075.
23
[24] Moradi-Dastjerdi R., Payganeh G., 2017, Transient heat transfer analysis of functionally graded CNT reinforced cylinders with various boundary conditions, Steel and Composite Structures 24(3): 359-367.
24
[25] Shams S., Soltani B., 2015, The effects of carbon nanotube waviness and aspect ratio on the buckling behavior of functionally graded nanocomposite plates using a meshfree method, Polymer Composites 38: 1-11.
25
[26] Moradi-Dastjerdi R., 2016, Wave propagation in functionally graded composite cylinders reinforced by aggregated carbon nanotube, Structural Engineering and Mechanics 57(3): 441-456.
26
[27] Moradi-Dastjerdi R., Payganeh G., Tajdari M., 2017, The effects of carbon nanotube orientation and aggregation on static behavior of functionally graded nanocomposite cylinders, Journal of Solid Mechanics 9(1): 198-212.
27
[28] Zhang L. W., Lei Z. X., Liew K. M., 2015, An element-free IMLS-Ritz framework for buckling analysis of FG – CNT reinforced composite thick plates resting on Winkler foundations, Engineering Analysis with Boundary Elements 58: 7-17.
28
[29] Zhang L. W., Song Z. G., Liew K. M., 2015, Nonlinear bending analysis of FG-CNT reinforced composite thick plates resting on Pasternak foundations using the element-free IMLS-Ritz method, Composite Structures 128: 165-175.
29
[30] Moradi-Dastjerdi R., Payganeh G., Rajabizadeh Mirakabad S., . Jafari Mofrad Taheri M., 2016, Static and free vibration analyses of functionally graded nano- composite plates reinforced by wavy carbon nanotubes resting on a pasternak elastic foundation, Mechanics of Advanced Materials and Structures 3: 123-135.
30
[31] Moradi-Dastjerdi R., Momeni-Khabisi H., 2016, Dynamic analysis of functionally graded nanocomposite plates reinforced by wavy carbon nanotube, Steel and Composite Structures 22(2): 277-299.
31
[32] Shi D., Feng X., Huang Y. Y., Hwang K. C., Gao H., 2004, The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube- reinforced composites, Journal of Engineering Materials and Technology 126: 250-257.
32
[33] Eshelby J. D., 1957, The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proceedings of the Royal Society of London Series A 241: 376-396.
33
[34] Mura T., 1982, Micromechanics of Defects in Solids, The Hague Martinus Nijhoff Pub.
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35
[36] Reddy J. N., 2004, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press.
36
[37] Efraim E., Eisenberger M. Ã., 2007, Exact vibration analysis of variable thickness thick annular isotropic and FGM plates, Journal of Sound and Vibration 299: 720-738.
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[38] Lancaster P., Salkauskas K., 1981, Surface generated by moving least squares methods, Mathematics of Computation 37: 141-158.
38
[39] Shen H., 2011, Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments , Part I : Axially-loaded shells, Composite Structures 93(8): 2096-2108.
39
[40] Ferreira A. J. M., Castro L. M. S., Bertoluzza S., 2009, A high order collocation method for the static and vibration analysis of composite plates using a first-order theory, Composite Structures 89(3): 424-432.
40
[41] Akhras G., Cheung M., Li W., 1994, Finite strip analysis for anisotropic laminated composite plates using higher-order deformation theory, Composite Structures 52: 471-477.
41
[42] Zhu P., Lei Z. X., Liew K. M., 2012, Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory, Composite Structures 94(4): 1450-1460.
42
ORIGINAL_ARTICLE
Size-Dependent Forced Vibration Analysis of Three Nonlocal Strain Gradient Beam Models with Surface Effects Subjected to Moving Harmonic Loads
The forced vibration behaviors are examined for nonlocal strain gradient nanobeams with surface effects subjected to a moving harmonic load travelling with a constant velocity in terms of three beam models namely, the Euler-Bernoulli, Timoshenko and modified Timoshenko beam models. The modification for nonlocal strain gradient Timoshenko nanobeams is exerted to the constitutive equations by exclusion of the nonlocality in the shear constitutive relation. Some analytical closed-form solutions for three nonlocal strain gradient beam models with simply supported boundary conditions are derived by using the Galerkin discretization method in conjunction with the Laplace transform method. The effects of the three beam models, the nonlocal and material length scale parameters, the velocity and excitation frequency of the moving harmonic load on the dynamic behaviors of nanobeams are discussed in some detail. Specifically, the critical velocities are examined in some detail. Numerical results have shown that the aforementioned parameters are very important factors for determining the dynamic behavior of the nanobeams accurately.
http://jsm.iau-arak.ac.ir/article_664215_f406244df25e8c9f901e372f0ccd934a.pdf
2019-03-30
39
59
10.22034/jsm.2019.664215
Nonlocal strain gradient elasticity theory
Euler-Bernoulli beam model
Timoshenko beam model
Moving harmonic load
Analytical solution
K
Rajabi
rajabi.kaveh@gmail.com
1
Department of Mechanical Engineering, College of Engineering, Sanandaj Branch, Islamic Azad University, Sanandaj, Iran
LEAD_AUTHOR
Sh
Hosseini Hashemi
2
School of Mechanical Engineering , Iran University of Science and Technology, Tehran, Iran
AUTHOR
A.R
Nezamabadi
3
Department of Mechanical Engineering, Arak Branch, Islamic Azad University, Arak, Iran
AUTHOR
[1] Kiani K., 2010, Longitudinal an7d transverse vibration of a single-walled carbon nanotube subjected to a moving nanoparticle accounting for both nonlocal and inertial effects, Physica E: Low-dimensional Systems and Nanostructures 42(9): 2391-2401.
1
[2] Pijper D., 2005, Acceleration of a nanomotor: electronic control of the rotary speed of a light-driven molecular rotor, Journal of the American Chemical Society 127(50): 17612-17613.
2
[3] Shirai Y., 2005, Directional control in thermally driven single-molecule nanocars, Nano Letters 5(11): 2330-2334.
3
[4] Shirai Y., 2006, Surface-rolling molecules, Journal of the American Chemical Society 128(14): 4854-4864.
4
[5] Shirai Y., 2006, Recent progress on nanovehicles, Chemical Society Reviews 35(11): 1043-1055.
5
[6] Gross L., 2005, Trapping and moving metal atoms with a six-leg molecule, Nature Materials 4(12): 892-895.
6
[7] Kiani K., Mehri B., 2010, Assessment of nanotube structures under a moving nanoparticle using nonlocal beam theories, Journal of Sound and Vibration 329(11): 2241-2264.
7
[8] Kiani K., 2010, Application of nonlocal beam models to double-walled carbon nanotubes under a moving nanoparticle, Part I: Theoretical formulations, Acta Mechanica 216(1-4): 165-195.
8
[9] Kiani K., 2011, Nonlocal continuum-based modeling of a nanoplate subjected to a moving nanoparticle, Part I: Theoretical formulations, Physica E: Low-dimensional Systems and Nanostructures 44(1): 229-248.
9
[10] Kiani K., Wang Q., 2012, On the interaction of a single-walled carbon nanotube with a moving nanoparticle using nonlocal Rayleigh, Timoshenko, and higher-order beam theories, European Journal of Mechanics - A/Solids 31(1): 179-202.
10
[11] Kiani K., 2010, Application of nonlocal beam models to double-walled carbon nanotubes under a moving nanoparticle, Part II: Parametric study, Acta Mechanica 216(1-4): 197-206.
11
[12] Arani A.G., Roudbari M., Amir S., 2012, Nonlocal vibration of SWBNNT embedded in bundle of CNTs under a moving nanoparticle, Physica B: Condensed Matter 407(17): 3646-3653.
12
[13] Kiani K., 2011, Nonlocal continuum-based modeling of a nanoplate subjected to a moving nanoparticle, Part II: Parametric studies, Physica E: Low-dimensional Systems and Nanostructures 44(1): 249-269.
13
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[18] Yi D., Wang T.C., Xiao Z., 2010, Strain gradient theory based on a new framework of non-local model, Acta Mechanica 212(1-2): 51-67.
18
[19] Akgöz B., Civalek Ö., 2011, Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams, International Journal of Engineering Science 49(11): 1268-1280.
19
[20] Akgöz B., Civalek Ö., 2012, Analysis of micro-sized beams for various boundary conditions based on the strain gradient elasticity theory, Archive of Applied Mechanics 82(3): 423-443.
20
[21] Wu J., Li X., Cao W., 2013, Flexural waves in multi-walled carbon nanotubes using gradient elasticity beam theory, Computational Materials Science 67: 188-195.
21
[22] Peddieson J., Buchanan G.R., McNitt R.P., 2003, Application of nonlocal continuum models to nanotechnology, International Journal of Engineering Science 41(3): 305-312.
22
[23] Lu P., 2006, Dynamic properties of flexural beams using a nonlocal elasticity model, Journal of Applied Physics 99(7): 073510.
23
[24] Reddy J., 2007, Nonlocal theories for bending, buckling and vibration of beams, International Journal of Engineering Science 45(2): 288-307.
24
[25] Murmu T., Pradhan S., 2009, Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory, Computational Materials Science 46(4): 854-859.
25
[26] Askes H., Aifantis E.C., 2011, Gradient elasticity in statics and dynamics: an overview of formulations, length scale identification procedures, finite element implementations and new results, International Journal of Solids and Structures 48(13): 1962-1990.
26
[27] Tian Y., 2013, Ultrahard nanotwinned cubic boron nitride, Nature 493(7432): 385-388.
27
[28] Li X., 2010, Dislocation nucleation governed softening and maximum strength in nano-twinned metals, Nature 464(7290): 877-880.
28
[29] Lim C., Zhang G., Reddy J., 2015, A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation, Journal of the Mechanics and Physics of Solids 78: 298-313.
29
[30] Ebrahimi F., Barati M.R., 2016, Flexural wave propagation analysis of embedded S-FGM nanobeams under longitudinal magnetic field based on nonlocal strain gradient theory, Arabian Journal for Science and Engineering 2016: 1-12.
30
[31] Farajpour A., 2016, A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment, Acta Mechanica 2016: 1-19.
31
[32] Hosseini S., Rahmani O., 2016, Exact solution for axial and transverse dynamic response of functionally graded nanobeam under moving constant load based on nonlocal elasticity theory, Meccanica 2016: 1-17.
32
[33] Li L., Hu Y., 2016, Wave propagation in fluid-conveying viscoelastic carbon nanotubes based on nonlocal strain gradient theory, Computational Materials Science 112: 282-288.
33
[34] Li L., Hu Y., Li X., 2016, Longitudinal vibration of size-dependent rods via nonlocal strain gradient theory, International Journal of Mechanical Sciences 115: 135-144.
34
[35] Li L., 2016, Size-dependent effects on critical flow velocity of fluid-conveying microtubes via nonlocal strain gradient theory, Microfluidics and Nanofluidics 20(5): 1-12.
35
[36] Li L., Li X., Hu Y., 2016, Free vibration analysis of nonlocal strain gradient beams made of functionally graded material, International Journal of Engineering Science 102: 77-92.
36
[37] Şimşek M., 2016, Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach, International Journal of Engineering Science 105: 12-27.
37
[38] Şimşek M., 2016, Axial vibration analysis of a nanorod embedded in elastic medium using nonlocal strain gradient theory, Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi 31(1): 213-221.
38
[39] Tang Y., Liu Y., Zhao D., 2016, Viscoelastic wave propagation in the viscoelastic single walled carbon nanotubes based on nonlocal strain gradient theory, Physica E: Low-dimensional Systems and Nanostructures 84: 202-208.
39
[40] Fernandes R., 2017, Nonlinear size-dependent longitudinal vibration of carbon nanotubes embedded in an elastic medium, Physica E: Low-dimensional Systems and Nanostructures 88: 18-25.
40
[41] Shen Y., Chen Y., Li L., 2016, Torsion of a functionally graded material, International Journal of Engineering Science 109: 14-28.
41
[42] Guo S., 2016, Torsional vibration of carbon nanotube with axial velocity and velocity gradient effect, International Journal of Mechanical Sciences 119: 88-96.
42
[43] Li X., 2017, Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory, Composite Structures 165: 250-265.
43
[44] Li L., Hu Y., 2017, Post-buckling analysis of functionally graded nanobeams incorporating nonlocal stress and microstructure-dependent strain gradient effects, International Journal of Mechanical Sciences 120: 159-170.
44
[45] Ebrahimi F., Barati M.R., Dabbagh A., 2016, A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates, International Journal of Engineering Science 107: 169-182.
45
[46] Wang G.-F., Feng X.-Q., 2009, Surface effects on buckling of nanowires under uniaxial compression, Applied Physics Letters 94(14): 141913.
46
[47] Hosseini S.A.H., Rahmani O., 2016, Surface effects on buckling of double nanobeam system based on nonlocal timoshenko model, International Journal of Structural Stability and Dynamics 16(10): 1550077.
47
[48] He J., Lilley C.M., 2008, Surface effect on the elastic behavior of static bending nanowires, Nano Letters 8(7): 1798-1802.
48
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49
[50] Abbasion S., 2009, Free vibration of microscaled Timoshenko beams, Applied Physics Letters 95(14): 143122.
50
[51] Ansari R., 2014, Nonlinear vibration analysis of Timoshenko nanobeams based on surface stress elasticity theory, European Journal of Mechanics - A/Solids 45: 143-152.
51
[52] Lei X.-w., 2012, Surface effects on the vibrational frequency of double-walled carbon nanotubes using the nonlocal Timoshenko beam model, Composites Part B: Engineering 43(1): 64-69.
52
[53] Lee H.-L., Chang W.-J., 2010, Surface effects on frequency analysis of nanotubes using nonlocal Timoshenko beam theory, Journal of Applied Physics 108(9): 093503.
53
[54] Wang G.-F., Feng X.-Q., 2009, Timoshenko beam model for buckling and vibration of nanowires with surface effects, Journal of Physics D: Applied Physics 42(15): 155411.
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[55] 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(1): 303-313.
55
[56] Wang Q., Wang C.M., 2007, The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes, Nanotechnology 18(7): 075702.
56
[57] Younesian D., Nankali A., Motieyan E., 2011, Optimal nonlinear energy sinks in vibration mitigation of the beams traversed by successive moving loads, Journal of Solid Mechanics 3(4): 323-331.
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[58] Rajabi K., Kargarnovin M., Gharini M., 2013, Dynamic analysis of a functionally graded simply supported Euler–Bernoulli beam subjected to a moving oscillator, Acta Mechanica 2013: 1-22.
58
[59] Pang M., Zhang Y.Q., Chen W.Q., 2015, Transverse wave propagation in viscoelastic single-walled carbon nanotubes with small scale and surface effects, Journal of Applied Physics 117(2): 024305.
59
[60] Naderi A., Saidi A., 2013, Modified nonlocal mindlin plate theory for buckling analysis of nanoplates, Journal of Nanomechanics and Micromechanics 4(4): A4013015.
60
[61] Shenoy V.B., 2005, Atomistic calculations of elastic properties of metallic fcc crystal surfaces, Physical Review B 71(9): 094104.
61
ORIGINAL_ARTICLE
Numerical Analysis of Composite Beams under Impact by a Rigid Particle
Analysis of a laminated composite beam under impact by a rigid particle is investigated. The importance of this project is to simulate the impact of objects on small scale aerial structures. The stresses are considered uni- axial bending with no torsion loading. The first order shear deformation theory is used to simulate the beam. After obtaining kinematic and potential energy for a laminated composite beam, the motion equations, boundary conditions and initial conditions are obtained by using Hamilton’s principle. The deformation of beam is considered large so these equations are nonlinear. Then by using the numerical methods such as generalize differential quadrature (GDQ) and Newmark methods, the equations will be converted in to a set of nonlinear algebraic equations. These nonlinear equations are solved by numerical methods such as Newton- Raphson. By solving the equations, the displacement of beam and rotation of cross section in terms of time for different number of points of beam for variety of orientation angle of layers are obtained. Then the displacements of impacted point of beam, stresses and contact forces in different times for variety of orientation of layers for different situations of impact are compared.
http://jsm.iau-arak.ac.ir/article_664217_048f8f8fd934ca28ce393e232caca260.pdf
2019-03-30
60
77
10.22034/jsm.2019.664217
Composite beam
Impact
Rigid mass
Large deformation
N
Akbari
nozar@ssau.ac.ir
1
Department of Aerospace Engineering, Shahid Sattari Aeronautical University of Science Technology, Tehran, Iran
LEAD_AUTHOR
B
Chabsang
2
Departmen of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran
AUTHOR
[1] Abrate S., 2011, Impact Engineering of Composite Structures, Springer Science & Business Media.
1
[2] Zener C., 1941, The intrinsic inelasticity of large plates, Physical Review 59(8): 669-673.
2
[3] Müller P., Böttcher R., Russell A., Trüe M., Aman S., Tomas J., 2016, Contact time at impact of spheres on large thin plates, Advanced Powder Technology 27(4): 1233-1243 .
3
[4] Boettcher R., Russell A., Mueller P., 2017, Energy dissipation during impacts of spheres on plates: Investigation of developing elastic flexural waves, International Journal of Solids and Structures 106: 229-239.
4
[5] Hunter S., 1957, Energy absorbed by elastic waves during impact, Journal of the Mechanics and Physics of Solids 5(3): 162-171.
5
[6] Reed J., 1985, Energy losses due to elastic wave propagation during an elastic impact, Journal of Physics D: Applied Physics 18(12): 2329.
6
[7] Weir G., Tallon S., 2005, The coefficient of restitution for normal incident, low velocity particle impacts, Chemical Engineering Science 60(13): 3637-3647.
7
[8] Kelly J. M., 1967, The impact of a mass on a beam, International Journal of Solids and Structures 3(2): 191-196.
8
[9] Sun C., Huang S., 1975, Transverse impact problems by higher order beam finite element, Computers & Structures 5 (5-6): 297-303.
9
[10] Yufeng X., Yuansong Q., Dechao Z., Guojiang S., 2002, Elastic impact on finite Timoshenko beam, Acta Mechanica Sinica 18(3): 252-263.
10
[11] Kiani Y., Sadighi M., Salami S. J., Eslami M., 2013, Low velocity impact response of thick FGM beams with general boundary conditions in thermal field, Composite Structures 104: 293-303.
11
[12] Rezvanian M., Baghestani A., Pazhooh M. D., Fariborz S., 2015, Off-center impact of an elastic column by a rigid mass, Mechanics Research Communications 63: 21-25.
12
[13] Ghatreh Samani K., Fotuhi A. R., Shafiei A. R., 2017, Analysis of composite beam, having initial geometric imperfection, subjected to off-center impact, Modares Mechanical Engineering 17(5): 185-192.
13
[14] Singh H., Mahajan P., 2016, Analytical modeling of low velocity large mass impact on composite plate including damage evolution, Composite Structures 149: 79-92.
14
[15] Shivakumar K. N., Elber W., Illg W., 1985, Prediction of impact force and duration due to low-velocity impact on circular composite laminates, Journal of Applied Mechanics 52(3): 674-680.
15
[16] Lam K., Sathiyamoorthy T., 1999, Response of composite beam under low-velocity impact of multiple masses, Composite Structures 44(2-3): 205-220.
16
[17] Ugural A. C., 2009, Stresses in Beams, Plates, and Shells, CRC Press.
17
[18] Elshafei M. A., 2013, FE Modeling and analysis of isotropic and orthotropic beams using first order shear deformation theory, Materials Sciences and Applications 4(01): 77.
18
[19] Reddy J. N., 2004, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC press.
19
[20] Newmark N. M., 1959, A method of computation for structural dynamics, Journal of the Engineering Mechanics Division 85(3): 67-94.
20
[21] Hilber H. M., Hughes T. J., Taylor R. L., 1977, Improved numerical dissipation for time integration algorithms in structural dynamics, Earthquake Engineering & Structural Dynamics 5(3): 283-292.
21
[22] Shu C., Wang C., 1999, Treatment of mixed and nonuniform boundary conditions in GDQ vibration analysis of rectangular plates, Engineering Structures 21(2): 125-134.
22
[23] Reddy J., 2004, An Introduction to Nonlinear Finite Element Analysis, United State, Oxford.
23
ORIGINAL_ARTICLE
Smart Flat Membrane Sheet Vibration-Based Energy Harvesters
The dynamic responses of membrane are completely dependent on Pre-tensioned forces which are applied over a boundary of arbitrary curvilinear shape. In most practical cases, the dynamic responses of membrane structures are undesirable. Whilst they can be designed as vibration-based energy harvesters. In this paper a smart flat membrane sheet (SFMS) model for vibration-based energy harvester is proposed. The SFMS is made of an orthotropic polyvinylidene fluoride (PVDF) flat layer that has piezoelectricity effect. For this aim, polarization vector of PVDF layer is considered parallel to the applied electric field intensity vector. Electrodynamics governing equations of transverse motion of SFMS including active and modified pre-tensioned force are exploited. Transverse displacement component is expanded by the separable form corresponding to the axial and transverse and the linear ODE of motion based on generalized shape coefficients is obtained using Galerkin method. Finally, the explicit relation between forced vibration of SFMS and current and voltage harvesting are obtained. Numerical energy harvesting analyses were developed for an orthotropic rectangle SFMS and the voltage as function of the time is calculated based on different resistances. Parametric simulation shows a 1 m length and 0.5 width SFMS has ability to produce a peak to peak voltage about of 30 mV.
http://jsm.iau-arak.ac.ir/article_664219_e2dc2db5c94bbb75247e6130e475b41f.pdf
2019-03-30
78
90
10.22034/jsm.2019.664219
Membrane
Smart structure
PVDF
Electrodynamics vibration, Energy harvesting
Y
Shahbazi
y.shahbazi@tabriziau.ac.ir
1
Architecture and Urbanism Department, Tabriz Islamic Art University, Tabriz, Iran
LEAD_AUTHOR
[1] Leissa Arthur W., Qatu Mohamad S., 2011, Vibration of Continuous Systems, McGraw-Hill Education.
1
[2] Jenkins Christopher H.M., Korde Umesh A., 2006, Membrane vibration experiments: An historical review and recent results, Journal of Sound and Vibration 295: 602-613.
2
[3] Preumont A., 2006, Mechatronics Dynamics of Electromechanical and Piezoelectric Systems Materials, Springer, Printed in the Netherlands.
3
[4] Yipeng W., Badel A., Formosa F., Liu W., Agbossou A. E., 2012, Piezoelectric vibration energy harvesting by optimized synchronous electric charge extraction, Journal of Intelligent Material Systems 24(12): 1445-1458.
4
[5] Lezgy-Nazargah M., Divandar S.M., Vidal P., Polit O., 2017, Assessment of FGPM shunt damping for vibration reduction of laminated composite beams, Journal of Sound and Vibration 389: 101-118.
5
[6] Priya S., 2007, Advances in energy harvesting using low proﬁle piezoelectric transducers, Journal of Electroceramics 19:165-182.
6
[7] Anton S.R., Sodano H.A., 2007, A review of power harvesting using piezoelectric materials (2003–2006), Smart Materials and Structures 16: R1–R21.
7
[8] Beeby S.P., Tudor M.J., White N.M., 2006, Energy harvesting vibration sources for microsystems applications, Measurement Science and Technology 17: R175–R195.
8
[9] Roundy S., Wright P.K., 2004, A piezoelectric vibration based generator for wireless electronics, Smart Materials and Structures 13: 1131-1142.
9
[10] Sodano H., Inman D.J., Park G., 2004, A review of power harvesting from vibration using piezoelectric materials, The Shock and Vibration Digest 36: 197-205.
10
[11] Erturk A., Inman D.J., 2008, Issues in mathematical modeling of piezoelectric energy harvesters, Smart Materials and Structures 17(6): 065016.
11
[12] Erturk A., Inman D.J., 2009, An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitation, Smart Materials and Structures 18(2): 025009.
12
[13] Priya S., Inman D.J., 2009, Energy Harvesting Technologies, Springer, New York.
13
[14] Goldschmidtboeing F., Woias P., 2008, Characterization of different beam shapes for piezoelectric energy harvesting, Journal of Micromechanics and Microengineering 18: 104013.
14
[15] Guyomar D., Badel A., Lefeuvre E., Richard C., 2005, Toward energy harvesting using active materials and conversion improvement by nonlinear processing, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 52(4): 584-595.
15
[16] Peng J., Chao C., Tang H., 2010, Piezoelectric micromachined ultrasonic transducer based on dome-shaped piezoelectric single layer, Microsystem Technologies 16: 1771-1775.
16
[17] Shahbazi Y., Chenaghlou M. R., Abedi K., Khosrowjerdi M. J., Preumont A., 2012, A new energy harvester using a cross-ply cylindrical membrane shell integrated with PVDF layers, Microsystem Technologies 18: 1981-1989.
17
ORIGINAL_ARTICLE
Fracture Parameters for Cracked Cylincal Shells
In this paper, 2D boundary element stress analysis is carried out to obtain the T-stress for multiple internal edge cracks in thick-walled cylinders for a wide range of cylinder radius ratios and relative crack depth. The T-stress, together with the stress intensity factor K, provides amore reliable two-parameter prediction of fracture in linear elastic fracture mechanics. T-stress weight functions are then derived from the T-stress solutions for two reference load conditions corresponding to the cases when the cracked cylinder is subject to a uniform and to a linear applied stress variation on the crack faces. The derived weight functions are then verified for several non-linear load conditions. Using the BEM results as reference T-stress solutions; the T-stress weight functions for thick-walled cylinder have also been derived. Excellent agreements between the BEM results and weight function predictions are obtained. The weight functions derived are suitable for obtaining T-stress solutions for the corresponding cracked thick-walled cylinder under any complex stress fields. Results of the study show that the two dimensional BEM analysis, together with weight function method, can be used to provide a quick and accurate estimate of T-stress for 2-D crack problems.
http://jsm.iau-arak.ac.ir/article_664221_46fbd1e945c36c4866982234067fab64.pdf
2019-03-30
91
104
10.22034/jsm.2019.664221
Fracture mechanics
T-stress
Contour integral approach
Thick-walled cylinders
Boundary element method
M
Kadri
mohammed84.kadri@univ-usto.dz
1
Laboratoire de Mécanique Appliquée, Université des Sciences et de la Technologie d’Oran , Algeria
LEAD_AUTHOR
A
Sahli
2
Laboratoire de Recherche des Technologies Industrielles, Université Ibn Khaldoun de Tiaret, Algeria
AUTHOR
S
Sahli
3
Université d'Oran 2 Mohamed Ben Ahmed, Algeria
AUTHOR
[1] Rice J.R., 1968, Path-independent integral and the approximate analysis of strain concentration by notches and cracks, Journal of Applied Mechanics 35(2): 379-386.
1
[2] Anderson T.L., 1995, Fracture Mechanics: Fundamentals and Applications, Boca Raton, CRC Press.
2
[3] Williams J.G., Ewing P.D., 1972, Fracture under complex stress—the angled crack problem, International Journal of Fracture 8(4): 416-441.
3
[4] Ueda Y., Ikeda K., Yao T., Aoki M., 1983, Characteristics of brittle failure under general combined modes including those under bi-axial tensile loads, Engineering Fracture Mechanics 18(6):1131-1158.
4
[5] Smith D.J., Ayatollahi M.R., Pavier M.J., 2001, The role of T-stress in brittle fracture for linear elastic materials under mixed-mode loading, Fatigue & Fracture of Engineering Materials & Structures 24(2):137-150.
5
[6] Cotterell B., Rice J.R., 1980, Slightly curved or kinked cracks, International Journal of Fracture 16(2):155-169.
6
[7] Du Z-Z., Hancock J.W., 1991, The effect of non-singular stresses on crack-tip constraint, Journal of the Mechanics and Physics of Solids 39(3): 555-567.
7
[8] O’Dowd N.P., Shih C.F., Dodds Jr R.H., 1995, The role of geometry and crack growth on constraint and implications for ductile/brittle fracture, In: Constraint effects in fracture theory and applications, American Society for Testing and Materials 2:134-159.
8
[9] Larsson S.G., Carlson A.J., 1973, Influence of non-singular stress terms and specimen geometry on small-scale yielding at crack tips in elastic–plastic materials, Journal of the Mechanics and Physics of Solids 21(4): 263-277.
9
[10] Leevers P.S., Radon J.C.D., 1982, Inherent stress biaxiality in various fracture specimen, International Journal of Fracture 19(4): 311-325.
10
[11] Cardew G.E., Goldthorpe M.R., Howard I.C., Kfouri A.P., 1985, Fundamentals of Deformation and Fracture, Eshelby Memorial Symposium Sheffield.
11
[12] Kfouri A.P., 1986, Some evaluations of the elastic T-term using Eshelby’s method, International Journal of Fracture 30(4): 301-315.
12
[13] Sham T.L., 1991, The determination of the elastic T-term using higher-order weight functions, International Journal of Fracture 48(2):81-102.
13
[14] Wang Y-Y., Parks D.M., 1992, Evaluation of the elastic T-stress in surface cracked plates using the line-spring method, International Journal of Fracture 56(1): 25-40.
14
[15] Chen C.S., Krause R., Pettit R.G., Banks-Sills L., Ingraffea A.R., 2001, Numerical assessment of T-stress computation using a p-version finite element method, International Journal of Fracture 107(2):177-199.
15
[16] Sladek J., Sladek V., Fedelinski P., 1997, Contour integrals for mixed-mode crack analysis: effect of nonsingular terms, Theoretical and Applied Fracture Mechanics 27:115-127.
16
[17] Nakamura T., Parks D.M., 1992, Determination of T-stress along three dimensional crack fronts using an interaction integral method, International Journal of Solids and Structures 29(13):1597-1611.
17
[18] Fett T., 2002, T -Stress Solutions and Stress Intensity Factors for 1-D Cracks, Dusseldorf, VDI Verlag.
18
[19] Wang X., 2002, Elastic T-stress for cracks in test specimens subjected to non-uniform stress distributions, Engineering Fracture Mechanics 69: 1339-1352.
19
[20] Zhao L.G., Chen Y.H.,1996, On the elastic T -term of a main crack induced by near tip microcracks, International Journal of Fracture 82: 363-379.
20
[21] Williams M.L., 1957, On the stress distribution at the base of a stationary crack, Journal of Applied Mechanics 24:109-114.
21
[22] Rice J.R., 1974, Limitations to the small scale yielding approximation for crack tip plasticity, Journal of the Mechanics and Physics of Solids 22:17-26.
22
[23] Suresh S., 1991, Fatigue of Materials, Cambridge University Press.
23
[24] Sladek J., Sladek V., 2000, Evaluation of the elastic T -stress in three-dimensional crack problems using an integral formula, International Journal of Fracture 101: 47-52.
24
[25] Rooke D.P., Cright D.J., 1 976, Compendium of Stress Intensity Factors, Willingon Press.
25
[26] Tada H., Paris P.C., Mn G.R., 1984, The Strew Analysir of Crarks Handbook , Paris Productions.
26
[27] Chen V.Z., 2000, Closed form solutions of T-stress in plate elasticity crack problems, International Journal of Solid Structure 37: 1629-1637.
27
[28] Tan C.L., 1987, The Boundary Element Method: A Short Course, Carleton University, OMawa, Ontdo.
28
[29] Aliabadi M.W., Rooke D.P., 1991, Numerical Fracture Mechanics, Kluwer Aeademic Publishers, Boston.
29
[30] Tan C.L., Wang X., 2003, The use of quarter-point crack tip elements for T-stress determination in boundary element method (BEM) analysis, Engineering Fracture Mechanics 70: 2247-2252.
30
[31] Betegon C., Hancock J.W., 1991, Two-parameter characterization of elastic-plastic crack tip field, Journal of Applied Mechanics 58: 104-110.
31
[32] 0'Dowd N.P., Shih C.F., 1991, Family of crack tip fields characterized by a triaxiality parameter-I : Structure of fields, Journal of the Mechanics and Physics of Solids 24: 989-1015.
32
[33] Wang Y.Y., 1993, On the Two-Parameter Characterization of Elastic-Plastic Crack Front Fields in Surface Cracked Plates, In: Hackett E.M., Schwalbe K.M., Dodds R.H., Editors.
33
[34] Sahli A., Rahmani O., 2009, Stress intensity factor solutions for two-dimensional elastostatic problems by the hypersingular boundary integral equation, Journal of Strain Analysis 44(4): 235-247.
34
[35] Yamada U., Ezawa Y., Nishiguchi I., 1979, Recommendations on singularity or crack tip elements, International Journal of Mechanical Engineering 14: 1525-1544.
35
[36] Blackbum W.S., 1977, The Mathematics of Finite Elements and Applications, Brunel University.
36
[37] Akin J.E., 1976, The generation of elements with singularities, International Journal of Mechanical Engineering 10: 1249-1259.
37
[38] Henshell R.D., Shaw K.G., 1975, Crack-tip finite elements are unnecessary, International Journal of Mechanical Engineering 9: 495-507.
38
[39] Barsoum R.S., 1976, On the use of isoparametric finite elements in linear fracture mechanics, International Journal of Mechanical Engineering 10: 25-37.
39
[40] Buecker H.F., 1989, A novel principle for the computation of stress intensity factor, Zeitschrift für Angewandte Mathematik und Mechanik 50: 129-146.
40
[41] Kfouri A.P., 1986, Some evaluations of the elastic T-stress using Eshelby's method, International Journal of Fracture 20: 301-315.
41
[42] Fett T., 1997, A Green's function for T-stress in an edge cracked rectangular plate, Engineering Fracture Mechanics 57: 365-373.
42
[43] Hooton D.G., Sherry A.H., Sanderson D.J., Ainsworth R.A., 1998, Application of R6 constraint methods using weight function for T-stress, ASME Pressure Vessel Piping Conference 365: 37-43.
43
[44] Andrasic C.P., Parker A.P., 1984, Dimensionless stress intensity factors for cracked thick cylinders under polynomial crack face loadings, Engineering Fracture Mechanics 19: 187-193.
44
[45] Wu X.R., Carlsson A.J., 1991, Weight Functions and Stress Intensity Factor Solutions, Pergamon Press.
45
ORIGINAL_ARTICLE
Experimental and Numerical Free Vibration Analysis of Hybrid Stiffened Fiber Metal Laminated Circular Cylindrical Shell
The modal testing has proven to be an effective and non-destructive test method for estimation of the dynamic stiffness and damping constant. The aim of the present paper is to investigate the modal response of stiffened Fiber Metal Laminated (FML) circular cylindrical shells using experimental and numerical techniques. For this purpose, three types of FML-stiffened shells are fabricated by a specially-designed method and the burning examination is used to determine the mechanical properties of them. Then, modal tests are conducted to investigate the vibration and damping characteristics of the FML-stiffened shells. A 3D finite element model is built using ABAQUS software to predict the modal characteristics of the FML-stiffened circular cylindrical shells with free-free ends. Finally, the achievements from the numerical and experimental analyses are compared with each other and good agreement has been obtained. Modal analyses of the FML-stiffened circular cylindrical shells are investigated for the first time in this paper. Thus, the results obtained from this study are novel and can be used as a benchmark for further studies.
http://jsm.iau-arak.ac.ir/article_664223_4d2474cd47cc4ae85b951c2da6a95a29.pdf
2019-03-30
105
119
10.22034/jsm.2019.664223
Free vibration
FML-stiffened shell
Modal test
Experimental study
A
Nazari
1
Department of Aerospace Engineering, Aerospace Research Institute, Tehran, Iran
AUTHOR
K
Malekzadeh
kmalekzadeh@mut.ac.ir
2
MalekAshtar University, Tehran, Iran
LEAD_AUTHOR
A.A
Naderi
3
Faculty of Mechanical Engineering, Emam Ali University, Tehran, Iran
AUTHOR
[1] Sharma C.B., 1974, Calculation of frequencies of fixed-free circular cylindrical shells, Journal of Sound & Vibration 35: 55-76.
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[2] Mead D.J., Bardell N.S., 1986, Free vibration of a thin cylindrical shell with discrete axial stiffeners, Sound and Vibration 111: 229-250.
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[3] Sharma C.B., Darvizeh M., Darvizeh A., 1996, Free vibration response of multilayered orthotropic fluid-filled circular cylindrical shells, Composite Structures 34: 349-355.
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[4] Wang C.M., Swaddiwudhipong S., Tian J., 1997, Ritz method for vibration analysis of cylindrical shells with ring stiffeners, Sound and Vibration 123: 123-134.
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[5] Gong S.W., Lam K.Y., 2000, Effects of structural damping and stiffness on impact response of layered structures, AIAA Journal 38: 1730-1735.
5
[6] Hosokawa K., Murayama M., Sakata T., 2000, Free vibration analysis of angle-ply laminated circular cylindrical shells with clamped edges, Science and Engineering of Composite Materials 9: 75-82.
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[7] Vogelesang L.B., Volt A., 2000, Development of fiber metal laminates for advanced aerospace structure, Journal of Material Processing Technology 103: 1-5.
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[8] Ruotolo R., 2001, A comparison of some thin shell theories used for the dynamic analysis of stiffened cylinders, Journal of Sound and Vibration 243: 847-860.
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[9] Ganapathi M., Patel B.P., Patel H.G., Pawargi D.S., 2003, Vibration analysis of laminatedvcross-ply cylindrical shells, Journal of Sound and Vibration 262(1): 65-86.
9
[10] Ferreira A.J.M., Roque C.M.C., Jorge R.M.N., 2007, Natural frequencies of FSDT cross-ply composite shells by multiquadrics, Journal of Composite Structure 77(3): 296-305.
10
[11] Alibeigloo A., 2009, Static and vibration analysis of axi-symmetric angle ply laminated cylindrical shell using state space differential quadrature method, International Journal of Pressure Vessels and Piping 86: 738-747.
11
[12] Torkamani S.h., Navazi H.M., Jafari A.A., Bagheri M., 2009, Structural similitude in free vibration of orthogonally stiffened cylindrical shells, Journal of Thin-Walled Structures 47: 1316-1330.
12
[13] Khalili S.M.R., Malekzadeh K., Davar A., Mahajan P., 2010, Dynamic response of pre-stressed Fiber Metal Laminate (FML) circular cylindrical shells subjected to lateral pressure pulse loads, Journal of Composite Structures 92: 1308-1317.
13
[14] Khalili S.M.R., Davar A., Malekzadeh 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.
14
[15] Zhao L., Wu J., 2013, Natural frequency and vibration modal analysis of composite laminated plate, Journal of Advanced Materials Research 711: 396-400.
15
[16] Carrera E., Zappino E., Filippi M., 2013, Free vibration analysis of thin-walled cylinders reinforced with longitudinal and transversal stiffeners, Journal of Vibration and Acoustics 135: 011019.
16
[17] Koruk H., Jason T., Dreyer J.T., Singh R., 2014, Modal analysis of thin cylindrical shells with cardboard liners and estimation of loss factors, Journal of Mechanical Systems and Signal Processing 45: 346-359.
17
[18] Shakouri M., Kouchakzadeh M.A., 2014, Free vibration analysis of joined conical shells: Analytical and experimental study, Thin-Walled Structures 85: 350-358.
18
[19] Attabadi P.B., Khedmati M.R., Attabadi M.B., 2014, Free vibration analysis orthotropic thin cylindrical shells with variable thickness by using spline functions, Latin American Journal of Solids and Structures 11: 2099-2121.
19
[20] Hemmatnezhad M., Rahimi G.H., Tajik M., Pellicano F., 2015, Experimental, numerical and analytical investigation of free vibrational behavior of GFRP-stiffened composite cylindrical shells, Journal of Composite Structures 120: 509-518.
20
[21] Rahimi G.H., Hemmatnezhad M., Ansari R., 2015, Prediction of vibrational behavior of grid-stiffened cylindrical shells, Journal of Advance in Acoustic and Vibration 73: 10-20.
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[22] Biswal M., Sahu S.K., Asha A.V., 2015, Experimental and numerical studies on free vibration of laminated composite shallow shells in hygrothermal environment, Journal of Composite Structures 127: 165-174.
22
[23] Yang J.S., Xiong J., Ma L., NaFeng L.,Yang Wang S., Zhi Wu L., 2016, Modal response of all-composite corrugated sandwich cylindrical shells, Journal of Composites Science and Technology 115: 9-20.
23
[24] Torabi K., Shariati-Nia M., Heidari-Rarani M., 2016, Experimental and theoretical investigation on transverse vibration of delaminated cross-ply composite beams, International Journal of Mechanical Sciences 115: 1-11.
24
[25] Hirwania C.K., Patila R.K., Pandaa S.K., Mahapatraa S.S., Srivastavac L., Buragohainc M.K., 2016, Experimental and numerical analysis of free vibration of delaminated curved panel, Aerospace Science and Technology 54: 353-370.
25
[26] El-Helloty A., 2016, Free vibration analysis of stiffened laminated composite plates, International Journal of Computer Applications 156: 12-23.
26
[27] Minhtu T., Van Loi N., 2016,Vibration analysis of rotating functionally graded cylindrical shells with orthogonal stiffeners, Latin American Journal of Solids and Structures 13: 2952-2962.
27
[28] Garcia C., Wilson J., Trendafilova I., Yang L., 2017, Vibratory behavior of glass fibre reinforced polymer (GFRP) interleaved with Nylon Nanofibers, Journal of Composite Structures 132: 6-18.
28
[29] Qina X.C., Donga C.Y., Wangb F., Gonga Y.P., 2017, Free vibration analysis of isogeometric curvi linearly stiffened shells, Journal of Thin-Walled Structures 116: 124-135.
29
ORIGINAL_ARTICLE
Effect of Thermal Environment on Vibration Analysis of Partially Cracked Thin Isotropic Plate Submerged in Fluid
Based on a non classical plate theory, an analytical model is proposed for the first time to analyze free vibration problem of partially cracked thin isotropic submerged plate in the presence of thermal environment. The governing equation for the cracked plate is derived using the Kirchhoff’s thin plate theory and the modified couple stress theory. The crack terms are formulated using simplified line spring model whereas the effect of thermal environment is introduced using thermal moments and in-plane forces. The influence of fluidic medium is incorporated in governing equation in form fluids forces associated with inertial effects of its surrounding fluids. Applying the Galerkin’s method, the derived governing equation of motion is reformulated into well known Duffing equation. The governing equation for cracked isotropic plate has also been solved to get central deflection which shows an important phenomenon of shift in primary resonance due to crack, temperature rise and internal material length scale parameter. To demonstrate the accuracy of the present model, few comparison studies are carried out with the published literature. The variation in natural frequency of the cracked plate with uniform rise in temperature is studied considering various parameters such as crack length, fluid level and internal material length scale parameter. Furthermore the variation of the natural frequency with plate thickness is also established.
http://jsm.iau-arak.ac.ir/article_664224_ae26c477e230049487273d0578d3f782.pdf
2019-03-30
120
143
10.22034/jsm.2019.664224
temperature
Crack
Vibration
Fluid-plate interaction
Shashank
Soni
shashanksoninitr@gmail.com
1
National Institute of Technology, Raipur, Chhattisgarh 492010, India
LEAD_AUTHOR
N.K
Jain
2
National Institute of Technology, Raipur, Chhattisgarh 492010, India
AUTHOR
P.V
Joshi
3
Indian Institute of Information Technology, Nagpur, Maharashtra, 440006, India
AUTHOR
[1] Murphy K.D., Ferreira D., 2001, Thermal buckling of rectangular plates, International Journal of Solids and Structures 38: 3979-3994.
1
[2] Yang J., Shen H.-S., 2002,Vibration characteristics and transient response of shear-deformable functionally graded plates in thermal environments, Journal of Sound and Vibration 255: 579-602.
2
[3] Jeyaraj P., Padmanabhan C., Ganesan N., 2008, Vibration and acoustic response of an isotropic plate in a thermal environment, Journal of Vibration and Acoustics 130: 51005.
3
[4] Jeyaraj P., Ganesan N., Padmanabhan C., 2009,Vibration and acoustic response of a composite plate with inherent material damping in a thermal environment, Journal of Sound and Vibration 320: 322-338.
4
[5] Li Q., Iu V.P., Kou K.P., 2009, Three-dimensional vibration analysis of functionally graded material plates in thermal environment, Journal of Sound and Vibration 324: 733-750.
5
[6] Kim Y.-W., 2005,Temperature dependent vibration analysis of functionally graded rectangular plates, Journal of Sound and Vibration 284: 531-549.
6
[7] Natarajan S., Chakraborty S., Ganapathi M. Subramanian M., 2014, A parametric study on the buckling of functionally graded material plates with internal discontinuities using the partition of unity method, European Journal of Mechanics - A/Solids 44: 136-147.
7
[8] Viola E., Tornabene F., Fantuzzi N., 2013, Generalized differential quadrature finite element method for cracked composite structures of arbitrary shape, Composite structures 106: 815-834.
8
[9] Rice J., Levy N., 1972, The part-through surface crack in an elastic plate, Journal of Applied Mechanics 39: 185-194.
9
[10] Delale F., Erdogan F., 1981, Line-spring model for surface cracks in a reissner plate, International Journal of Engineering Science 19: 1331-1340.
10
[11] Israr A., Cartmell M.P., Manoach E., Trendafilova I., Ostachowicz W., Krawczuk M., Zak A., 2009, Analytical modelling and vibration analysis of cracked rectangular plates with different loading and boundary conditions, Journal of Applied Mechanics 76: 1-9.
11
[12] Ismail R., Cartmell M.P., 2012, An investigation into the vibration analysis of a plate with a surface crack of variable angular orientation, Journal of Sound and Vibration 331: 2929-2948.
12
[13] Joshi P.V., Jain N.K., Ramtekkar G.D., 2014, Analytical modeling and vibration analysis of internally cracked rectangular plates, Journal of Sound and Vibration 333: 5851-5864.
13
[14] Joshi P. V., Jain N.K., Ramtekkar G.D., 2015, Effect of thermal environment on free vibration of cracked rectangular plate: An analytical approach, Thin–Walled Structures 91: 38-49.
14
[15] Joshi P. V., Jain N.K., Ramtekkar G.D., Virdi G.S., 2016, Crossmark, Thin–Walled Structures 109:143-158.
15
[16] Soni S., Jain N.K., Joshi P. V., 2018, Vibration analysis of partially cracked plate submerged in fl uid, Journal of Sound and Vibration 412: 28-57.
16
[17] Soni S., Jain N.K., Joshi P.V., 2017, Analytical modeling for nonlinear vibration analysis of partially cracked thin magneto-electro-elastic plate coupled with fluid, Nonlinear Dynamics 90: 137-170.
17
[18] Tsiatas G.C., 2009, A new Kirchhoff plate model based on a modified couple stress theory, International Journal of Solids and Structures 46: 2757-2764.
18
[19] Altan S.B., Aifantis E.C., 1992, On the structure of the mode III crack-tip in gradient elasticity, Scripta Materialia 26: 319-324.
19
[20] Park S.K., Gao X.-L., 2006, Bernoulli–Euler beam model based on a modified couple stress theory, Journal of Micromechanics Microengineering 16: 2355-2359.
20
[21] Mousavi S.M., Paavola J., 2014, Analysis of plate in second strain gradient elasticity, Archive of Applied Mechanics 84: 1135-1143.
21
[22] Yin L., Qian Q., Wang L., Xia W., 2010,Vibration analysis of microscale plates based on modified couple stress theory, Acta Mechanica Solida Sinica 23: 386-393.
22
[23] Papargyri-Beskou S., Beskos D.E., 2007, Static, stability and dynamic analysis of gradient elastic flexural Kirchhoff plates, Archive of Applied Mechanics 78: 625-635.
23
[24] Yang F., Chong C.M., Lam D.C.C., Tong P., 2002, Couple stress based strain gradient theory for elasticity, International Journal of Engineering Science 39: 2731-2743.
24
[25] Chen W., Xu M., Li L., 2012, A model of composite laminated Reddy plate based on new modified couple stress theory, Composite structures 94: 2143-2156.
25
[26] Gao X.L., Zhang G.Y., 2016, A non-classical Kirchhoff plate model incorporating microstructure, surface energy and foundation effects, Continuum Mechanics and Thermodynamics 28: 195-213.
26
[27] Gupta A., Jain N.K., Salhotra R., Joshi P.V., 2015, Effect of microstructure on vibration characteristics of partially cracked rectangular plates based on a modified couple stress theory, International Journal of Mechanical Sciences 100: 269-282.
27
[28] Gupta A., Jain N.K., Salhotra R., Rawani A.M., Joshi P.V., 2015, Effect of fibre orientation on non-linear vibration of partially cracked thin rectangular orthotropic micro plate: An analytical approach, International Journal of Mechanical Sciences 105: 378-397.
28
[29] Lamb H., 2016, On the vibrations of an elastic plate in contact with water author ( s ), Proceedings of the Royal Society of London Series A 98: 205-216.
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[31] Muthuveerappan G., Ganesan N., Veluswami M.A., 1979, A note on vibration of a cantilever plate immersed, Journal of Sound and Vibration 63(3): 385-391.
31
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32
[33] Fu Y., Price W.G., 1987, Interactions between a partially or totally immersed vibrating cantilever plate and the surrounding fluid, Journal of Sound and Vibration 118: 495-513.
33
[34] Kwak M.K., Kim K.C., 1991, Axisymmetric vibration of circular plates in contact with fluid, Journal of Sound and Vibration 146: 381-389.
34
[35] Amabili M., Frosali G., Kwak M.K., 1996, Free vibrations of annular plates coupled with fluids, Journal of Sound and Vibration 191: 825-846.
35
[36] Haddara M.R., Cao S., 1996, A study of the dynamic response of submerged rectangular flat plates, Marine Structures 9: 913-933.
36
[37] Soedel S.M., Soedel W., 1994, On the free and forced vibration of a plate supporting a free Sloshing surface liquid, Journal of Sound and Vibration 171(2): 159-171.
37
[38] Kerboua Y., Lakis A.A., Thomas M., Marcouiller L., 2008,Vibration analysis of rectangular plates coupled with fluid, Applied Mathematical Modelling 32: 2570-2586.
38
[39] Hosseini-Hashemi S., Karimi M., Rokni H., 2012, Natural frequencies of rectangular Mindlin plates coupled with stationary fluid, Applied Mathematical Modelling 36: 764-778.
39
[40] Liu T., Wang K., Dong Q.W., Liu M.S., 2009, Hydroelastic natural vibrations of perforated plates with cracks, Procedia Engineering 1: 129-133.
40
[41] Si X.H., Lu W.X., Chu F.L., 2012, Modal analysis of circular plates with radial side cracks and in contact with water on one side based on the Rayleigh – Ritz method, Journal of Sound and Vibration 331: 231-251.
41
[42] Si X., Lu W., Chu F., 2012, Dynamic analysis of rectangular plates with a single side crack and in contact with water on one side based on the Rayleigh – Ritz method, Journal of Fluids and Structures 34: 90-104.
42
[43] Jones R.M., 2006, Buckling of Bars, Plates, and Shells, Bull Ridge Corporation.
43
ORIGINAL_ARTICLE
Free Vibration Analysis of Functionally Graded Piezoelectric Material Beam by a Modified Mesh Free Method
A mesh-free method based on moving least squares approximation (MLS) and weak form of governing equations including two dimensional equations of motion and Maxwell’s equation is used to analyze the free vibration of functionally graded piezoelectric material (FGPM) beams. Material properties in beam are determined using a power law distribution. Essential boundary conditions are imposed by the transformation method. The mesh-free method is verified by comparison with a finite element method (FEM) which performed for FGPM beams. Comparisons showed that this model has a good accuracy. After validation of the presented model, a parametric study was carried out to investigate the effect of mechanical and electrical boundary conditions, slenderness ratio and distribution of constituent materials on natural frequencies of FGPM beams. It is concluded that slenderness ratio has more significant effect on lower frequencies. On the other hand higher frequencies are affected by the volume fraction power index much more than lower frequencies.
http://jsm.iau-arak.ac.ir/article_664225_f7ff55f5c6c68e516a641ac40d5b8ff5.pdf
2019-03-30
144
154
10.22034/jsm.2019.664225
Mesh-free method
Functionally graded piezoelectric beam
Free vibration
MLS shape function
M
Foroutan
foroutan@razi.ac.ir
1
Department of Mechanical Engineering, Razi University, Kermanshah, Iran
LEAD_AUTHOR
Sh
Sharafi
2
Department of Mechanical Engineering, Razi University, Kermanshah, Iran
AUTHOR
S
Mohammadi
3
Department of Mechanical Engineering, Razi University, Kermanshah, Iran
AUTHOR
[1] Sharma P., Parashar S.K., 2016, Free vibration analysis of shear-induced flexural vibration of FGPM annular plate using Generalized Differential Quadrature method, Composite Structures 155: 213-222.
1
[2] Kruusing A., 2000, Analysis and optimization of loaded cantilever beam microactuators, Smart Materials and Structures 9(2): 186.
2
[3] Hauke T., 2000, Bending behavior of functionally gradient materials, Ferroelectrics 238(1): 195-202.
3
[4] Huang D., Ding H., Chen W., 2010, Static analysis of anisotropic functionally graded magneto-electro-elastic beams subjected to arbitrary loading, European Journal of Mechanics-A/Solids 29(3): 356-369.
4
[5] Li Y., Feng W., Cai Z., 2014, Bending and free vibration of functionally graded piezoelectric beam based on modified strain gradient theory, Composite Structures 115: 41-50.
5
[6] Wu C.-P., Syu Y.-S., 2007, Exact solutions of functionally graded piezoelectric shells under cylindrical bending, International Journal of Solids and Structures 44(20): 6450-6472.
6
[7] Li X.-F., Peng X.-L., Lee K.Y., 2010, The static response of functionally graded radially polarized piezoelectric spherical shells as sensors and actuators, Smart Materials and Structures 19(3): 035010.
7
[8] Hsu M.-H., 2005, Electromechanical analysis of piezoelectric laminated composite beams, Journal of Marine Science and Technology 13(2): 148-155.
8
[9] Razavi H., Babadi A.F., Beni Y.T., 2017, Free vibration analysis of functionally graded piezoelectric cylindrical nanoshell based on consistent couple stress theory, Composite Structures 160: 1299-1309.
9
[10] Zhang T., Shi Z., Spencer Jr B., 2008, Vibration analysis of a functionally graded piezoelectric cylindrical actuator, Smart Materials and Structures 17(2): 025018.
10
[11] Xiang H., Shi Z., 2009, Static analysis for functionally graded piezoelectric actuators or sensors under a combined electro-thermal load, European Journal of Mechanics-A/Solids 28(2): 338-346.
11
[12] Doroushi A., Eslami M., Komeili A., 2011, Vibration analysis and transient response of an FGPM beam under thermo-electro-mechanical loads using higher-order shear deformation theory, Journal of Intelligent Material Systems and Structures 22(3): 231-243.
12
[13] Behjat B., Khoshravan M., 2012, Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates, Composite Structures 94(3): 874-882.
13
[14] Sedighi M., Shakeri M., 2009, A three-dimensional elasticity solution of functionally graded piezoelectric cylindrical panels, Smart Materials and Structures 18(5): 055015.
14
[15] Behjat B., 2009, Static, dynamic, and free vibration analysis of functionally graded piezoelectric panels using finite element method, Journal of Intelligent Material Systems and Structures 20(13): 1635-1646.
15
[16] Babaei M., Chen Z., 2009, The transient coupled thermo-piezoelectric response of a functionally graded piezoelectric hollow cylinder to dynamic loadings, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences.
16
[17] Liu G., Gu Y., 2005, An Introduction to Meshfree Methods and Their Programming, Springer, Dordrecht, Netherlands.
17
[18] Nayroles B., Touzot G., Villon P., 1992, Generalizing the finite element method: diffuse approximation and diffuse elements, Computational Mechanics 10(5): 307-318.
18
[19] Chuaqui T., Roque C., 2017, Analysis of functionally graded piezoelectric timoshenko smart beams using a multiquadric radial basis function method, Composite Structures 176: 640-653.
19
[20] Safaei B., Moradi-Dastjerdi R., Chu F., 2018, Effect of thermal gradient load on thermo-elastic vibrational behavior of sandwich plates reinforced by carbon nanotube agglomerations, Composite Structures 192: 28-37.
20
[21] Moradi-Dastjerdi R., Pourasghar A., 20216, Dynamic analysis of functionally graded nanocomposite cylinders reinforced by wavy carbon nanotube under an impact load, Journal of Vibration and Control 22(4): 1075-1062.
21
[22] Moradi-Dastjerdi R., Payganeh G., 2017, Thermoelastic dynamic analysis of wavy carbon nanotube reinforced cylinders under thermal loads, Steel and Composite Structures 25(3): 315-326.
22
[23] Reddy J., Chin C., 1998, Thermomechanical analysis of functionally graded cylinders and plates, Journal of Thermal Stresses 21(6): 593-626.
23
ORIGINAL_ARTICLE
Effect of Micropolarity on the Propagation of Shear Waves in a Piezoelectric Layered Structure
This paper studies the propagation of shear waves in a composite structure consisting of a piezoelectric layer perfectly bonded over a micropolar elastic half space. The general dispersion equations for the existence of shear waves are obtained analytically in the closed form. Some particular cases have been discussed and in one special case the relation obtained is in agreement with existing results of the classical –Love wave equation. The micropolar and piezoelectric effects on the phase velocity are obtained for electrically open and mechanically free structure. To illustrate the utility of the problem numerical computations are carried out by considering PZT-4 as a piezoelectric and aluminium epoxy as micropolar elastic material. It is observed that the micropolarity present in the half space influence the phase velocity significantly in a particular region. The micropolar effects on the phase velocity in the piezoelectric coupled structure can be used to design high performance acoustic wave devices.
http://jsm.iau-arak.ac.ir/article_664226_28a0be85fcc2c62de7ff4ce5041339f9.pdf
2019-03-30
155
165
10.22034/jsm.2019.664226
Shear wave
Micropolar
Piezoelectric
Dispersion
Phase velocity
R
Kumar
rajneesh_kuk@rediffmail.com
1
Department of Mathematics, Kurukshetra University, Kurukshetra 136119, India
AUTHOR
K
Singh
kbgill1@gmail.com
2
Department of Mathematics, Lovely Professional University, Phagwara(Research Scholar Punjab Technical University, Jalandhar), India
LEAD_AUTHOR
D.S
Pathania
3
Department of Mathematics, Guru Nanak Dev Engineering College, Ludhiana, India
AUTHOR
[1] Bleustein J.L., 1968, A new surface wave in piezoelectric materials, Applied Physics Letter 13(12): 412-413.
1
[2] Mindlin R.D., 1952, Forced thickness-shear and flexural vibrations of piezoelectric, Journal of Applied Physics 23: 83-88.
2
[3] Tiersten H. F., 1963, Thickness vibrations of piezoelectric plates, The Journal of the Acoustical Society of America 35: 53-58.
3
[4] Curtis R.G., Redwood M., 1973, Transverse surface waves on a piezoelectric material carrying a metal layer of finite thickness, Journal of Applied Physics 44: 2002-2007.
4
[5] Wang Q., Quek S.T., Varadan V.K., 2001, Love waves in piezoelectric coupled solid media, Smart Materials and Structures 10: 380-388.
5
[6] Qian Z.-H., Jin F., Wang Z., Kishimoto K., 2004, Dispersion relations for SH-wave propagation in periodic piezoelectric composite, International Journal of Engineering Science 42(7): 673-689.
6
[7] Qian Z.-H., Jin F., Wang Z., Kishimoto K., 2004, Love waves propagation in a piezoelectric layered structure with initial stresses, Acta Mechanica 171(1-2): 41-57.
7
[8] Qian Z.-H., Jin F., Hirose S., 2011, Dispersion characteristics of transverse surface waves in piezoelectric coupled solid media with hard metal interlayer, Ultrasonics 51: 853-856.
8
[9] Liu J., Wang Z.K., 2005, The propagation behavior of Love waves in a functionally graded layered piezoelectric structure, Smart Materials and Structures 14(1): 137-146.
9
[10] Liu J., Cao X.S., Wang Z.K., 2008, Love waves in a smart functionally graded piezoelectric composite structure, Acta Mechanica 208(1-2): 63-80.
10
[11] Son M.S., Kang Y.J., 2011, The effect of initial stress on the propagation behavior of SH waves in piezoelectric coupled plates, Ultrasonics 51: 489-495.
11
[12] Saroj P.K., Sahu S.A., 2017, Reflection of plane wave at traction-free surface of a pre-stressed functionally graded piezoelectric material (FGPM) half-space, Journal of Solid Mechanics 9(2): 411-422.
12
[13] Arefi M., 2016, Surface effect and non-local elasticity in wave propagation of functionally graded piezoelectric nano-rod excited to applied voltage, Applied Mathematics and Mechanics 37: 289-302.
13
[14] Arefi M., 2016, Analysis of wave in a functionally graded magneto-electroelastic nano-rod using nonlocal elasticity model subjected to electric and magnetic potentials, Acta Mechanica 227(9): 2529-2542.
14
[15] Arefi M., Zenkour A.M., 2016, Free vibration, wave propagation and tension analyses of a sandwich micro/nano rod subjected to electric potential using strain gradient theory, Material Research Express 3(11):115704.
15
[16] Arefi M., Zenkour A.M., 2017, Nonlocal electro-thermo-mechanical analysis of a sandwich nanoplate containing a Kelvin–Voigt viscoelastic nanoplate and two piezoelectric layers, Acta Mechanica 228(2): 475-494.
16
[17] Arefi M., Zenkour A.M., 2017, Size-dependent free vibration and dynamic analyses of piezo-electromagnetic sandwich nanoplates resting on viscoelastic foundation, Physica B 521: 188-197.
17
[18] Arefi M., Zenkour A.M., 2017, Vibration and bending analysis of a sandwich microbeam with two integrated piezo-magnetic face-sheets, Composite Structures 159: 479-490.
18
[19] Arefi M., Zenkour A.M., 2017, Influence of micro-length-scale parameters and inhomogeneities on the bending, free vibration and wave propagation analyses of a FG Timoshenko’s sandwich piezoelectric microbeam, Journal of Sandwich Structures & Materials (in press).
19
[20] Arefi M., Zenkour A.M., 2017 ,Wave propagation analysis of a functionally graded magneto-electro-elastic nanobeam rest on Visco-Pasternak foundation, Mechanics Research Communications 79: 51-62.
20
[21] Voigt W., 1887, Theoretische Studien über die Elastizitätsverhältnisse der Krystalle, Abhandlungen der Königlichen Gesellschaft der Wissenschaften in Göttingen, German.
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[22] Eringen A.C., Suhubi E.S., 1964, Nonlinear theory of simple micro-elastic solid-I, International Journal of Engineering Science 2: 189-203.
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[23] Eringen A.C., 1966, Linear theory of Micropolar elasticity, Journal of Mathematics and Mechanics 15: 909-923.
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[24] Eringen A.C., 1999, Microcontinuum Field Theories-I, New York, Springer-Verlag.
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[25] Singh B., Kumar R., 1998, Reflection and refraction of plane waves at an interface between micropolar elastic solid and viscoelastic solid, International Journal of Engineering Science 36(2): 119-135.
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[26] Tomer S., 2005, Wave propagation in a micropolar elastic plate with voids, Journal of Vibration and Control 11: 849-863.
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28
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29
[30] KaurT., Sharma S.K., Singh A.K., 2017, Shear wave propagation in vertically heterogeneous viscoelastic layer over a micropolar elastic half-space, Mechanics of Advanced Materials and Structures 24(2): 149-156.
30
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31
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34
[35] Gauthier R.D., 1982, Experimental Investigation on Micropolar Media, Mechanics of Micropolar Media, World Scientific, Singapore.
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36
ORIGINAL_ARTICLE
On Static Bending, Elastic Buckling and Free Vibration Analysis of Symmetric Functionally Graded Sandwich Beams
This article presents Navier type closed-form solutions for static bending, elastic buckling and free vibration analysis of symmetric functionally graded (FG) sandwich beams using a hyperbolic shear deformation theory. The beam has FG skins and isotropic core. Material properties of FG skins are varied through the thickness according to the power law distribution. The present theory accounts for a hyperbolic distribution of axial displacement whereas transverse displacement is constant through the thickness i.e effects of thickness stretching are neglected. The present theory gives hyperbolic cosine distribution of transverse shear stress through the thickness of the beam and satisfies zero traction boundary conditions on the top and bottom surfaces of the beam. The equations of the motion are obtained by using the Hamilton’s principle. Closed-form solutions for static, buckling and vibration analysis of simply supported FG sandwich beams are obtained using Navier’s solution technique. The non-dimensional numerical results are obtained for various power law index and skin-core-skin thickness ratios. The present results are compared with previously published results and found in excellent agreement.
http://jsm.iau-arak.ac.ir/article_664227_008bb7e3e1a8208dd0730276194d4920.pdf
2019-03-30
166
180
10.22034/jsm.2019.664227
Hyperbolic shear deformation theory
FG sandwich beam
Static bending
Elastic buckling
Free vibration
A.S
Sayyad
attu_sayyad@yahoo.co.in
1
Department of Civil Engineering, SRES’s Sanjivani College of Engineering, Savitribai Phule Pune University, Kopargaon-423601, Maharashtra, India
LEAD_AUTHOR
P.V
Avhad
2
Department of Civil Engineering, SRES’s Sanjivani College of Engineering, Savitribai Phule Pune University, Kopargaon-423601, Maharashtra, India
AUTHOR
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[18] Sayyad A. S., Ghugal Y. M., 2017, Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature, Composite Structures 171: 486-504.
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[19] Sayyad A. S., Ghugal Y. M., 2018, Modeling and analysis of functionally graded sandwich beams: A review, Mechanics of Advanced Materials and Structures 0(0): 1-20.
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[20] Nguyen T. K., Vo T. P., Nguyen B. D., Lee J., 2016, An analytical solution for buckling and vibration analysis of functionally graded sandwich beams using a quasi-3D shear deformation theory, Composite Structures 156: 238-252.
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[24] Osofero A. I., Vo T. P., Thai H. T., 2014, Bending behaviour of functionally graded sandwich beams using a quasi-3D hyperbolic shear deformation theory, Journal of Engineering Research 19(1): 1-16.
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[25] Osofero A. I., Vo T. P., Nguyen T. K., Lee J., 2016, Analytical solution for vibration and buckling of functionally graded sandwich beams using various quasi-3D theories, Journal of Sandwich Structures and Materials 18(1): 3-29.
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[26] Bennai R., Atmane H. A., Tounsi A., 2015, A new higher-order shear and normal deformation theory for functionally graded sandwich beams, Steel and Composite Structures 19(3): 521-546.
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[29] Giunta G., Crisafulli D., Belouettar S., Carrera E., 2013, A thermomechanical analysis of functionally graded beams via hierarchical modelling, Composite Structures 95: 676-690.
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[30] Vo T. P., Thai H. T., Nguyen T. K., Inam F., Lee J., 2015, Static behaviour of functionally graded sandwich beams using a quasi-3D theory, Composites Part B 68: 59-74.
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[31] Vo T. P., Thai H. T., Nguyen T. K., Inam F., Lee J., 2015, A quasi-3D theory for vibration and buckling of functionally graded sandwich beams, Composite Structures 119: 1-12.
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[33] Yarasca J., Mantari J. L., Arciniega R. A., 2016, Hermite–Lagrangian finite element formulation to study functionally graded sandwich beams, Composite Structures 140: 567-581.
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[35] Tossapanon P., Wattanasakulpong N., 2016, Stability and free vibration of functionally graded sandwich beams resting on two-parameter elastic foundation, Composite Structures 142: 215-225.
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[36] Karamanli A., 2017, Bending behaviour of two directional functionally graded sandwich beams by using a quasi-3D shear deformation theory, Composite Structures 174: 70-86.
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[37] Mashat D. S., Carrera E., Zenkour A. M., Al Khateeb S. A., Filippi M., 2014, Free vibration of FGM layered beams by various theories and finite elements, Composites Part B 59: 269-278.
37
[38] Trinh L. C., Vo T. P., Osofero A. I., Lee J., 2016, Fundamental frequency analysis of functionally graded sandwich beams based on the state space approach, Composite Structures 156: 263-275.
38
[39] Wattanasakulpong N., Prusty B. G., Kelly D. W., Hoffman M., 2012, Free vibration analysis of layered functionally graded beams with experimental validation, Materials and Design 36: 182-190.
39
[40] Yang Y., Lam C. C., Kou K. P., Iu V. P., 2014, Free vibration analysis of the functionally graded sandwich beams by a meshfree boundary-domain integral equation method, Composite Structures 117: 32-39.
40
[41] Sayyad A. S., Ghugal Y. M., 2017, A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates, International Journal of Applied Mechanics 9: 1-36.
41
[42] Sayyad A. S., Ghugal Y. M., 2018, Analytical solutions for bending, buckling, and vibration analyses of exponential functionally graded higher order beams, Asian Journal of Civil Engineering 19(5): 607-623.
42
[43] Alipour M. M., Shariyat M., 2013, Analytical zigzag-elasticity transient and forced dynamic stress and displacement response prediction of the annular FGM sandwich plates, Composite Structures 106: 426-445.
43
[44] Alipour M. M., Shariyat M., 2014, An analytical global–local Taylor transformation-based vibration solution for annular FGM sandwich plates supported by nonuniform elastic foundations, Archives of Civil and Mechanical Engineering 14(1): 6-24.
44
[45] Alipour M. M., Shariyat M., 2014, Analytical stress analysis of annular FGM sandwich plates with non-uniform shear and normal tractions, employing a zigzag-elasticity plate theory, Aerospace Science and Technology 32(1): 235-259.
45
[46] Shariyat M., Hosseini S. H., 2015, Accurate eccentric impact analysis of the preloaded SMA composite plates, based on a novel mixed-order hyperbolic global–local theory, Composite Structures 124: 140-151.
46
[47] Shariyat M., Mozaffari A., Pachenari M. H., 2017, Damping sources interactions in impact of viscoelastic composite plates with damping treated SMA wires, using a hyperbolic plate theory, Applied Mathematical Modelling 43: 421-440.
47
[48] Soldatos K. P., 1992, A transverse shear deformation theory for homogeneous monoclinic plates, Acta Mechanica 94: 195-200.
48
[49] Wakashima K., Hirano T., Niino M., 1990, Space applications of advanced structural materials, Proceedings of an International Symposium (ESA SP).
49
ORIGINAL_ARTICLE
Study of the Effect of an Open Transverse Crack on the Vibratory Behavior of Rotors Using the h-p Version of the Finite Element Method
In this paper, we use the hybrid h-p version of the finite element method to study the effect of an open transverse crack on the vibratory behavior of rotors, the one-dimensional finite element Euler-Bernoulli beam is used for modeling the rotor, the shape functions used are the Hermite cubic functions coupled to the special Legendre polynomials of Rodrigues. The global matrices of the equation of motion of the cracked rotor are derived by the application of the Lagrange equation taking into account the local variation in the shaft’s stiffness due to the presence of the crack, and the stiffness of the cracked element of the shaft are determined using the time-varying stiffness method. Numerical results generated by a program developed in MATLAB show the rapidity of the convergence of the h-p version of FEM compared to the classical version, after the validation of our results with theoretical and experimental results and other obtained with the simulator ANSYS Workbench, a parametric study was provided to show the influence of the depth and position of the crack on the vibratory behavior of a symmetrical and asymmetrical rotor.
http://jsm.iau-arak.ac.ir/article_664228_6a267353940b8cec5e04fcfe0b4b68bd.pdf
2019-03-30
181
200
10.22034/jsm.2019.664228
Rotor
Open transverse crack
h-p version of FEM
Time-varying stiffness
F
Ahmed
fellah-gim@hotmail.fr
1
IS2M Laboratory, Faculty of Technology, University of Tlemcen, Algeria
LEAD_AUTHOR
H
Abdelhamid
2
IS2M Laboratory, Faculty of Technology, University of Tlemcen, Algeria
AUTHOR
B
Brahim
3
IS2M Laboratory, Faculty of Technology, University of Tlemcen, Algeria
AUTHOR
S
Ahmed
4
IS2M Laboratory, Faculty of Technology, University of Tlemcen, Algeria
AUTHOR
[1] Gallagher R.H., 1975, Finite Element Analysis: Fundamentals, Prentice Hall Civil Engineering and Engineering Mechanics, Pearson College Div.
1
[2] Zienkiewicz C., 1977, The Finite Element Method, McGraw-Hill.
2
[3] Szabo B.A., 1979, Some recent developments in the finite element analysis, Computers & Mathematics Applications, 5(2): 99-115.
3
[4] Babuška I., Szabo B.A., Katz I.N., 1981, The p-version of the finite element method, SIAM Journal on Numerical Analysis 18(3): 515-545.
4
[5] Meirovitch L., Bahuh H., 1983, On the inclusion principle for the hierarchical finite element method, International Journal for Numerical Methods in Engineering 19: 281-291.
5
[6] Gui W., Babuška I., 1986, The h, p and h-p versions of the finite element method in 1 dimension, part I, The error analysis of the p-version, Numerische Mathematik 49(6): 577-612.
6
[7] Babuška I., Suri M., 1987, The h-p version of the finite element method with quasi uniform meshes, Mathematical Modeling and Numerical Analysis 21(2): 199-238.
7
[8] Babuška I., Guo B.Q., 1992, The h, p and h-p version of the finite element method: Basis theory and applications, Advances in Engineering Software 15 (3-5): 159-174.
8
[9] Boukhalfa A., Hadjoui A., 2010, Free vibration analysis of an embarked rotating composite shaft using the h-p version of the FEM, Latin American Journal of Solids and Structures 7(2): 105-141.
9
[10] Saimi A., Hadjoui A., 2016, An engineering application of the h-p version of the finite elements method to the dynamics analysis of a symmetrical on-board rotor, European Journal of Computational Mechanics 25(5): 1779-7179.
10
[11] Wauer J., 1990, Dynamics of cracked rotors: literature survey, Applied Mechanics Reviews 43(1): 13-17.
11
[12] Dimarogonas A.D., 1996, Vibration of cracked structures: a state of the art review, Engineering Fracture Mechanics 55(5): 831-857.
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[13] Sabnavis G., Kirk R.G., Kasarda M., Quinn D.D., 2004, Cracked shaft detection and diagnostics: a literature review, The Shock and Vibration Digest 36(4): 287-296.
13
[14] Gasch R., 1993, A survey of the dynamic behavior of a simple rotating shaft with a transverse crack, Journal of Sound and Vibration 160: 313-332.
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[15] Edwards S., Lees A. W., Friswell M. I., 1998, Fault diagnosis of rotating machinery, The Shock and Vibration Digest 30: 4-13.
15
[16] Davies W. G. R., Mayes I. W., 1984, The vibration behavior of a multi-shaft, multi-bearing system in the presence of a propagating transverse crack, Journal of Vibration, Acoustics, Stress, and Reliability in Design 106: 146-153.
16
[17] Chasalevris A.C., Papadopoulos C.A., 2008, Coupled horizontal and vertical vibrations of a stationary shaft with two cracks, Journal of Sound and Vibration 309: 507-528.
17
[18] Mazanoglu K., Yesilyurt I., Sabuncu M., 2009, Vibration analysis of multiple-cracked non-uniform beams, Journal of Sound and Vibration 320(4–5): 977-989.
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[19] Darpe A.K., Gupta K., Chawla A., 2004, Transient response and breathing behaviour of a cracked Jeffcott rotor, Journal of Sound and Vibration 272: 207-243.
19
[20] Petal T.H., Darpe A.K., 2008, Inﬂuence of crack breathing model on nonlinear dynamics of a cracked rotor, Journal of Sound and Vibration 311: 953-972.
20
[21] AL-Shudeifat M.A., Eric A., Butcher Carl R.S., 2010, General harmonic balance solution of a cracked rotor-bearing-disk system for harmonic and sub-harmonic analysis: Analytical and experimental approach, International Journal of Engineering Science 48: 921-935.
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[22] Huang S.C., Huang Y.M., Shiah S.M., 1993, Vibration and stability of a rotating shaft containing a transverse crack, Journal of Sound Vibration 162: 387-401.
22
[23] Sinou J-J., 2007, Effects of a crack on the stability of a non-linear rotor system, International Journal of Non-Linear Mechanics 42(7): 959-972.
23
[24] Guo C., AL-Shudeifat M.A., Yan J., Bergman L.A., McFarland D.M., Butcher E.A., 2013, Stability analysis for transverse breathing cracks in rotor systems, European Journal of Mechanics and Solids 42: 27-34.
24
[25] AL-Shudeifat M.A., 2015, Stability analysis and backward whirl investigation of cracked rotors with time-varying stiffness, Journal of Sound and Vibration 348: 365-380.
25
[26] Dimarogonas A.D., Papadopoulos C.A., 1983, Vibration of cracked shafts in bending, Journal of Sound and Vibration 91(4): 583-593.
26
[27] Silani M., Ziaei-Rad S., Talebi H., 2013, Vibration analysis of rotating systems with open and breathing cracks, Applied Mathematical Modeling 37(24): 9907-9921.
27
[28] AL-Shudeifat M.A., 2013, On the finite element modeling of an asymmetric cracked rotor, Journal of Sound and Vibration 332(11): 2795-2807.
28
[29] Qinkai H., Fulei C., 2013, Dynamic response of cracked rotor-bearing system under time-dependent base movements, Journal of Sound and Vibration 332(25): 6847-6870.
29
[30] Sinou J-J., Lees A.W., 2005,The influence of cracks in rotating shafts, Journal of Sound and Vibration 285(4-5): 1015-1037.
30
[31] AL-Shudeifat M.A., Butcher E.A., 2011, New breathing functions for the transverse breathing crack of the cracked rotor system: approach for critical and subcritical harmonic analysis, Journal of Sound and Vibration 330(3): 526-544.
31
[32] Guo C., AL-Shudeifat M.A., Yan J., Bergman L.A., McFarland D.M., Butcher E.A., 2013, Stability analysis for transverse breathing cracks in rotor systems, European Journal of Mechanics and Solids 42: 27-34.
32
[33] Pilkey W.D., 2002, Analysis and Design of Elastic Beams, John Wiley and Sons, New York.
33
[34] Bardell N.S., 1996, An engineering application of the h-p version of the finite element method to the static analysis of a Euler-bernoulli beam, Computers & Structures 59(2): 195-211.
34
ORIGINAL_ARTICLE
Influence of the Imperfect Interface on Love-Type Mechanical Wave in a FGPM Layer
In this study, we consider the propagation of the Love-type wave in piezoelectric gradient covering layer on an elastic half-space having an imperfect interface between them. Dispersion relation has been obtained in the form of determinant for both electrically open and short cases. The effects of different material gradient coefficients of functionally graded piezoelectric material (FGPM) and imperfect boundary on the phase velocity of Love-type waves are discussed. Also, the influence of mechanically and electrically imperfect interface on the surface wave phase velocity is obtained and shown graphically. The dispersion curves are plotted and the effects of material properties of both FGPM and orthotropic material are studied. Moreover, dispersion relation of the considered microstructure depends substantially on the material gradient coefficients and width of the guiding plate. Numerical results are highlighted graphically and are validated with existing literature. The present study is the prior attempt to show the interfacial imperfection influence with the considered structure on wave phase velocity. The outcomes are widely applicable and useful for the development and characterization of Love-type mechanical waves in FGPM-layered media, SAW devices and other piezoelectric devices.
http://jsm.iau-arak.ac.ir/article_664229_3388e38bf7dda6770544755eb14f871e.pdf
2019-03-30
201
209
10.22034/jsm.2019.664229
FGPM
Love-type mechanical wave
Imperfect
Dispersion relation
Analytical analysis
S
Chaudhary
drsoniyac@mits.ac.in
1
Madanapalle Institute of Technology and Science, Madanapalle, Andhra Pradesh, India
LEAD_AUTHOR
A
Singhal
2
Madanapalle Institute of Technology and Science, Madanapalle, Andhra Pradesh, India--- Indian Institute of Technology (ISM) Dhanbad, Jharkhand, India
AUTHOR
S.A
Sahu
3
Indian Institute of Technology (ISM) Dhanbad, Jharkhand, India
AUTHOR
[1] Love A.E.H., 1911, Some Problems of Geodynamics, Cambridge University Press.
1
[2] Du J., Jin X., Wang J., Xian K., 2007, Love wave propagation in functionally graded piezoelectric material layer, Ultrasonics 46: 13-22.
2
[3] Qian Z., Jin F., Wang Z., Kishimoto K., 2007, Transverse surface waves on a piezoelectric material carrying a functionally graded layer of finite thickness, International Journal of Engineering Science 45: 455-466.
3
[4] Eskandari M., Shodja H.M., 2008, Love waves propagation in functionally graded piezoelectric materials with quadratic variation, Journal of Sound and Vibration 313: 195-204.
4
[5] Cao X.S., Jin F., Jeon I., Lu T.J., 2009, Propagation of love waves in a functionally graded piezoelectric material (FGPM) layered composite system, International Journal of Solids and Structures 46: 4123-4132.
5
[6] Singhal A., Sahu S.A., Chaudhary S., 2018, Approximation of surface wave frequency in Piezo-composite structure, Composite Part B: Engineering 144: 19-28.
6
[7] Singhal A., Sahu S.A., Chaudhary S., 2018, Liouville green approximation: An analytical approach to study the elastic wave vibrations in composite structure of piezo material, Composite Structure 184: 714-727.
7
[8] Fan H., Yang J.S., Xu L.M., 2006, Antiplane piezoelectric surface wave over a ceramic half-space with an imperfectly bonded layer, Ferroelectric and Frequency Control 53(9): 1695-1698.
8
[9] Li L., Wei P.J., Guo X., 2016, Rayleigh wave on the half-space with a gradient piezoelectric layer and imperfect interface, Applied Mathematical Modelling 40(19): 8326-8337.
9
[10] Chaudhary S., Sahu S.A., Singhal A., 2017, Analytical model for Rayleigh wave propagation in piezoelectric layer overlaid orthotropic substratum, Acta Mechanica 228: 529-547.
10
[11] Wang Z.K., Shang F.L., 1997, Cylindrical buckling of piezoelectric laminated plates, Acta Mechanica Solida Sinica 18: 101-108.
11
[12] Du J., Jin X., Wang J., Xian K., 2007, Love wave propagation in functionally graded piezoelectric material layer, Ultrasonics 46(1): 13-22.
12
[13] Saroj P.K., Sahu S.A., Chaudhary S., Chattopadhyay A., 2015, Love-type waves in functionally graded piezoelectric material (FGPM) sandwiched between initially stressed layer and elastic substrate, Waves in Random and Complex Media 25(4): 608-627.
13
[14] Cao X., Jin F., Jeon I., Lu T.J., 2009, Propagation of Love waves in a functionally graded piezoelectric material (FGPM) layered composite system, International Journal of Solids and Structures 46(22-23): 4123-4132.
14
ORIGINAL_ARTICLE
Influence of Addendum Modification Factor on Root Stresses in Normal Contact Ratio Asymmetric Spur Gears
Tooth root crack is considered as one of the crucial causes of failure in the gearing system and it occurs at the tooth root due to an excessive bending stress developed in the root region. The modern power transmission gear drives demand high bending load capacity, increased contact load capacity, low weight, reduced noise and longer life. These subsequent conditions are satisfied by the aid of precisely designed asymmetric tooth profile which turns out to be a suitable alternate for symmetric spur gears in applications like aerospace, automotive, gear pump and wind turbine industries. In all step up and step down gear drives (gear ratio > 1), the pinion (smaller in size) is treated as a vulnerable one than gear (larger in size) which is primarily due to the development of maximum root stress in the pinion tooth. This paper presents an idea to improve the bending load capacity of asymmetric spur gear drive system by achieving the same stresses between the asymmetric pinion and gear fillet regions which can be accomplished by providing an appropriate addendum modification. For this modified addendum the pinion and gear teeth proportion equations have been derived. In addition, the addendum modification factors required for a balanced maximum fillet stress condition has been determined through FEM for different parameters like drive side pressure angle, number of teeth and gear ratio. The bending load capacity of the simulated addendum modified asymmetric spur gear drives were observed to be prevalent (very nearly 7%) to that of uncorrected asymmetric gear drives.
http://jsm.iau-arak.ac.ir/article_664230_a6f4516631c85986a43f55c971fff78f.pdf
2019-03-30
210
221
10.22034/jsm.2019.664230
Asymmetric gear
Addendum modification factor
Finite element model
Fillet stress factor
R Prabhu
Sekar
prabhusekar.r@gmail.com
1
Mechanical Engineering Department, Motilal Nehru National Institute of Technology, Allahabad, India
LEAD_AUTHOR
R
Ravivarman
2
Research Scholar Department of Mechanical Engineering, Pondicherry Engineering college, Pondicherry, India
AUTHOR
[1] Buckingham E., 1988, Analytical Mechanics of Gears, Dover Publications, Inc.
1
[2] Kapelevich A., 2000, Geometry and design of involute spur gears with asymmetric teeth, Mechanism and Machine Theory 35: 117-130.
2
[3] Muni D.V., kumar V.S., Muthuveerappan G., 2007, Optimization of asymmetric spur gear drives for maximum bending strength using direct gear design method, Mechanics based design of structures and machines 35: 127-145.
3
[4] Yang S.C., 2007, Study on internal gear with asymmetric involute teeth, Mechanism and Machine Theory 42: 974-994.
4
[5] Muni D.V., Muthuveerappan G., 2009, A comprehensive study on the asymmetric internal spur gear drives through direct and conventional gear design, Mechanics Based Design of Structures and Machines 37: 431-461.
5
[6] Karat F., Ekwaro-Osire S., Cavdar K., Babalik F.C., 2008, Dynamic analysis of involute spur gears with asymmetric teeth, International Journal of Mechanical Sciences 50: 1598-1610.
6
[7] Costopoulos Th., Spitas V., 2009, Reduction of gear fillet stresses using one side asymmetric teeth, Mechanism and Machine Theory 44: 1524-1534.
7
[8] Alipiev O., 2011, Geometric design of involute spur gear drives with symmetric and asymmetric teeth using the realized potential method, Mechanism and Machine Theory 46: 10-32.
8
[9] Sekar P., Muthuveerappan G., 2014, Load sharing based maximum fillet stress analysis of asymmetric helical gear designed through direct design method, Mechanism and Machine Theory 80: 84-102.
9
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ORIGINAL_ARTICLE
Nonlinear Modeling of Bolted Lap Jointed Structure with Large Amplitude Vibration of Timoshenko Beams
This paper aims at investigating the nonlinear behavior of a system which is consisting of two free-free beams which are connected by a nonlinear joint. The nonlinear system is modelled as an in-extensional beam with Timoshenko beam theory. In addition, large amplitude vibration assumption is taken into account in order to obtain exact results. The nonlinear assumption in the system necessities existence of the curvature-related and inertia-related nonlinearities. The nonlinear partial differential equations of motion for the longitudinal, transverse, and rotation are derived using the Hamilton’s principle. A set of coupled nonlinear ordinary differential equations are further obtained with the aid of Galerkin method. The frequency-response curves are presented in the section of numerical results to demonstrate the effect of the different dimensionless parameters. It is shown that the nonlinear bolted-lap joint structure exhibits a hardening-type behavior. Furthermore, it is found that by adding a nonlinear spring the system exhibits a stronger hardening-type behavior. In addition, it is found that the system shows nonlinear behavior even in the absence of the nonlinear spring due to the nonlocal nonlinearity assumption. Moreover, it is shown that considering different engineering beam theories lead to different results and it is found that the Euler-Bernoulli beam theory over-predict the resonance frequency of the structure by ignoring rotary inertia and shear deformation.
http://jsm.iau-arak.ac.ir/article_664231_66dcb4ba96892cb177c7bc9fda142bd5.pdf
2019-03-30
222
235
10.22034/jsm.2019.664231
Bolted lap joint structure
Local nonlinearity
Nonlocal nonlinearity
Timoshenko Beam Theory
Nonlinear vibration
M
Jamal-Omidi
j_omidi@mut.ac.ir
1
Department of Aerospace Engineering, Space Research Institute, Malek Ashtar University of Technology, Tehran, Iran
LEAD_AUTHOR
F
Adel
2
Department of Aerospace Engineering, Space Research Institute, Malek Ashtar University of Technology, Tehran, Iran
AUTHOR
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