ORIGINAL_ARTICLE
Vibration Response of an Elastically Connected Double-Smart Nanobeam-System Based Nano-Electro-Mechanical Sensor
Nonlocal vibration of double-smart nanobeam-systems (DSNBSs) under a moving nanoparticle is investigated in the present study based on Timoshenko beam model. The two smart nanobeams (SNB) are coupled by an enclosing elastic medium which is simulated by Pasternak foundation. The energy method and Hamilton’s principle are used to establish the equations of motion. The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, elastic medium coefficients, external voltage, length of SNB and the mass of attached nanoparticle on the frequency of piezoelectric nanobeam. The results depict that the imposed external voltage is an effective controlling parameter for vibration of the piezoelectric nanobeam. Also increase in the mass of attached nanoparticle gives rise to a decrease in the natural frequency. This study might be useful for the design and smart control of nano-devices.
http://jsm.iau-arak.ac.ir/article_514634_7b1490248d121b56aa9e11d78b2519bd.pdf
2015-06-30T11:23:20
2019-10-21T11:23:20
121
130
DSNBSs
Nonlocal vibration
Pasternak foundation
Timoshenko beam model
Exact solution
A
Ghorbanpour Arani
aghorban@kashanu.ac.ir
true
1
Faculty of Mechanical Engineering, University of Kashan---
Institute of Nanoscience & Nanotechnology, University of Kashan
Faculty of Mechanical Engineering, University of Kashan---
Institute of Nanoscience & Nanotechnology, University of Kashan
Faculty of Mechanical Engineering, University of Kashan---
Institute of Nanoscience & Nanotechnology, University of Kashan
LEAD_AUTHOR
S.A
Mortazavi
true
2
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University of Kashan
AUTHOR
R
Kolahchi
true
3
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University of Kashan
AUTHOR
A.H
Ghorbanpour Arani
true
4
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University of Kashan
AUTHOR
[1] Eringen A.C., 1972, Nonlocal polar elastic continua, International Journal of Engineering Science 10: 1-16.
1
[2] Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54: 4703- 4710.
2
[3] Ghorbanpour Arani A., Atabakhshian V., Loghman A., Shajari A.R., Amir S., 2012, Nonlinear vibration of embedded SWBNNTs based on nonlocal Timoshenko beam theory using DQ method, Physica B: Condensed Matter 407: 2549-2555.
3
[4] Wang Q., 2005, Wave propagation in carbon nanotubes via nonlocal continuum mechanics, Journal of Applied Physics 98: 124301.
4
[5] Wang L.F., Hu H.Y., 2005, Flexural wave propagation in single-walled carbon nanotubes, Physical Review B 71: 195412.
5
[6] Narendar S., Roy Mahapatra D., Gopalakrishnan S., 2011, Prediction of nonlocal scaling parameter for armchair and zigzag single-walled carbon nanotubes based on molecular structural mechanics, nonlocal elasticity and wave propagation, International Journal of Engineering Science 49: 509-522.
6
[7] Yan Z., Jiang L.Y., 2011, The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects, Nanotechnology 2: 245703.
7
[8] Reddy J.N., 2007, Nonlocal theories for bending, buckling and vibration of beams, International Journal of Engineering Science 45: 288-307.
8
[9] Huang G.Y., Yu S.W., 2006, Effect of surface piezoelectricity on the electromechanical behavior of a piezoelectric ring, physica Satus Solidi B 243: 22-24.
9
[10] Yan Z., Jiang L.Y., 2008, The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects, Nanotechnology 22: 245703.
10
[11] Simsek M., 2011, Nonlocal effects in the forced vibration of an elastically connected double-carbon nanotube system under a moving nanoparticle, Computational Materials Science 50: 2112-2123.
11
[12] Ke L.L., Wang Y.Sh., Wang Zh.D., 2008, Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory, Composite Structures 94: 2038-2047.
12
[13] Han J.H., Lee I., 1998, Analysis of composite plates with piezoelectric actuators for vibration control using layerwise displacement theory, Composite B: Engineering 29: 621-632.
13
[14] Ghorbanpour Arani A., Kolahchi R., Mosallaie Barzoki A.A., 2011, Effect of material in-homogeneity on electro-thermo-mechanical behaviors of functionally graded piezoelectric rotating shaft, Applied Mathematical Modelling 35: 2771-2789.
14
[15] Wang Q., 2002, On buckling of column structures with a pair of piezoelectric layers, Engineering Structures 24: 199-205.
15
[16] Mosallaie Barzoki A.A., Ghorbanpour Arani A., Kolahchi R., Mozdianfard M.R., 2012, Electro-thermo-mechanical torsional buckling of a piezoelectric polymeric cylindrical shell reinforced by DWBNNTs with an elastic core, Applied Mathematical Modelling 36: 2983-2995.
16
[17] Mohammadimehr M., Saidi A.R., Ghorbanpour Arani A., Arefmanesh A., Han Q., 2010, Torsional buckling of a DWCNT embedded on Winkler and Pasternak foundations using nonlocal theory, Journal of Mechanical Science and Technology 24: 1289-1299.
17
[18] Ding H.J., Wang H.M., Ling D.S., 2003, Analytical solution of a pyroelectric hollow cylinder for piezothermoelastic axisymmetric dynamic problems, Journal of Thermal Stresses 26: 261-276.
18
[19] Wang Q., 2002, Axisymmetric wave propagation in a cylinder coated with apiezoelectric layer, International Journal of Solids and Structures 39: 3023-3037.
19
[20] Shen Zh.B., Tang H.L., Li D.K., Tang G.J, 2012, Vibration of single-layered graphene sheet-based nanomechanical sensor via nonlocal Kirchhoff plate theory, Computational Materials Science 6: 201-205.
20
ORIGINAL_ARTICLE
Semi Analytical Analysis of FGM Thick-Walled Cylindrical Pressure Vessel with Longitudinal Variation of Elastic Modulus under Internal Pressure
In this paper, a numerical analysis of stresses and displacements in FGM thick-walled cylindrical pressure vessel under internal pressure has been presented. The elastic modulus is assumed to be varying along the longitude of the pressure vessel with an exponential function continuously. The Poisson’s ratio is assumed to be constant. Whereas most of the previous studies about FGM thick-walled pressure vessels are on the basis of changing material properties along the radial direction, in this research, elastic analysis of cylindrical pressure vessel with exponential variations of elastic modulus along the longitudinal direction, under internal pressure, have been investigated. For the analysis of the vessel, the stiffness matrix of the cylindrical pressure vessel has been extracted by the usage of Galerkin Method and the numerical solution for axisymmetric cylindrical pressure vessel under internal pressure have been presented. Following that, displacements and stress distributions depending on inhomogeneity constant of FGM vessel along the longitudinal direction of elastic modulus, are illustrated and compared with those of the homogeneous case. The values which have been used in this study are arbitrary chosen to demonstrate the effect of inhomogeneity on displacements and stress distributions. Finally, the results are compared with the findings of finite element method (FEM).
http://jsm.iau-arak.ac.ir/article_514636_22addba9637927356b2519dfcabaa483.pdf
2015-06-30T11:23:20
2019-10-21T11:23:20
131
145
Thick-walled cylinder
Cylindrical pressure vessel
FGM
Longitudinal variations of elastic modulus
Exponential
M
Shariati
mshariati44@um.ac.ir
true
1
Department of Mechanical Engineering, Ferdosi University
Department of Mechanical Engineering, Ferdosi University
Department of Mechanical Engineering, Ferdosi University
AUTHOR
H
Sadeghi
true
2
Department of Mechanical Engineering, Shahrood University
Department of Mechanical Engineering, Shahrood University
Department of Mechanical Engineering, Shahrood University
AUTHOR
M
Ghannad
true
3
Department of Mechanical Engineering, Shahrood University
Department of Mechanical Engineering, Shahrood University
Department of Mechanical Engineering, Shahrood University
AUTHOR
H
Gharooni
gharooni.hamed@gmail.com
true
4
Department of Mechanical Engineering, Shahrood University
Department of Mechanical Engineering, Shahrood University
Department of Mechanical Engineering, Shahrood University
LEAD_AUTHOR
[1] Fukui Y., Yamanaka N., 1992, Elastic analysis for thick-walled tubes of functionally graded materials subjected to internal pressure, JSME International Journal Series I 35(4): 891-900.
1
[2] Tutuncu N., Ozturk M., 2001, Exact solution for stresses in functionally graded pressure vessel, Composites Part B: Engineering 32: 683-686.
2
[3] Jabbari M., Sohrab pour S., Eslami M.R., 2002, Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads, International Journal of Pressure Vessel and Piping 79: 493-497.
3
[4] Eipakchi H.R., Khadem S.E., Rahimi G.H., 2008, Axisymmetric stress analysis of a thick conical shell with varying thickness under nonuniform internal pressure, Journal of Engineering Mechanics 134: 601-610.
4
[5] Eslami M.R., Babaei M.H., Poultangari R., 2005, Thermal and mechanical stresses in a functionally graded thick sphere, International Journal of Pressure Vessel and Piping 82: 522-527.
5
[6] Dai H.L., Fu Y.M., Dong Z.M., 2006, Exact solutions for functionally graded pressure vessels in a uniform magnetic field, International Journal of Solids and Structures 43: 5570-5580.
6
[7] Naghdabadi R., Kordkheili S.A., 2005, A finite element formulation for analysis of functionally graded plates and shells, ASME Journal of Applied Mechanics 74: 375-386.
7
[8] Hongjun X., Zhifei S., Taotao Z., 2006, Elastic analyses of heterogeneous hollow cylinders, Mechanics Research Communications 33(5): 681-691.
8
[9] Zhifei S., Taotao Z., Hongjun X., 2007, Exact solutions of heterogeneous elastic hollow cylinders, Composite Structures 79: 140-147.
9
[10] Tutuncu N., 2007, Stresses in thick-walled FGM cylinders with exponentially-varying properties, Engineering Structures 29: 2032-2035.
10
[11] Ghannad M., Nejad M.Z., 2010, Elastic analysis of pressurized thick hollow cylindrical shells with clamped-clamped ends, Mechanika 5(85): 11-18.
11
[12] Ghannad M., Rahimi G.H., Zamani Nejad M., 2012, Determination of displacements and stresses in pressurized thick cylindrical shells with variable thickness using perturbation technique, Mechanika 18(1): 14-21.
12
[13] Gharooni H., Ghannad M., 2012, Analytical solution of rotary pressurized FGM cylinder by the usage of first order shear deformation theory, 11th Conference of Iranian Aerospace Society 15024: 195.
13
[14] Liu L., Li J., Ding M., Yang X., 2007, Development of SiC/(W, Ti)C gradient ceramic nozzle materials for sand blasting surface treatments, International Journal of Refractory Metals and Hard Materials 25(2): 130-137.
14
[15] Liu L., Deng J., 2008, Study on erosion wear mechanism of SiC/(W,Ti)C gradient ceramic nozzle material, Journal of Key Engineering Materials 375(376): 440-444.
15
[16] Asemi K., Salehi M., Akhlaghi M., 2011, Elastic solution of a two-dimensional functionally graded thick truncated cone with finite length under hydrostatic combined loads, Acta Mechanica 217(1-2): 119-134.
16
[17] Masoud Asgari M., Akhlaghi M., 2010, Transient thermal stresses in two-dimensional functionally graded thick hollow cylinder with finite length, Archive of Applied Mechanics 80(4): 353-376.
17
[18] Ghannad M., Rahimi G.H., Zamani Nejad M., 2013, Elastic analysis of pressurized thick cylindrical shells with variable thickness made of functionally graded materials, Composites: Part B 45: 388-396.
18
ORIGINAL_ARTICLE
An Experimental and Numerical Study of Forming Limit Diagram of Low Carbon Steel Sheets
The forming limit diagram (FLD) is probably the most common representation of sheet metal formability and can be defined as the locus of the principal planar strains where failure is most likely to occur. Low carbon steel sheets have many applications in industries, especially in automotive parts, therefore it is necessary to study the formability of these steel sheets. In this paper, FLDs, were determined experimentally for two grades of low carbon steel sheets using out-of-plane (dome) formability test. The effect of different parameters such as work hardening exponent (n), anisotropy (r) and thickness on these diagrams were studied. In addition, the out-of-plane stretching test with hemispherical punch was simulated by finite element software Abaqus. The limit strains occurred with localized necking were specified by tracing the thickness strain and its first and second derivatives versus time at the thinnest element. Good agreement was achieved between the predicted data and the experimental data.
http://jsm.iau-arak.ac.ir/article_514637_afb98a56a8b5db411ebae70ff3f736aa.pdf
2015-06-30T11:23:20
2019-10-21T11:23:20
146
157
Forming Limit Diagram
Out-of-plane
Localized necking
Finite Element
M
Kadkhodayan
kadkhoda@um.ac.ir
true
1
Department of Mechanical Engineering ,Islamic Azad University, Mashhad Branch
Department of Mechanical Engineering ,Islamic Azad University, Mashhad Branch
Department of Mechanical Engineering ,Islamic Azad University, Mashhad Branch
LEAD_AUTHOR
H
Aleyasin
true
2
Department of Mechanical Engineering ,Islamic Azad University, Mashhad Branch
Department of Mechanical Engineering ,Islamic Azad University, Mashhad Branch
Department of Mechanical Engineering ,Islamic Azad University, Mashhad Branch
AUTHOR
[1] Brun R., Chambard A., Lai M., De Luca P., 1999, Actual and virtual testing techniques for a numerical definition of materials, Numisheet 99.
1
[2] Cao J., Yao H., Karafillis A., Boyce M.C., 2000, Prediction of localized thinning in sheet metal using a general anisotropic yield criterion, International Journal of Plasticity 16: 1105-1129.
2
[3] Clift S.E., Hartley P., Sturgess C.E.N., Rowe G.W., 1990, Fracture prediction in plastic deformation processes, International Journal of Mechanical Sciences 32: 1-17.
3
[4] Friedman P.A., Pan J., 2000, Effects of plastic anisotropy and yield criteria on prediction of forming limit curves, International Journal of Mechanical Sciences 42: 29-48.
4
[5] Geiger M., Merklein M., 2003, Determination of forming limit diagrams- a new analysis method for characterization of materials formability, Annals of the CIRP 52: 213-216.
5
[6] Goodwin G.M., 1968, Application of strain analysis to sheet metal forming problems in the press shop, SAE Technical Paper 680093, doi:10.4271/680093.
6
[7] Hecker S.S., 1975, Simple technique for determining forming limit curves, Sheetmetal Industries Ltd 52: 671-676.
7
[8] Hill R., 1948, A theory of yielding and plastic flow of anisotropic metals, Proceedings A 193: 281-297.
8
[9] Huang H.M., Pan J., Tang S.C., 2000, Failure prediction in anisotropic sheet metals under forming operations with consideration of rotating principal stretch directions, International Journal of Plasticity 16: 611-633.
9
[10] Marciniak Z., Kuczynski K., 1967, Limit strains in the processes of stretch forming sheet metal, International Journal of Mechanical Sciences 9: 609-620.
10
[11] Narayanasamy R., Sathiya Narayanan C., 2006, Forming limit diagram for Indian interstitial free steels, Materials & Design Journal 27: 882-899.
11
[12] Ozturk F., Lee D., 2004, Analysis of forming limits using ductile fracture criteria, Journal of Materials Processing Technology 147: 397-404.
12
[13] Pepelnjak T., Petek A., Kuzman K., 2005, Analysis of the forming limit diagram in digital environment, Advanced Material Research 6/8: 697-704.
13
[14] Petek A., Pepelnjak T., Kuzman K., 2005, An improved method for determining a forming limit diagram in the digital environment, Journal of Mechanical Engineering 51: 330-345.
14
[15] Raghavan K.S., 1995, A simple technique to generate in-plane forming limit curves and selected applications, Metallurgical and Materials Transactions A 26(8): 2075-2084.
15
[16] Takuda H., Mori K., Takakura N., Yamaguchi K., 2000, Finite element analysis of limit strains in biaxial stretching of sheet metals allowing for ductile fracture, International Journal of Mechanical Sciences 42: 785-798.
16
[17] Wu P.D., Jain M., Savoie J., MacEwen S.R., Tugcu P, Neale K.W., 2003, Evaluation of anisotropic yield functions for aluminum sheets, International Journal of Plasticity 19: 121-138.
17
[18] Yoshida T., Katayama T., Usuda M., 1995, Forming-limit analysis of hemispherical-punch stretching using the three-dimensional finite element method, Journal of Materials Processing Technology 50: 226-237.
18
ORIGINAL_ARTICLE
Free Vibration Analyses of Functionally Graded CNT Reinforced Nanocomposite Sandwich Plates Resting on Elastic Foundation
In this paper, a refined plate theory is applied to investigate the free vibration analysis of functionally graded nanocomposite sandwich plates reinforced by randomly oriented straight carbon nanotube (CNT). The refined shear deformation plate theory (RSDT) uses only four independent unknowns and accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The motion equations are derived using Hamilton’s energy principle and Navier’s method and is applied to solve this equation. The sandwich plates are considered simply supported and resting on a Winkler/Pasternak elastic foundation. The material properties of the functionally graded carbon nanotube reinforced composites (FG-CNTRCs) are graded along the thickness and estimated though the Mori–Tanaka method. Effects of CNT volume fraction, geometric dimensions of sandwich plate, and elastic foundation parameters are investigated on the natural frequency of the FG-CNTRC sandwich plates.
http://jsm.iau-arak.ac.ir/article_514639_f8a09a9440dd8c3d4179bba643fd405d.pdf
2015-06-30T11:23:20
2019-10-21T11:23:20
158
172
Sandwich plates
Mori–Tanaka approach
Refined plate theory
Carbon nanotubes
Navier’s solution
R
Moradi-Dastjerdi
rasoul.moradi@iaukhsh.ac.ir
true
1
Young Researchers and Elite Club, Khomeinishahr Branch, Islamic Azad University
Young Researchers and Elite Club, Khomeinishahr Branch, Islamic Azad University
Young Researchers and Elite Club, Khomeinishahr Branch, Islamic Azad University
LEAD_AUTHOR
Gh
Payganeh
true
2
School of Mechanical Engineering, Shahid Rajaee Teacher Training University
School of Mechanical Engineering, Shahid Rajaee Teacher Training University
School of Mechanical Engineering, Shahid Rajaee Teacher Training University
AUTHOR
H
Malek-Mohammadi
true
3
School of Mechanical Engineering, Shahid Rajaee Teacher Training University
School of Mechanical Engineering, Shahid Rajaee Teacher Training University
School of Mechanical Engineering, Shahid Rajaee Teacher Training University
AUTHOR
[1] Wagner H.D., Lourie O., Feldman Y., 1997, Stress-induced fragmentation of multiwall carbon nanotubes in a polymer matrix, Applied Physics Letters 72: 188-190.
1
[2] Griebel M., Hamaekers J., 2004, Molecular dynamic simulations of the elastic moduli of polymer-carbon nanotube composites, Computer Methods in Applied Mechanics and Engineering 193: 1773-1788.
2
[3] Fidelus J.D., Wiesel E., Gojny F.H., Schulte K., Wagner H.D., 2005, Thermo-mechanical properties of randomly oriented carbon/epoxy nanocomposites, Composite Part A 36: 1555-1561.
3
[4] Song Y.S., Youn J.R., 2006, Modeling of effective elastic properties for polymer based carbon nanotube composites, Polymer 47:1741-1748.
4
[5] Han Y., Elliott J., 2007, Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites, Computational Materials Science 39: 315-323.
5
[6] Zhu R., Pan E., Roy A.K., 2007, Molecular dynamics study of the stress–strain behavior of carbon-nanotube reinforced Epon 862 composites, Materials Science and Engineering A 447: 51-57.
6
[7] Manchado M.A.L., Valentini L., Biagiotti J., Kenny J.M., 2005, Thermal and mechanical properties of single-walled carbon nanotubes-polypropylene composites prepared by melt processing, Carbon 43: 1499-1505.
7
[8] Qian D., Dickey E.C., Andrews R., Rantell T., 2000, Load transfer and deformation mechanisms in carbon nanotube–polystyrene composites, Applied Physics Letters 76: 2868-2870.
8
[9] Mokashi V.V., Qian D., Liu Y.J., 2007, A study on the tensile response and fracture in carbon nanotube-based composites using molecular mechanics, Composites Science and Technology 67: 530-540.
9
[10] Wuite J., Adali S., 2005, Deflection and stress behaviour of nanocomposite reinforced beams using a multiscale analysis, Composite Structures 71: 388-396.
10
[11] Reddy J.N., 2000, Analysis of functionally graded plates, International Journal for Numerical Methods in Engineering
11
47: 663-684.
12
[12] Cheng Z.Q., Batra R.C., 2000, Deflection relationships between the homogeneous Kirchhoff plate theory and different functionally graded plate theories, Archive of Mechanics 52:143-158.
13
[13] Cheng Z.Q., Batra R.C., 2000, Exact correspondence between eigenvalues of membranes and functionallygraded simplysupported polygonal plates, Journal of Sound and Vibration 229: 879-895.
14
[14] Shen H.S., 2011, Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: Axially-loaded shells, Composite Structures 93: 2096-2108.
15
[15] Ke L.L., Yang J., Kitipornchai S., 2010, Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams, Composite Structures 92: 676-683.
16
[16] Mori T., Tanaka K., 1973, Average stress in matrix and average elastic energy of materials with Misfitting inclusions, Acta Metallurgica 21: 571-574.
17
[17] Yas M.H., Heshmati M., 2012, Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load, Applied Mathematical Modelling 36: 1371-1394.
18
[18] Sobhani Aragh B., Nasrollah Barati A.H., Hedayati H., 2012, Eshelby–Mori–Tanaka approach for vibrational behavior of continuously graded carbon nanotube–reinforced cylindrical panels, Composites Part B 43: 1943-1954.
19
[19] Pourasghar A., Yas M.H., 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.
20
[20] Moradi-Dastjerdi R., Pourasghar A., Foroutan M., 2013, The effects of carbon nanotube orientation and aggregation on vibrational behavior of functionally graded nanocomposite cylinders by a mesh-free method, Acta Mechanica 224: 2817-2832.
21
[21] Pasternak P.L., 1954, On a New Method of Analysis of an Elastic Foundation by Means of Two Foundation Constants, Cosudarstrennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture, Moscow, USSR.
22
[22] 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: 2040-2048.
23
[23] Zenkour AM., 2006, Generalized shear deformation theory for bending analysis of functionally graded plates, Applied Mathematical Modelling 30: 67-84.
24
[24] Zenkour AM., 2009, The refined sinusoidal theory for FGM plates on elastic foundations, International Journal of Mechanical Sciences 51: 869-880.
25
[25] Merdaci S., Tounsi A., A.Houari M.S., Mechab I., Hebali H., Benyoucef S., 2011, Two new refined shear displacement models for functionally graded sandwich plates, Archive of Applied Mechanics 81:1507-1522.
26
[26] Thai H.T., Choi D.H., 2011, A refined plate theory for functionally graded plates resting on elastic foundation, Composites Science and Technology 71: 1850-1858.
27
[27] Akavci SS., 2007, Buckling and free vibration analysis of symmetric and antisymmetric laminated composite plates on an elastic foundation, Journal of Reinforced Plastics and Composites 26: 1907-1919.
28
[28] Benyoucef S., Mechab I., Tounsi A., Fekrar A., Ait Atmane H., Adda Bedia EA., 2010, Bending of thick functionally graded plates resting on Winkler-Pasternak elastic foundations, Mechanics of Composite Materials 46: 425-434.
29
[29] Ait Atmane H., Tounsi A., Mechab I., Adda Bedia EA., 2010, Free vibration analysis of functionally graded plates resting on Winkler-Pasternak elastic foundations using a new shear deformation theory, International Journal of Mechanics and Materials in Design 6: 113-121.
30
[30] Shi D.L., Feng X.Q., Yonggang Y.H., Hwang K.C., Gao H., 2004, The effect of nanotube waviness and agglomeration on the elasticproperty of carbon nanotube reinforced composites, Journal of Engineering Materials and Technology 126: 250-257.
31
[31] Matsunaga H., 2008, Free vibration and stability of functionally graded plates according to a 2D higher-order deformation theory, Composite Structures 82: 499-512.
32
[32] Akhavan H., Hosseini-Hashemi Sh., Rokni Damavandi Taher H., Alibeigloo A., Vahabi Sh., 2009, Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part II: Frequency analysis, Computational Materials Science 44: 951-961.
33
ORIGINAL_ARTICLE
Surface Stress Effect on the Nonlocal Biaxial Buckling and Bending Analysis of Polymeric Piezoelectric Nanoplate Reinforced by CNT Using Eshelby-Mori-Tanaka Approach
In this article, the nonlocal biaxial buckling load and bending analysis of polymeric piezoelectric nanoplate reinforced by carbon nanotube (CNT) considering the surface stress effect is presented. This plate is subjected to electro-magneto-mechanical loadings. Eshelby-Mori-Tanaka approach is used for defining the piezoelectric nanoplate material properties. Navier’s type solution is employed to obtain the critical buckling load of polymeric piezoelectric nanoplate for classical plate theory (CPT) and first order shear deformation theory (FSDT). The influences of various parameters on the biaxial nonlocal critical buckling load with respect to the local critical buckling load ratio () of nanoplate are examined. Surface stress effects on the surface biaxial critical buckling load to the non-surface biaxial critical buckling load ratio () can not be neglected. Moreover, the effect of residual surface stress constant on is higher than the other surface stress parameters on it. increases by applying the external voltage and magnetic fields. The nonlocal deflection to local deflection of piezoelectric nanocomposite plate ratio () decreases with an increase in the nonlocal parameter for both theories. And for FSDT, decreases with an increase in residual stress constant and vice versa for CPT.
http://jsm.iau-arak.ac.ir/article_514643_e37879e19ea9f769695c4944b4dd1f13.pdf
2015-06-30T11:23:20
2019-10-21T11:23:20
173
190
Polymeric piezoelectric nanoplate
Buckling
Bending
Surface stress effect
Eshelby-Mori-Tanaka approach
SWCNT
M
Mohammadimehr
mmohammadimehr@kashanu.ac.ir
true
1
Department of Solid Mechanics ,Faculty of Mechanical Engineering, University of Kashan
Department of Solid Mechanics ,Faculty of Mechanical Engineering, University of Kashan
Department of Solid Mechanics ,Faculty of Mechanical Engineering, University of Kashan
LEAD_AUTHOR
B
Rousta Navi
true
2
Department of Solid Mechanics ,Faculty of Mechanical Engineering, University of Kashan
Department of Solid Mechanics ,Faculty of Mechanical Engineering, University of Kashan
Department of Solid Mechanics ,Faculty of Mechanical Engineering, University of Kashan
AUTHOR
A
Ghorbanpour Arani
aghorban@kashanu.ac.ir
true
3
Institute of Nanoscience & Nanotechnology, University of Kashan
Institute of Nanoscience & Nanotechnology, University of Kashan
Institute of Nanoscience & Nanotechnology, University of Kashan
AUTHOR
[1] Schmidt D., Shah D., Giannelis EP., 2002, New advances in polymer/layered silicate nanocomposites, Current Opinion in Solid State and Material Science 6(3): 205-212.
1
[2] Thostenson E., Li C., Chou T., 2005, Review nanocomposites in context, Journal Composite Science Technology 65:491-516.
2
[3] Ghorbanpour Arani A., Hashemian M., Loghman A., Mohammadimehr M., 2011, Study of dynamic stability of the double-walled carbon nanotube under axial loading embedded in an elastic medium by the energy method, Journal of applied mechanics and technical physics 52 (5): 815-824.
3
[4] Mohammadimehr M., Rahmati A. H., 2013, Small scale effect on electro-thermo-mechanical vibration analysis of single-walled boron nitride nanorods under electric excitation, Turkish Journal of Engineering & Environmental Sciences 37: 1-15.
4
[5] Ghorbanpour Arani A., Rahnama Mobarakeh M., Shams Sh., Mohammadimehr M., 2012, The effect of CNT volume fraction on the magneto-thermo-electro-mechanical behavior of smart nanocomposite cylinder, Journal of Mechanical Science and Technology 26 (8): 2565-2572.
5
[6] Jaffe B., Cook W.R., Jaffe H., 1971, Piezoelectric Ceramics, New York, Academic.
6
[7] Xu S., Yeh Y.W., Poirier G., McAlpine M.C., Register R.A., Yao N., 2013, Flexible piezoelectric PMN-PT nanowire-based na nocomposite and device, Nano Letters 13: 2393-2398.
7
[8] Samaei A.T., Abbasion S., Mirsayar M.M., 2011, Buckling analysis of a single-layer graphene sheet embedded in an elastic medium based on nonlocal Mindlin plate theory, Mechanical Resereach Communication 38: 481-485.
8
[9] Farajpour A., Shahidi A.R., Mohammadi M., Mahzoon M., 2013, Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics, Composite Structure 94: 1605-1615.
9
[10] Aksencer T., Aydogdu M., 2011, Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory, Physica E 43: 954-959.
10
[11] Narendar S., 2011, Buckling analysis of micro-/nano-scale plates based on two-variable refined plate theory incorporating nonlocal scale effects, Composite Structure 93: 3093-3103.
11
[12] Analooei H.R., Azhari M., Heidarpour A., 2013, Elastic buckling and vibration analyses of orthotropic nanoplates using nonlocal continuum mechanics and spline finite strip method, Appllied Mathematical Modeling 37: 6703-6717.
12
[13] Murmu T., Sienz J., Adhikari S., Arnold C., 2013, Nonlocal buckling of double-nanoplate-systems under biaxial compression, Composite Part B 44: 84-94.
13
[14] Ansari R., Sahmani S., 2013, Prediction of biaxial buckling behavior of single-layered graphene sheets based on nonlocal plate models and molecular dynamics simulations, Appllied Mathematical Modeling 37: 7338-7351.
14
[15] Ghorbanpour Arani A., Kolahchi R., Vossough H., 2012, Buckling analysis and smart control of SLGS using elastically coupled PVDF nanoplate based on the nonlocal Mindlin plate theory, Physica B 407: 4458-4465.
15
[16] Murmu T., Pradhan S.C., 2009, Buckling of biaxially compressed orthotropic plates at small scales, Mechanical Research Communication 36: 933-938.
16
[17] Farajpour A., Danesh M., Mohammadi M., 2011, Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics, Physica E 44: 719-727.
17
[18] Gurtin M.E., Murdoch A.I., 1978, Surface stress in solids, International Journal of Solids Structure 14: 431-440.
18
[19] Tian L., Rajapakse R.K.N.D., 2007, Finite element modelling of nanoscale inhomogeneities in an elastic matrix, Computer Material Science 41: 44-53.
19
[20] Wang G.F., Feng X.Q., 2009, Timoshenko beam model for buckling and vibration of nanowires with surface effects, Physics D 42: 155-411.
20
[21] Wang K.F., Wang B.L., 2013, Effect of surface energy on the non-linear postbuckling behavior of nanoplates, International Journal of Nonlinear Mechanics 55: 19-24.
21
[22] Alzahrani E.O., Zenkour A.M., Sobhy M., 2013, Small scale effect on hygro-thermo-mechanical bending of nanoplates embedded in an elastic medium, Composite Structure 105: 163-172.
22
[23] Alibeigloo A., 2013, Static analysis of functionally graded carbon nanotube-reinforced composite plate embedded in piezoelectric layers by using theory of elasticity, Composite Structure 95: 612-622.
23
[24] 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 Structure 94: 1450-1460.
24
[25] 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 Structure 98: 160-168.
25
[26] Jafari Mehrabadi S., Sobhani Aragh B., Khoshkhahesh V., Taherpour A., 2012, Mechanical buckling of rectangular nanocomposite plate reinforced by aligned and straight single-walled carbon nanotubes, Composite Part B 43: 2031-2040.
26
[27] Shi D.L., Feng X.Q., 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 Material Technology 126: 250-257.
27
[28] Rahmati A.H., Mohammadimehr M., 2014, Vibration analysis of non-uniform and non-homogeneous boron nitride nanorods embedded in an elastic medium under combined loadings using DQM, Physica B: Condensed Matter 440: 88-98.
28
[29] Mohammadimehr M., Saidi A. R., Ghorbanpour Arani A., Arefmanesh A., Han Q., 2011, Buckling analysis of double-walled carbon nanotubes embedded in an elastic medium under axial compression using non-local Timoshenko beam theory, Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science 225: 498-506.
29
[30] Ansari R., Sahmani S., 2011, Surface stress effects on the free vibration behavior of nanoplates, International Journal of Engineering Science 49: 1204-1215.
30
[31] Wang L., 2012, Surface effect on buckling configuration of nanobeams containing internal flowing fluid: A nonlinear analysis, Physica E 44: 808-812.
31
[32] Kraus J., 1984, Electromagnetics, USA, McGrawHill Inc.
32
[33] Ghorbanpour Arani A., Amir S., Shajari A.R., Mozdianfard M.R., Khoddami Maraghi Z., Mohammadimehr M., 2012, Electro-thermal non-local vibration analysis of embedded DWBNNTs, Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science 226: 1410-1422.
33
[34] Shen H.S., Zhu Z.H., 2012, Postbuckling of sandwich plates with nanotube-reinforced composite face sheets resting on elastic foundations, European Journal of Mechanical A/Solids 35: 10-21.
34
ORIGINAL_ARTICLE
Upper Bound Analysis of Tube Extrusion Process Through Rotating Conical Dies with Large Mandrel Radius
In this paper, an upper bound approach is used to analyze the tube extrusion process through rotating conical dies with large mandrel radius. The material under deformation in the die and inside the container is divided to four deformation zones. A velocity field for each deformation zone is developed to evaluate the internal powers and the powers dissipated on all frictional and velocity discontinuity surfaces. By minimization of the total power with respect to the slippage parameter between tube and the die and equating it with the required external power, the extrusion pressure is determined. The corresponding results for rotating conical dies are also determined by using the finite element code, ABAQUS. The analytical results show a good coincidence with the results by the finite element method with a slight overestimation. Finally, the effects of various process parameters such as mandrel radius, friction factor, etc., upon the relative extrusion pressure are studied.
http://jsm.iau-arak.ac.ir/article_514645_93defe31a9730aa40298be41603c546b.pdf
2015-06-30T11:23:20
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191
203
Tube extrusion
Rotating conical die
Upper bound method
H
Haghighat
hhaghighat@razi.ac.ir
true
1
Mechanical Engineering Department, Razi University, Kermanshah
Mechanical Engineering Department, Razi University, Kermanshah
Mechanical Engineering Department, Razi University, Kermanshah
LEAD_AUTHOR
M.M
Mahdavi
true
2
Mechanical Engineering Department, Razi University, Kermanshah
Mechanical Engineering Department, Razi University, Kermanshah
Mechanical Engineering Department, Razi University, Kermanshah
AUTHOR
[1] Ma X., Barnett M., 2005, An upper bound analysis of forward extrusion through rotating dies, In Proceedings of the 8th ESAFORM Conference on Material Forming, Bucharest, Romania.
1
[2] Bochniak W., Korbel A., 1999, Extrusion of CuZn39Pb2 alloy by the KOBO method, Engineering Transactions 47: 351-367.
2
[3] Bochniak W., Korbel A., 2000, Plastic flow of aluminum extruded, under complex conditions, Matererials Science and Technology 16: 664-674.
3
[4] Bochniak W., Korbel A., 2003, KOBO-type forming: forging of metals under complex conditions of the process, Journal of Materials Processing Technology 134: 120-134.
4
[5] Kim Y.H., Park J.H., 2003, Upper bound analysis of torsional backward extrusion process, Journal of Materials Processing Technology 143-144: 735-740.
5
[6] Ma X., Barnett M., Kim Y. H., 2004, Forward extrusion through steadily rotating conical dies, Part I: experiments, International Journal of Mechanical Sciences 46: 449- 464.
6
[7] Ma X., Barnett M., Kim Y. H., 2004, Forward extrusion through steadily rotating conical dies, Part II: theoretical analysis, International Journal of Mechanical Sciences 46: 465-489.
7
[8] Maciejewski J., Mroz Z., 2008, An upper-bound analysis of axisymmetric extrusion assisted by cyclic torsion, Journal of Materials Processing Technology 206: 333-344.
8
ORIGINAL_ARTICLE
Application of Case I and Case II of Hill’s 1979 Yield Criterion to Predict FLD
Forming limit diagrams (FLDs) are calculated based on both the Marciniak and Kuczynski (M-K) model and the analysis proposed by Jones and Gillis (J-G). J-G analysis consisted of plastic deformation approximation by three deformation phases. These phases consisted of homogeneous deformation up to the maximum load (Phase I), deformation localization under constant load (phase II) and local necking with a precipitous drop in load (phase III). In the present study, case I and case II of Hill’s non-quadratic yield function were used for the first time. It is assumed that sheets obey the power-law flow rule and in-plane isotropy is satisfied. Calculated FLDs from this analysis are compared with the experimental data of aluminum alloys 3003-O, 2036-T4 and AK steel reported by other references. Calculated FLDs showed that limit strain predictions based on case I and case II of the Hill’s non-quadratic yield function are fairly well correlated to experiments when J-G model is used.
http://jsm.iau-arak.ac.ir/article_514646_94db053790db61eba8672e5304416e9e.pdf
2015-06-30T11:23:20
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204
222
Yield function
Forming limit diagrams
Localization
M
Aghaie-Khafri
maghaei@kntu.ac.ir
true
1
Faculty of Mechanical Engineering, K.N. Toosi University of Technology
Faculty of Mechanical Engineering, K.N. Toosi University of Technology
Faculty of Mechanical Engineering, K.N. Toosi University of Technology
LEAD_AUTHOR
M
Torabi-Noori
true
2
Faculty of Mechanical Engineering, K.N. Toosi University of Technology
Faculty of Mechanical Engineering, K.N. Toosi University of Technology
Faculty of Mechanical Engineering, K.N. Toosi University of Technology
AUTHOR
[1] Keeler S.P., 1969, Circular grid system: a valuable aid for evaluation sheet forming, Sheet Metal Industrial 45: 633-640.
1
[2] Goodwin G.M., 1969, Application of strain analysis to sheet metal forming problems, Metall Ital 60: 767-771.
2
[3] Liu J., Liu W., Xue W., 2013, Forming limit diagram prediction of 5052/polyethylene/AA5052 sandwich sheets, Materials and Design 46: 112-120.
3
[4] Aghaie-Khafri M., Mahmudi R., 2005, The effect of preheating on the formability of an Al–Fe–Si alloy sheet, Journal of Materials Processing Technology 169: 38-43.
4
[5] Friedman P.A., Pan J., 2000, Effects of plastic anisotropy and yield criteria on prediction of forming limit curves, International Journal of Mechanical Sciences 42: 29-48.
5
[6] Zhang L., Wang J., 2012, Modeling the localized necking in anisotropic sheet metals, International Journal of Plasticity 39: 103-118.
6
[7] Velmanirajan K., Syed Abu Thaheer A., Narayanasamy R., Ahamed Basha C., 2012, Numerical modelling of aluminium sheets formability using response surface methodology, Materials and Design 41: 239-254.
7
[8] Hart E.W., 1967, Theory of the tensile test, Acta Metallurgica 15: 351-355.
8
[9] Hill R., 1952, On discontinuous plastic states with special reference to localized necking in thin sheets, Journal of the Mechanics and Physics of Solids 1: 19-30.
9
[10] Gillis P.P., Jones S.E., 1979, Tensile deformation of a flat sheet, International Journal of Mechanical Sciences 21: 109-117.
10
[11] Marciniak Z., Kuczynski K., 1967, Limit strains in the processes of stretch-forming sheet metal, International Journal of Mechanical Sciences 9: 609-620.
11
[12] Mohebbi M.S., Akbarzadeh A., 2012, Prediction of formability of tailor welded blanks by modification of MK model, International Journal of Mechanical Sciences 61: 44-51.
12
[13] Jones S.E., Gillis P.P., 1984, An analysis of biaxial stretching of a ﬂat sheet, Metallurgical Transactions A 15: 133-138.
13
[14] Choi W., Gillis P.P., Jones S.E ., 1989, Calculation of the forming limit diagram, Metallurgical Transactions A 20:1975-1987.
14
[15] Choi W., Gillis P.P., Jones S.E., 1989, Forming Limit Diagrams: Concepts, Methods and Applications, edited by Wagoner R.H., Chan K.S., Keeler S.P., Published, TMS Warendale.
15
[16] Jones S.E., Gillis P.P., 1984, Analysis of biaxial stretching of a flat sheet, Metallurgical Transactions A 15: 133-138.
16
[17] Jones S.E., Gillis P.P., 1984, Generalized quadratic flow law for sheet metals, Metallurgical Transactions A 15: 129-132.
17
[18] Pishbin H., Gillis P.P., 1992, Forming limit diagrams calculated using Hill’s nonquadratic yield criterion, Metallurgical Transactions A 23: 2817-2831.
18
[19] Aghaie-Khafri M., Mahmudi R., 2004, Predicting of plastic instability and forming limit diagrams, International Journal of Mechanical Sciences 46: 1289-1306.
19
[20] Aghaie-Khafri M., Mahmudi R., Pishbin H., 2002, Role of yield criteria and hardening laws in the prediction of forming limit diagrams, Metallurgical Transactions A 33: 1363-1371.
20
[21] Noori H., Mahmudi R., 2007, Prediction of forming limit diagrams in sheet metals using different yield criteria, Metallurgical Transactions A 38: 2040-2052.
21
[22] Rezaee-Bazzaz A., Noori H., Mahmudi R., 2011, Calculation of forming limit diagrams using Hill’s 1993 yield criterion, International Journal of Mechanical Sciences 53: 262-270.
22
[23] Chung K., Kim H., Lee C., 2014, Forming limit criterion for ductile anisotropic sheets as a material property and its deformation path insensitivity. Part I: Deformation path insensitive formula based on theoretical models, International Journal of Plasticity 58: 3-34.
23
[24] Avila A.F., Vieira E.L.S., 2003, Proposing a better forming limit diagram prediction: a comparative study, Journal of Materials Processing Technology 141: 101-108.
24
[25] Chiba R., Takeuchi H., Kuroda M., Kuwabara T., 2013, Theoretical and experimental study of forming-limit strain of half-hard AA1100 aluminium alloy, Computational Materials Science 77: 61-71.
25
[26] Panich S., Barlat F., Uthaisangsuk V., Suranuntchai S., Jirathearanat S., 2013, Experimental and theoretical formability analysis using strain and stress based forming limit diagram for advanced high strength steels, Materials & Design 51 : 756-766.
26
[27] Assempour A., Hashemi R., Abrinia K., Ganjiani M., Masoumi E., 2009, A methodology for prediction of forming limit stress diagrams considering the strain path effect, Computational Materials Science 45: 195-204.
27
[28] Kuroda M., Tvergaard V., 2000, Forming limit diagrams for anisotropic metal sheets with different yield criteria, International Journal of Solids and Structures 37: 5037-5059.
28
[29] Hill R., 1979, Theoretical plasticity of textured aggregates, Mathematical Proceedings of the Cambridge Philosophical Society 75: 179-191.
29
[30] Lian J., Zhou D., Baudelet B., 1989, Application of Hill’s new yield theory to sheet metal forming part I. Hill’s 1979 criterion and its application to predicting sheet forming limit, International Journal of Mechanical Sciences 31: 237-247.
30
[31] Considére A., 1885, Annales des Ponts et Chaussées 9: 574-775.
31
[32] Bridgeman P.W., 1952, Studies in Large Plastic Flow and Fracture, McGraw-Hill, New York.
32
[33] Ghosh A.K., 1977, The Influence of Strain Hardening and Strain-Rate Sensitivity on Sheet Metal Forming, Trans ASME: Journal of Engineering Materials and Technology 99: 264-274.
33
[34] Hecker S.S., 1975, Formability of aluminum alloy sheets, Trans ASME: Journal of Engineering Materials and Technology 97: 66-73.
34
[35] Hill R., 1993, A user-friendly theory of orthotropic plasticity in sheet metals, International Journal of Mechanical Sciences 35:19-25.
35
ORIGINAL_ARTICLE
Wave Propagation in Fibre-Reinforced Transversely Isotropic Thermoelastic Media with Initial Stress at the Boundary Surface
The reflection and transmission of thermoelastic plane waves at an imperfect boundary of two dissimilar fibre-reinforced transversely isotropic thermoelastic solid half-spaces under hydrostatic initial stress has been investigated. The appropriate boundary conditions are applied at the interface to obtain the reflection and transmission coefficients of various reflected and transmitted waves with incidence of quasi-longitudinal (qP), quasi-thermal (qT) & quasi- transverse (qSV) waves respectively at an imperfect boundary and deduced for normal stiffness, transverse stiffness, thermal contact conductance and welded boundaries.The reflection and transmission coefficients are functions of frequency, initial stress and angle of incidence. There amplitude ratios are computed numerically and depicted graphically for a specific model to show the effect of initial stress. Some special cases are also deduced from the present investigation.
http://jsm.iau-arak.ac.ir/article_514649_7793e53f78c6f6bdbf9256f77404d22d.pdf
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223
238
Fibre-reinforced
Hydrostatic initial stress
Reflection
Transmission
Thermoelasticity
R
Kumar
rajneesh_kuk@rediffmail.com
true
1
Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, India
Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, India
Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, India
AUTHOR
S.K
Garg
true
2
Department of Mathematics, Deen Bandhu Chotu Ram Uni. of Sc. & Tech., Sonipat, Haryana,India
Department of Mathematics, Deen Bandhu Chotu Ram Uni. of Sc. & Tech., Sonipat, Haryana,India
Department of Mathematics, Deen Bandhu Chotu Ram Uni. of Sc. & Tech., Sonipat, Haryana,India
AUTHOR
S
Ahuja
sanjeev_ahuja81@hotmail.com
true
3
University Institute of Engg. & Tech., Kurukshetra University, Kurukshetra, Haryana, India
University Institute of Engg. & Tech., Kurukshetra University, Kurukshetra, Haryana, India
University Institute of Engg. & Tech., Kurukshetra University, Kurukshetra, Haryana, India
LEAD_AUTHOR
[1] Spencer A.J.M., 1941, Deformation of Fibre-Reinforced Materials, Clarendon Press, Oxford.
1
[2] Lord H.W., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15(5):299-309.
2
[3] Green A.E., Lindsay K.A.,1971, Thermoelasticity, Journal of Elasticity 2(1):1-7.
3
[4] Dhaliwal R.S., Sherief H.H.,1980, Generalized thermoelasticity for anisotropic media, The Quarterly of Applied Mathematics 33(1):1-8.
4
[5] Erdem A.U., 1995, Heat Conduction in fiber-reinforced rigid bodies, 10 Ulusal Ist Bilimi ve Tekmgi Kongrest, 6-8 Eylul, Ankara.
5
[6] Kumar R., Rani R., 2010, Study of wave motion in an anisotropic fibre-reinforced thermoelastic solid, Journal of Solid Mechanics 2(1):91-100.
6
[7] Deresiewicz H., 1960, Effect of boundaries on waves in a thermoelastic solid, Journal of the Mechanics and Physics of Solids 8(3):164-172.
7
[8] Sinha A.N., Sinha S.B., 1974, Reflection of thermoelastic waves at a solid half-space with thermal relaxation, Journal of Physics of the Earth 22(2):237-244.
8
[9] Sinha S.B., Elsibai K.A.,1966, Reflection of thermoelastic waves at a solid half-space with two relaxation times, Journal of Thermal Stresses 19(8):763-777.
9
[10] Sinha S.B., Elsibai K.A., 1997, Reflection and transmission of thermoelastic waves at an interface of two semi-infinite media with two relaxation times, Journal of Thermal Stresses 20(2):129-146.
10
[11] Singh B., 2002, Reflection of thermo-viscoelastic waves from free surface in the presence of magnetic field, Proceedings of the National Academy of Sciences, India,72A II,109-120.
11
[12] Abd-Alla A.N., Yahia A.A., Abo-Dabah S.M., 2003, On reflection of the generalized magneto-thermo-viscoelastic plane waves, Chaos, Solitons Fractals 16(2):211-231.
12
[13] Singh B., 2006, Reflection of SV waves from the free surface of an elastic solid in generalized thermoelastic diffusion, Journal of Sound and Vibration 291(3-5):764-778.
13
[14] Song Y.Q., Zhang Y.C., Xu H.Y., Lu B.H.,2006, Magneto-thermoelastic wave propagation at the interface between two micropolar viscoelastic media, Applied Mathematics and Computation 176 (2):785-802.
14
[15] Singh S., Khurana S., 2001, Reflection and transmission of P and SV waves at the interface between two monoclinic elastic half-spaces, Proceedings of the National Academy of Sciences, India ,71(A) IV.
15
[16] Kumar R., Singh M., 2008, Reflection/transmission of plane waves at an imperfectly bonded interface of two orthotropic generalized thermoelastic half space, Materials Science and Engineering 472(1-2):83-96.
16
[17] Biot M.A., 1965, Mechanics of Incremental Deformations, John Wiley and Sons, New York.
17
[18] Chattopadhyay A., Bose S., Chakraborty M., 1982, Reflection of elastic waves under initial stress at a free surface, The Journal of the Acoustical Society of America 72(1):255-263.
18
[19] Sidhu R.S., Singh S.J., 1983, Comments on “Reflection of elastic waves under initial stress at a free surface, The Journal of the Acoustical Society of America 74(5):1640-1642.
19
[20] Dey S., Roy N., Dutta A.,1985, Reflection and transmission of P-waves under initial stresses at an interface, Indian Journal of Pure and Applied Mathematics 16:1051-1071.
20
[21] Selim M.M., 2008, Reflection of plane waves at free surface of an initially stressed dissipative medium, Proceedings of World Academy of Sciences, Engineering and Technology.
21
[22] Montanaro A., 1999, On singular surface in isotropic linear thermoelasticity with initial stress, The Journal of the Acoustical Society of America 106(31):1586-1588.
22
[23] Singh B., Kumar A., Singh J.,2006, Reflection of generalized thermoelastic waves from a solid half-space under hydrostatic initial stress, Applied Mathematics and Computation 177(1):170-177.
23
[24] Singh B.,2008, Effect of hydrostatic initial stresses on waves in a thermoelastic solid half-space, Applied Mathematics and Computation 198(2):494-505.
24
[25] Othman M.I.A., Song Y., 2007, Reflection of plane waves from an elastic solid half-space under hydrostatic initial stress without energy dissipation, International Journal Solids and Structures 44 (17):5651-5664.
25
[26] Abd-Alla A.El.N., Alsheikh F.A., 2009, The effect of the initial stresses on the reflection and transmission of plane quasi-vertical transverse waves in piezoelectric materials, World Academy of Science, Engineering and Technology 3.
26
[27] Chattopadhyay A., Venkateswarlu R.L.K., Chattopadhyay A., 2007, Reflection and transmission of quasi P and SV waves at the interface of fibre-reinforced media, Advanced Studies in Theoretical Physics 1(2):57-73.
27
[28] Abbas I.A., Othman M.I.A., 2012, Generalized thermoelastic interaction in a fibre-reinforced anisotropic half-space under hydrostatic initial stress, Journal of Vibration and Control 18(2):175-182
28
[29] Singh S. S. and Zorammuana C., 2013, Incident longitudinal wave at a fibre-reinforced thermoelastic half-space, Journal of Vibration and Control 20(12):1895-1906.
29