ORIGINAL_ARTICLE
Nonlocal DQM for Large Amplitude Vibration of Annular Boron Nitride Sheets on Nonlinear Elastic Medium
One of the most promising materials in nanotechnology such as sensors, actuators and resonators is annular Boron Nitride sheets (ABNSs) due to excelled electro-thermo-mechanical properties. In this study, however, differential quadrature method (DQM) and nonlocal piezoelasticity theory are used to investigate the nonlinear vibration response of embedded single-layered annular Boron Nitride sheets (SLABNSs). The interactions between the SLABNSs and its surrounding elastic medium are simulated by nonlinear Pasternak foundation. A detailed parametric study is conducted to elucidate the influences of the nonlocal parameter, elastic medium, temperature change and maximum amplitude on the nonlinear frequency of the SLABNSs. Results indicate that with increasing nonlocal parameter, the frequency of the coupled system becomes lower. The results are in good agreement with the previous researches.
http://jsm.iau-arak.ac.ir/article_514607_65c6e9cdac5a7fb85065a2acbaaeb122.pdf
2014-12-30T11:23:20
2019-10-20T11:23:20
334
346
Nonlinear vibration
SLABNS
DQM
Nonlocal piezoelasticity theory
Nonlinear elastic medium
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
R
Kolahchi
true
2
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University of Kashan
AUTHOR
S.M.R
Allahyari
true
3
Faculty of Mechanical Engineering, University of Kashan, Kashan
Faculty of Mechanical Engineering, University of Kashan, Kashan
Faculty of Mechanical Engineering, University of Kashan, Kashan
AUTHOR
[1] Salvetat J.P., Bonard J.M., Thomson N.H., Kulik A.J., Forro L., Benoit W., Zuppiroli L., 1999, Mechanical properties of carbon nanotubes, Applied Physics A 69: 255-260.
1
[2] Baughman R.H., Zakhidov A.A., De Heer W.A., 2002, Carbon nanotubes--the route toward applications, Science 297:787-792.
2
[3] Ma R., Golberg D., Bando Y., Sasaki T., 2004, Syntheses and properties of B–C–N and BN nanostructures, The Royal Society 362: 2161-2186.
3
[4] Li Y., Dorozhkin P.S., Bando Y., Golberg D., 2005, Controllable modification of SiC nanowires encapsulated in BN nanotubes, Advanced Materials 17:545-549.
4
[5] Behfar K., Naghdabadi R., 2005, Nanoscale vibrational analysis of a multi-layered graphene sheet embedded in an elastic medium, Composite Science and Technology 65:1159-1164.
5
[6] Liew K.M., He X.Q., Kitipornchai S., 2006, Predicting nanovibration of multi-layered graphene sheets embedded in an elastic matrix, Acta Materiala 54:4229-4236.
6
[7] Pradhan S.C., Phadikar J.K., 2009, Nonlocal elasticity theory for vibration of nanoplates, Journal of Sound and Vibration 325:206-223.
7
[8] Shen L., Shen H.S., Zhang C.L., 2008, Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments, Computational Material Science 48:680-685.
8
[9] Ansari R., Rajabiehfard R., Arash B., 2010, Nonlocal finite element model for vibrations of embedded multi-layered graphene sheets, Computational Material Science 49:831-838.
9
[10] Pradhan S.C., Kumar A., 2010, Vibration analysis of orthotropic graphene sheets embedded in Pasternak elastic medium using nonlocal elasticity theory and differential quadrature method, Computational Material Science 50:239-245.
10
[11] Ghorbanpour Arani A., Kolahchi R., Mosallaie Barzoki A.A., Mozdianfard M.R., Noudeh Farahani S.M., 2012, Elastic foundation effect on nonlinear thermo-vibration of embedded double-layered orthotropic graphene sheets using differential quadrature method, Proceeding of IMech Part C: Journal of Mechanical Engineering Science 227:1-8.
11
[12] Mohammadi M., Ghayour M., Farajpour A., 2012, Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model, Composite Part B: Engineering 45:32-42.
12
[13] Salehi-Khojin A., Jalili N., 2008, Buckling of boron nitride nanotube reinforced piezoelectric polymeric composites subject to combined electro-thermo-mechanical loadings, Composite Science and Technology 68:1489-1501.
13
[14] Khodami Maraghi Z., Ghorbanpour Arani A., Kolahchi R., Amir S., Bagheri M.R., 2013, Nonlocal vibration and instability of embedded DWBNNT conveying viscose fluid, Composites Part B: Engineering 45:423-432.
14
[15] Ghorbanpour Arani A., Kolahchi R., Vossough H., 2012, Nonlocal wave propagation in an embedded DWBNNT conveying fluid via strain gradient theory, Physica B 407: 4281-4286.
15
[16] Ghorbanpour Arani A., Kolahchi R., Khoddami Maraghi Z., 2013, Nonlinear vibration and instability of embedded double-walled boron nitride nanotubes based on nonlocal cylindrical shell theory, Applied Mathematical Modeling 37: 7685-7707.
16
[17] Ke L.L., Wang Y.S., Wang Z.D., 2012, Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory, Composite Structures 94:2038-2047.
17
[18] 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.
18
[19] Salajeghe S., Khadem S.E., Rasekh M., 2012, Nonlinear analysis of thermoelastic damping in axisymmetric vibration of micro circular thin-plate resonators, Applied Mathematical Modeling 36:5991-6000.
19
[20] Malekzadeh P., Afsari A., Zahedinejad P., Bahadori R., 2010, Three-dimensional layerwise-finite element free vibration analysis of thick laminated annular plates on elastic foundation, Applied Mathematical Modeling 34:776-790.
20
[21] Sepahi O., Forouzan M.R., Malekzadeh P., 2010, Large deflection analysis of thermo-mechanical loaded annular FGM plates on nonlinear elastic foundation via DQM, Composite Structures 92: 2369-2378.
21
ORIGINAL_ARTICLE
Influence of the Elastic Foundation on the Free Vibration and Buckling of Thin-Walled Piezoelectric-Based FGM Cylindrical Shells Under Combined Loadings
In this paper, the influence of the elastic foundation on the free vibration and buckling of thin-walled piezoelectric-based functionally graded materials (FGM) cylindrical shells under combined loadings is investigated. The equations of motion are obtained by using the principle of Hamilton and Maxwell's equations and the Navier's type solution used to solve these equations. Material properties are changed according to power law in the direction of thickness. In this study, the effects of Pasternak elastic foundation coefficients and also the effects of material distribution, geometrical ratios and loading conditions on the natural frequencies are studied. It is observed that by increasing Pasternak elastic medium coefficients, the natural frequencies of functionally graded piezoelectric materials (FGPM) cylindrical shell always increases. The mode shapes of FGPM cylindrical shell has been shown in this research and the results show that the distribution of the radial displacements is more significant than circumferential and longitudinal displacements.
http://jsm.iau-arak.ac.ir/article_514608_4d70235e3f92c53466ff09c80efd0fbf.pdf
2014-12-30T11:23:20
2019-10-20T11:23:20
347
365
Buckling
Free Vibration
Elastic foundation
mode shapes
Thin-walled cylindrical shell
FGPM
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
M
Moradi
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
Loghman
aloghman@kashanu.ac.ir
true
3
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
[1] Yamanouchi M., Koizumi M., Hirai T., Shiota I., 1990, Functionally gradient materials, Proceedings of the first International Symposium on Functionally Gradient Materials 327-332.
1
[2] Koizumi M., 1993, The concept of FGM ceramic transactions, Functionally Graded Materials 34: 3-10.
2
[3] Pasternak P., 1954, On a New Method of Analysis of an Elastic Foundation by Means of Two Foundation Constants, Gosudarstvenneo Izdatelstvo Literaturi po Stroitelstvu Arkhitekture, Moscow, USSR.
3
[4] Loy CT., Lam KY., Reddy JN., 1999, Vibration of functionally graded cylindrical shells, International Journal of Mechanical Sciences 41: 309-324.
4
[5] Pradhan SC., Loy CT., Lam KY., Reddy JN., 2000, Vibration characteristics of functionally graded cylindrical shells under various boundary conditions, Applied Acoustics 61: 111-129.
5
[6] Najafizadeh M.M., Isvandzibaei M.R., 2007, Vibration of functionally graded cylindrical shells based on higher order shear deformation plate theory with ring support, Acta Mechanica 191: 75-91.
6
[7] Shah AG., Mahmood T., Naeem MN., Iqbal Z., Arshad SH., 2009, Vibrations of functionally graded cylindrical shells based on elastic foundations, Acta Mechanica 211: 293-307.
7
[8] Bhangale RK., Ganesan N., 2005, Free vibration studies of simply supported non-homogeneous functionally graded magneto-electro-elastic finite cylindrical shells, Journal of Sound and Vibration 288: 412-422.
8
[9] Kadoli R., Ganesan N., 2006, Buckling and free vibration analysis of functionally graded cylindrical shells subjected to a temperature-specified boundary condition, Journal of Sound and Vibration 289: 450-480.
9
[10] Malekzadeh P., Heydarpour Y., 2012, Free vibration analysis of rotating functionally graded cylindrical shells in thermal environment, Composite Structures 94: 2971-2981.
10
[11] Ebrahimi MJ., Najafizadeh MM., 2014, Free vibration analysis of two-dimensional functionally graded cylindrical shells, Applied Mathematical Modelling 38: 308-324.
11
[12] Sheng GG., Wang X., 2013, Nonlinear vibration control of functionally graded laminated cylindrical shells, Composites Part B: Engineering 52: 1-10.
12
[13] Du C., Li Y., 2013, Nonlinear resonance behavior of functionally graded cylindrical shells in thermal environments, Composite Structures 102: 164-174.
13
[14] Sofiyev AH., Kuruoglu N., 2013, Torsional vibration and buckling of the cylindrical shell with functionally graded coatings surrounded by an elastic medium, Composites Part B: Engineering 45: 1133-1142.
14
[15] Sheng GG., Wang X., 2013, An analytical study of the non-linear vibrations of functionally graded cylindrical shells subjected to thermal and axial loads, Composite Structures 97: 261-268.
15
[16] Rafiee M., Mohammadi M., Aragh BS., Yaghoobi H., 2013, Nonlinear free and forced thermo-electro-aero-elastic vibration and dynamic response of piezoelectric functionally graded laminated composite shells, Composite Structures 103: 188-196.
16
[17] Ghorbanpour Arani A., Bakhtiari R., Mohammadimehr M., Mozdianfard M.R., 2011, Electromagnetomechanical responses of a radially polarized rotating functionally graded piezoelectric shaft, Turkish Journal of Engineering & Environmental Sciences 36(1): 33-44.
17
[18] Khoshgoftar MJ., Ghorbanpour Arani A., Arefi M., 2009, Thermoelastic analysis of a thick walled cylinder made of functionally graded piezoelectric material, Smart Material Structures 18: 115007-115015.
18
[19] Sheng GG., Wang X., 2010, Thermoelastic vibration and buckling analysis of functionally graded piezoelectric cylindrical shells, Applied Mathematical Modelling 34: 2630-2643.
19
[20] Fernandes A., Pouget J., 2006, Structural response of composite plates equipped with piezoelectric actuators, Computer and Structures 84: 1459-1470.
20
[21] Bagherizadeh E., Kiani Y., Eslami M.R., 2011, Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation, Composite Structures 93: 3063-3071.
21
[22] Pouresmaeeli S., Fazelzadeh S.A., Ghavanloo E., 2012, Exact solution for nonlocal vibration of double-orthotropic nanoplates embedded in elastic medium, Composites Part B: Engineering 43: 3384-3390.
22
[23] Jafari A.A., Khalili S.M.R., Azarafza R., 2005, Transient dynamic response of composite circular cylindrical shells under radial impulse load and axial compressive loads, Thin-Walled Structures 43: 1763-1786.
23
[24] Dong K., Wang X., 2007, Wave propagation characteristics in piezoelectric cylindrical laminated shells under large deformation, Composite Structures 77: 171-181.
24
[25] Ghorbanpour Arani A., Fesharaki J.J., Mohammadimehr M., Golabi S., 2010, Electro-magneto-thermo-mechanical behaviors of a radially polarized FGPM thick hollow sphere, Journal of Solid Mechanics 2: 305-315.
25
[26] Heyliger P., 1997, A note on the static behavior of simply supported laminated piezoelectric cylinders, International Journal of Solid and Structures 34: 3781-3794.
26
[27] He Y., 2004, Heat capacity, thermal conductivity, and thermal expansion of barium titanate-based ceramics, Thermochimica Acta 419: 135-141.
27
[28] Ramirez F., Heyliger P.R., Pan E., 2006, Free vibration response of two-dimensional magneto-electro-elastic laminated plates, Journal of Sound and Vibrations 292: 626-644.
28
[29] Arani A.G., Jafarzadeh Jazi A., Abdollahian M., Mozdianfard M.R., Mohammadimehr M., Amir S., Exact solution for electrothermoelastic behaviors of a radially polarized FGPM Rotating Disk, Journal of Solid Mechanics 3: 244-257.
29
[30] Timoshenko S.P., 1922, On the transverse vibrations of bars of uniform cross-section, Philosophical Magazine 43: 125-131.
30
ORIGINAL_ARTICLE
Effect of Exponentially-Varying Properties on Displacements and Stresses in Pressurized Functionally Graded Thick Spherical Shells with Using Iterative Technique
A semi-analytical iterative method as one of the newest analytical methods is used for the elastic analysis of thick-walled spherical pressure vessels made of functionally graded materials subjected to internal pressure. This method is accurate, fast and has a reasonable order of convergence. It is assumed that material properties except Poisson’s ratio are graded through the thickness direction of the sphere according to an exponential distribution. For different values of inhomogeneity constant, distributions of radial displacement, radial stress, circumferential stress, and von Mises equivalent stress, as a function of radial direction, are obtained. A numerical solution, using finite element method (FEM), is also presented. Good agreement was found between the semi-analytical results and those obtained through FEM.
http://jsm.iau-arak.ac.ir/article_514609_daba96cb9823ab0c4d017834bffe8185.pdf
2014-12-30T11:23:20
2019-10-20T11:23:20
366
377
Iterative technique
Elastic analysis
Functionally graded material (FGM)
Thick sphere
Exponential
M
Zamani Nejad
m_zamani@yu.ac.ir
true
1
Mechanical Engineering Department, Yasouj University
Mechanical Engineering Department, Yasouj University
Mechanical Engineering Department, Yasouj University
LEAD_AUTHOR
A
Rastgoo
arastgo@ut.ac.ir
true
2
Mechanical Engineering Department, University of Tehran
Mechanical Engineering Department, University of Tehran
Mechanical Engineering Department, University of Tehran
AUTHOR
A
Hadi
true
3
Mechanical Engineering Department, University of Tehran
Mechanical Engineering Department, University of Tehran
Mechanical Engineering Department, University of Tehran
AUTHOR
[1] Zenkour A. M., 2012, Dynamical bending analysis of functionally graded infinite cylinder with rigid core, Applied Mathematics and Computation 218: 8997-9006.
1
[2] Kalali A. T., Hadidi-Moud S., 2013, A semi-analytical approach to elastic-plastic stress analysis of FGM pressure vessels, Journal of Solid Mechanics 5(1): 63-73.
2
[3] Shariyat M., 2009, A rapidly convergent nonlinear transfinite element procedure for transient thermoelastic analysis of temperature-dependent functionally graded cylinders, Journal of Solid Mechanics 1(4): 313-327.
3
[4] Tutuncu N., Ozturk M., 2000, Exact solutions for stresses in functionally graded pressure vessels, Composites Part B-Engineering 32(8): 683-686.
4
[5] You L. H., Zhang J. J., You X. Y., 2005, Elastic analysis of internally pressurized thick-walled spherical pressure vessels of functionally graded materials, International Journal of Pressure Vessels and Piping 82(5): 347-354.
5
[6] Chen Y. Z., Lin X. Y., 2008, Elastic analysis for thick cylinders and spherical pressure vessels made of functionally graded materials, Computational Materials Science 44(2): 581-587.
6
[7] Li X. F., Peng X. L., 2009, Kang Y. A., Pressurized hollow spherical vessels with arbitrary radial nonhomogeneity, AIAA Journal 47(9): 2262-2265.
7
[8] Tutuncu N., Temel B., 2009, A novel approach to stress analysis of pressurized FGM cylinders, disks and spheres, Composite Structures 91(3): 385-390.
8
[9] Nejad M. Z., Rahimi G. H., Ghannad M., 2009, Set of field equations for thick shell of revolution made of functionally graded materials in curvilinear coordinate system, Mechanika 77(3): 18-26.
9
[10] Borisov A. V., 2010, Elastic analysis of multilayered thick-walled spheres under external load, Mechanika 84(4): 28-32.
10
[11] Nie G. J., Zhong Z., Batra R. C., 2011, Material tailoring for functionally graded hollow cylinders and spheres, Composites Science and Technology 71(5): 666-673.
11
[12] Ghannad M., Nejad M. Z., 2012, Complete closed-form solution for pressurized heterogeneous thick spherical shells, Mechanika 18(5): 508-516.
12
[13] Nejad M. Z., Abedi M., Lotfian M. H., Ghannad M., 2012, An exact solution for stresses and displacements of pressurized FGM thick-walled spherical shells with exponential-varying properties, Journal of Mechanical Science and Technology 26(12): 4081-4087.
13
[14] Hassani A., Hojjati M. H., Farrahi G., Alashti R. A., 2011, Semi-exact elastic solutions for thermo-mechanical analysis of functionally graded rotating disks, Composite Structures 93: 3239-3251.
14
[15] Adomian G., 1998, A review of the decomposition method in applied mathematics, Journal of Mathematical Analysis and Applications 135: 501-544.
15
[16] He J.H., 1999, Homotopy perturbation technique, Computer Methods in Applied Mechanics and Engineering 178: 257-262.
16
[17] He J.H., 2004, Comparison of homotopy perturbation method and homotopy analysis method, Applied Mathematics and Computation 156: 527-539.
17
[18] He J.H., 2004, Asymptotology by homotopy perturbation method, Applied Mathematics and Computation 156: 591-596.
18
[19] He J.H., 2005, Homotopy perturbation method for bifurcation of nonlinear problems, International Journal of Nonlinear Sciences and Numerical Simulation 6: 207-208.
19
[20] He J.H., 2005, Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons & Fractals 26: 695-700.
20
[21] He J.H., 2006, Some asymptotic methods for strongly nonlinear equations, International Journal of Modern Physics B 20: 1141-1199.
21
[22] Olver P. J., 1996, Applications of Lie Groups to Differential Equations, Berlin, Springer.
22
[23] Gardner C. S., Kruskal M. D., Miura R. M., 1967, Method for solving the Korteweg-de Vries equation, Physical Review Letters 19: 1095-1097.
23
[24] Hirota R., 1971, Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons, Physical Review Letters 27: 1192-1194.
24
[25] Wang M. L., Exact solutions for a compound KdV-Burgers equation, Physical Review Letters 213: 279-287.
25
[26] He J.H., 2000, Variational iteration method for autonomous ordinary differential systems, Applied Mathematics and Computation 114: 115-123.
26
[27] He J.H., 1998, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Computer Methods in Applied Mechanics and Engineering 167: 57-68.
27
[28] He J.H., 1998, Approximate solution of nonlinear differential equations with convolution product nonlinearities, Computer Methods in Applied Mechanics and Engineering 167: 69-73.
28
[29] He J.H., Wu X.H., 2006, Construction of solitary solution and compacton-like solution by variational iteration method, Chaos Solitons & Fractals 29: 108-113.
29
[30] Hojjati M. H., Jafari S., 2007, Variational iteration solution of elastic non uniform thickness and density rotating disks, Far East Journal of Applied Mathematics 29: 185-200.
30
[31] Hojjati M. H., Jafari S., 2008, Semi-exact solution of elastic non-uniform thickness and density rotating disks by homotopy perturbation and Adomian’s decomposition methods, International Journal of Pressure Vessels and Piping 85: 871-878.
31
[32] Hojjati M. H., Jafari S., 2009, Semi-exact solution of non-uniform thickness and density rotating disks, International Journal of Pressure Vessels and Piping 86: 307-318.
32
[33] Asghari M., Ghafoori E., 2010, A three-dimensional elasticity solution for functionally graded rotaing disks, Composite Structures 92: 1092-1099.
33
[34] Temimi H., Ansari A. R., 2011, A semi-analytical iterative technique for solving nonlinear problems, Computers & Mathematics with Applications 61: 203-210.
34
[35] Temimi H., Ansari A. R., 2011, A new iterative technique for solving nonlinear second order multi-point boundary value problems, Applied Mathematics and Computation 218: 1457-1466.
35
ORIGINAL_ARTICLE
A Cohesive Zone Model for Crack Growth Simulation in AISI 304 Steel
Stable ductile crack growth in 3 mm thick AISI 304 stainless steel specimens has been investigated experimentally and numerically. Multi-linear Isotropic Hardening method coupled with the Von-Mises yield criterion was adopted for modeling elasto-plastic behavior of the material. Mode-I CT fracture specimens have been tested to generate experimental load-displacement-crack growth data during stable crack growth. The critical fracture energy (JIc) was then determined using the finite elements results in conjunction with the experimental data. The effect of in-plane constraints on the numerical-experimental JIc calculation was then investigated. The results of finite element solution were used to tailor an exponential CZM model for simulation of mode-I stable crack growth in CT specimens. It is found that the adopted CZM is generally insensitive to the applied constraints to the crack tip stress state and thus it can effectively be used for simulating crack growth in this material.
http://jsm.iau-arak.ac.ir/article_514610_34ed2330e62064812a02812396c95950.pdf
2014-12-30T11:23:20
2019-10-20T11:23:20
378
388
Cohesive zone model
Finite Element
CT specimen
In-plane constraint
AISI 304 steel
F
Javidrad
f_javidrad@yahoo.com
true
1
Center for Postgraduate Studies, Aeronautical University of Science and Technology, Tehran
Center for Postgraduate Studies, Aeronautical University of Science and Technology, Tehran
Center for Postgraduate Studies, Aeronautical University of Science and Technology, Tehran
LEAD_AUTHOR
M
Mashayekhy
true
2
Center for Postgraduate Studies, Aeronautical University of Science and Technology, Tehran
Center for Postgraduate Studies, Aeronautical University of Science and Technology, Tehran
Center for Postgraduate Studies, Aeronautical University of Science and Technology, Tehran
AUTHOR
[1] Kim J., Gao X., Srivatsan T.S., 2003, Modeling of crack growth in ductile solids: a three-dimensional analysis, International Journal of Solids and Structures 40(26): 7357-7374.
1
[2] Wei Z., Deng X., Sutton M.A., Yang J., Cheng C. S., Zavattieri P., 2011, Modeling of mixed-mode crack growth in ductile thin sheets under combined in-plane and out-of-plane loading, Engineering Fracture Mechanics 78(17): 3082-3101.
2
[3] Zhu X.K., Joyce J.A., 2012, Review of fracture toughness (G, K, J, CTOD, CTOA) testing and standardization, Engineering Fracture Mechanics 85(1): 1-46.
3
[4] Pirondi A., Fersini D., 2009, Simulation of ductile crack growth in thin panels using the crack tip opening angle, Engineering Fracture Mechanics 76(1): 88-100.
4
[5] Li H., Fu M.W., Lu J., Yang H., 2011, Ductile fracture: experiments and computations, International Journal of Plasticity 27( 2): 147-180.
5
[6] Jackiewicz J., Kuna M., 2003, Non-local reqularization for FE simulation of damage in ductile materials, Computational Materials Science 28(3-4): 784-695.
6
[7] Barenblatt G.I., 1959, Equilibrium cracks formed during brittle fracture, Journal of Applied Mathematics and Mechanics 23: 1273-1282.
7
[8] Dugdale D.S., 1960, Yielding of steel sheets containing slits, Journal of the Mechanics and Physics of Solids 8: 100-104.
8
[9] Rahulkumar P., Jagota A., Bennison S.J., Saigal S., 2000, Cohesive element modeling of viscoelastic fracture: application to peel testing of polymers, International Journal of Solids and Structures 37: 1873-1897.
9
[10] Siegmund T., Brocks W., 2000, A numerical study on the correlation between the work of separation and the dissipation rate in ductile fracture, Engineering Fracture Mechanics 67: 139-154.
10
[11] Camacho G.T., Ortiz, M., 1996, Computational modeling of impact damage in brittle materials, International Journal of Solids and Structures 33: 2899-2938.
11
[12] Mohammed I., Liechti K.M., 2000, Cohesive zone modeling of crack nucleation at bimaterial corners, Journal of the Mechanics and Physics of Solids 48: 735-764.
12
[13] Roesler J., Paulino G.H., Park K., Gaedicke C., 2007, Concrete fracture prediction using bilinear softening, Cement and Concrete Composites 29: 300-312.
13
[14] Shim D. J., Paulino G.H., Dodds Jr. R.H., 2006, J resistance behavior in functionally graded materials using cohesive zone and modified boundary layer models, International Journal of Fracture 13: 91-117.
14
[15] Aronsson C.G., Backlund J., 1986, Tensile fracture of laminates with cracks, Journal of Composite Materials 20: 287-307.
15
[16] Espinosa H.D., Dwivedi S., Lu H.C., 2000, Modeling impact induced delamination of woven fiber reinforced composites with contact/cohesive laws, Computer Methods in Applied Mechanics and Engineering 183: 259-290.
16
[17] Song S.J., Wass A.M., 1995, Energy-based mechanical model for mixed-mode failure of laminated composites, AIAA Journal 33: 739-745.
17
[18] Kubair D.V., Geubelle P.H., Huang Y.Y., 2003, Analysis of rate –dependent cohesive model for dynamic crack propagation, Engineering Fracture Mechanics 70: 685-704.
18
[19] Liong R. T., 2011, Application of the Cohesive Zone Model to the Analysis of Rotors with a Transverse Crack, Karlsruher Institut Fur Technologie, KIT Scientific Publishing, Karlsruhe, Germany.
19
[20] Wang J.T., 2010, Relating Cohesive Zone Models to Linear Elastic Fracture Mechanics, NASA/TM-2010-216692, National Aeronautics and Space Administration, USA.
20
[21] Scheider I., Brocks W., 2003, Simulation of cup-cone fracture using the cohesive model, Engineering Fracture Mechanics 70: 1943-1961.
21
[22] Cornec A., Schonfeld W., Schwalbe K. H., Scheider I., 2009, Application of the cohesive model for predicting the residual strength of a large scale fuselage structure with a two-bay crack, Engineering Failure Analysis 16: 2541-2558.
22
[23] Li W., Siegmund T., 2002, An analysis of crack growth in thin-sheet metal via a cohesive zone model, Engineering Fracture Mechanics 69: 2073-2093.
23
[24] Chen J., Fox D., 2012, Numerical investigation into multi-delamination failure of composite t-piece specimens under mixed-mode loading using a modified cohesive zone model, Composite Structures 94(6): 2010-2016.
24
[25] Tvergaard V., Needleman A., 1984, Analysis of the cup-cone fracture in a round tensile bar, Acta Metallurgica 32: 157-169.
25
[26] Needleman A., Tvergaard V., 1984, An analysis of ductile rupture in notched bars, Journal of the Mechanics and Physics of Solids 32: 461-490.
26
[27] Li H., Chandra N., 2003, Analysis of crack growth and crack-tip plasticity in ductile materials using cohesive zone models, International Journal of Plasticity 19: 849-882.
27
[28] Tvergaard V., 2001, Crack growth predictions by cohesive zone model for ductile fracture, Journal of the Mechanics and Physics of Solids 49: 2191-2207.
28
[29] Geubelle P.H., Baylor J., 1998, Impact-induced delamination of laminated composites: a 2D simulation, Composites 29: 589-602.
29
[30] Fernandes R.M.R.P., Chousal J.A.G., De Moura M.F.S.F., Xavier J., 2013, Determination of the cohesive laws of composite bonded joints under mode-II loading, Composites Part B: Engineering 52: 269-274.
30
[31] Dourado N., Pereira F.A.M., De Moura M.F.S.F., Morais J.J.L., Dias M.I.R., 2013, Bone fracture characterization using the end notched flexure tests, Materials Science and Engineerin C 33(1): 405-410.
31
[32] Zou Z., Reid S.R., Li S., 2003, A continuum damage model for delamination in laminated composites, Journal of the Mechanics and Physics of Solids 51(2): 333-356.
32
[33] Xu X. P., Needleman A., 1993, Void nucleation by inclusion debonding in a crystal matrix, Modeing and Simulation in Materials Science and Engineering 1: 111-132.
33
[34] Hsu C. L., Lo J., Yu J., Lee X. G., Tan P., 2003, Residual strength analysis using CTOA criteria for fuselage structures containing multiple site damage, Engineering Fracture Mechanics 70: 525-545.
34
[35] James M.A., Newman Jr. J.C., 2003, The effect of crack tunneling on crack growth: experiments and CTOA analysis, Engineering Fracture Mechanics 70: 457-468.
35
[36] Anandarajah A., 2010, Computational Methods in Elasticity and Plasticity: Solids and Porous Media, Springer Science International.
36
ORIGINAL_ARTICLE
Nonlinear Vibration Analysis of the Beam Carrying a Moving Mass Using Modified Homotopy
In the present study, the analysis of nonlinear vibration for a simply-supported flexible beam with a constant velocity carrying a moving mass is studied. The amplitude of vibration assumed high and its deformation rate is assumed slow. Due to the high amplitude of vibrations, stretching is created in mid-plane, resulting in, the nonlinear strain-displacement relations is obtained, Thus, Nonlinear terms governing the vibrations equation is revealed. Modified homotopy equation is employed for solving the motion equations. The results shown that this method has high accuracy. In the following, analytical expressions for nonlinear natural frequencies of the beams have been achieved. Parametric studies indicated that, due to increasing of the velocity concentrated mass, the nonlinear vibration frequency is reduced. On the other hand, whatever the mass moves into the middle of beam, beam frequency decreases.
http://jsm.iau-arak.ac.ir/article_514611_64c43ed760938831ead683b766feb64f.pdf
2014-12-30T11:23:20
2019-10-20T11:23:20
389
396
Non-linear vibration
Modified homotopy
Concentrated mass
M
Poorjamshidian
true
1
Department of Mechanical Engineering, Imam Hossein University
Department of Mechanical Engineering, Imam Hossein University
Department of Mechanical Engineering, Imam Hossein University
AUTHOR
J
Sheikhi
true
2
Civil Engineering, Imam Hossein University
Civil Engineering, Imam Hossein University
Civil Engineering, Imam Hossein University
AUTHOR
S
Mahjoub-Moghadas
true
3
Department of Mechanical Engineering, Imam Hossein University
Department of Mechanical Engineering, Imam Hossein University
Department of Mechanical Engineering, Imam Hossein University
LEAD_AUTHOR
M
Nakhaie
true
4
Department of Mechanical Engineering, Imam Hossein University
Department of Mechanical Engineering, Imam Hossein University
Department of Mechanical Engineering, Imam Hossein University
AUTHOR
[1] Ahmadian M.T., Mojahedi M., 2009, Free vibration analysis of a nonlinear beam using homotopy and modified lindstedt-poincare methods, Journal of Solid Mechanic 2(1): 29-36.
1
[2] Nayfeh A.H., Mook D.T., 1979, Nonlinear Oscillations, First Ed, New York, Wiley.
2
[3] Shames I.H., Dym C.L., 1985, Energy and Finite Element Methods in Structural Mechanics, First Ed, New York, McGraw-Hill.
3
[4] Malatkar P., 2003, Nonlinear Vibrations of Cantilever Beams and Plates, Virginia, Virginia Polytechnic Institute.
4
[5] Pirbodaghi T., Ahmadian M.T., Fesanghary M., 2009, On the homotopy analysis method for non-linear vibration of beams, Mechanics Research Communications 36(2):143-148.
5
[6] Sedighi H. M., Shirazi K. H., Zare J., 2012, An analytic solution of transversal oscillation of quantic non-linear beam with homotopy analysis method, International Journal of Non-Linear Mechanics 47(1): 777-784.
6
[7] Foda M.A., 1998, Influence of shear deformation and rotary inertia on nonlinear free vibration of a beam with pinned Ends, Journal Computers and Structures 71(20): 663-670.
7
[8] Rafiee R., 2012, Analysis of nonlinear vibrations of a carbon nanotube using perturbation technique, Journal of Mechanics Modares 12(1): 60-67.
8
[9] Ramezani A., Alasty A., Akbari J., 2006, Effects of rotary inertia and shear deformation on nonlinear free vibration of microbeams, ASME Journal of Vibration and Acoustics 128(2): 611-615.
9
[10] Sedighi H. M., Shirazi K. H., Zare J., 2012, Novel equivalent function for deadzone nonlinearity: applied to analytical solution of beam vibration using He’s parameter expanding method, Latin Am Journal of Solids Structure 9(1): 130-138.
10
[11] Barari A., Kaliji H.D., Ghadami M., Domairry G., 2011, Non-linear vibration of Euler- Bernoulli beams, Latin Am Journal of Solids Structure 8(2): 139-148.
11
[12] Aghababaei O., Nahvi H., Ziaei-Rad S., 2009 , Dynamic bifurcation and sensitivity analysis on dynamic responses of geometrically imperfect base excited cantilevered beams, Journal of Vibro engineering 13(1): 52-65.
12
[13] Sarma B.S., Vardan T.K., Parathap H., 1988, On various formulation of large amplitude free vibration of beams, Journal of Computers and Structures 29(1): 959-966.
13
[14] Parnell L.A., Cobble M.H., 1976, Lateral displacement of a cantilever beam with a concentrated mass, Journal of Sound and Vibration 44(2): 499-510.
14
[15] Chin C.M., Nayfeh A.H., 1997, Three-to-one internal resonance in hinged-clamped beams, Journal of the Nonlinear Dynamics 12(1): 129-154.
15
[16] Pan L., 2007, Stability and local bifurcation in a simply-supported beam carrying a moving mass, Acta Mechanica Solida Sinica 20(2):123-129.
16
[17] Rafieipor H., Lotfavar A., Shalamzari S.H., 2012, Nonlinear vibration analysis of functionally graded beam on winkler-pasternak foundation under mechanical and thermal loading via homotopy analysis method, Journal of Mechanics Modares 12(5): 87-101.
17
[18] Beléndez A., 2009, Homotopy perturbation method for a conservative x1/3 force nonlinear oscillator, Journal of Computers and Mathematics with Applications 58(3): 2267-2273.
18
[19] Xu M.R., Xu S.P., Guo H.Y., 2010, Determination of natural frequencies of fluid-conveying pipes using homotopy perturbation method, Journal of Computers and Mathematics with Applications 60:520-527.
19
ORIGINAL_ARTICLE
Plastic Wave Propagation Model for Perforation of Metallic Plates by Blunt Projectiles
In this paper, a six-stage interactive model is presented for the perforation of metallic plates using blunt deformable projectiles when plastic wave propagation in both target and projectile is considered. In this analytical model, it is assumed that the projectile and target materials are rigid – plastic linear work hardened. The penetration of the projectile into the target is divided into six stages and governing equations are derived. The analytical model shows that residual velocity, diameter of the flattening area of the projectile, and ballistic limit velocity, show close agreement with the data from experiment.
http://jsm.iau-arak.ac.ir/article_514612_062800a208f4a543fb2e0b6dc1e254b7.pdf
2014-12-30T11:23:20
2019-10-20T11:23:20
397
409
Projectile
Target
Plastic wave
Plugging
Perforation
Impact
S
Feli
felisaeid@gmail.com
true
1
Department of Mechanical Engineering, Razi University, Kermanshah
Department of Mechanical Engineering, Razi University, Kermanshah
Department of Mechanical Engineering, Razi University, Kermanshah
LEAD_AUTHOR
S
Noritabar
true
2
Department of Mechanical Engineering, Razi University, Kermanshah
Department of Mechanical Engineering, Razi University, Kermanshah
Department of Mechanical Engineering, Razi University, Kermanshah
AUTHOR
[1] Backman M. E., Goldsmith W., 1978, The mechanics of penetration of projectiles into targets, International Journal of Engineering Science 16:1-99.
1
[2] Anderson J. R., Morris B. L., Littlefield D. L., 1992, A penetration mechanics database, Southwest Research Institute Report 3593/001.
2
[3] Goldsmith W., 1999, Non ideal projectile impact on targets, International Journal of Impact Engineering 22: 95-395.
3
[4] Whiffin A.C., 1948, The use of flat-ended projectiles for determining dynamical yield stress. II. Test on various metallic materials, Proceedings the Royal Society 194 (1038): 300-322.
4
[5] Taylor G.I., 1948, The use of flat-ended projectiles for determining dynamical yield stress. I. Theoretical consideration, Proceedings the Royal Society 194 (1038): 289-299.
5
[6] Hashmi M. S. J., Thompson P.J., 1977, A numerical method of analysis for the mushrooming of flat- ended projectiles impinging on a flat rigid anvil, International Journal of Mechanical Sciences 19: 273-283.
6
[7] Awerbuch J., Bodner S.R., 1974, Analysis of the mechanics of perforation of projectiles in metallic plates, International Journal of Solids and Structures 10(1): 671-684.
7
[8] Ravid M., Bodner S. R., 1983, Dynamic perforation of viscoplastic plates by rigid projectiles, International Journal of Engineering Science 21: 577-591.
8
[9] Liss J., Goldsmith W., Kelly J.M., 1983, A phenomenological penetration model of plates, International Journal of Impact Engineering 1(4): 321-341.
9
[10] Wenxue Y., Lanting Z., Xiaoqing M. , Strong W. J., 1983, Plate perforation by deformable projectiles- a plastic wave theory, International Journal of Impact Engineering 1(4): 393-412.
10
[11] Chen X.W., Li Q.M., 2003, Shear plugging and perforation of ductile circular plates struck by a blunt projectile, International Journal of Impact Engineering 28: 513-536.
11
[12] Zukas J.A., 1990, High Velocity Impact Dynamic, John Wily and Sons.
12
[13] Lai W.M., Rubin D., Kremp E., 1999, Introduction to Continuum Mechanics, Third Edition, Butterworth-Heinemann.
13
[14] Forrestal M.J. , Hanchak S., 1999, Penetration experiments on HY-100 steel plates with 4340 Rc 38 and maraging T-250 steel rod projectiles, International Journal of Impact Engineering 22: 923-933.
14
[15] Liu D., Stronge W.J., 2000, Ballistic limit of metal plates struck by blunt deformable missiles: experiments, International Journal of Solids and Structures 37: 1403-1423.
15
[16] Borvik T., Langseth M., Hopperstad O.S., 1999, Ballistic penetration of steel plates, International Journal of Impact Engineering 22:855-886.
16
ORIGINAL_ARTICLE
Crack Interaction Studies Using XFEM Technique
In this paper, edge crack problems under mechanical loads have been analysed using extended finite element method (XFEM) as it has proved to be a competent method for handling problems with discontinuities. The XFEM provides a versatile technique to model discontinuities in the solution domain without re-meshing or conformal mesh. The stress intensity factors (SIF) have been calculated by domain based interaction integral method. The effect of crack orientation and interaction under mechanical loading has been studied. Analytical solutions, which are available for two dimensional displacement fields in linear elastic fracture mechanics, have been used for crack tip enrichment. From the present analysis, it has been observed that there is monotonous decrease in the SIF-1 value with the increase in inclination, while SIF-II values first increases then it also decreases. Next study was performed for first edge crack in the presence of second crack on opposite edge. The results were obtained by changing the distance between the crack tips as well as by changing the orientation of second crack. SIFs values decrease with increase in distances between the crack tips for collinear cracks. In next study, for the first crack in presence of inclined second edge crack and it was found that SIFs increase initially with the increase in inclination and decrease after that. It emphasizes the fact that cracks at larger distances act more or less independently. In next study, with the use of level set method crack growth path is evaluated without remeshing for plate with hole, soft inclusion & hard inclusion under mode-I loading and compare with available published results.
http://jsm.iau-arak.ac.ir/article_514613_b9c487bcb03d6ca765e6928da9e78ffd.pdf
2014-12-30T11:23:20
2019-10-20T11:23:20
410
421
XFEM
Crack interaction
Fracture mechanics
K
Sharma
kamals@barc.gov.in
true
1
Reactor Safety Divison, Bhabha Atomic Research Centre, Trombay, Mumbai
Reactor Safety Divison, Bhabha Atomic Research Centre, Trombay, Mumbai
Reactor Safety Divison, Bhabha Atomic Research Centre, Trombay, Mumbai
LEAD_AUTHOR
[1] Belytschko T., Black T., 1999, Elastic crack growth in finite elements with minimal remeshing, International Journal for Numerical Methods in Engineering 45: 601-620.
1
[2] Melenk J. M., Babuska I., 1996, The partition of unity finite element method: basic theory and applications, Computer Methods in Applied Mechanics and Engineering 139: 289-314.
2
[3] Babuska I., Melenk J. M., 1997, The partition of unity method, International Journal for Numerical Methods in Engineering 40: 727-758.
3
[4] Fleming M., Chu Y. A., Moran B., Belytschko T., 1997, Enriched element-free Galerkin methods for crack-tip fields, International Journal for Numerical Methods in Engineering 40 : 1483-1504.
4
[5] Moës N., Dolbow J., Belytschko T., 1999, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering 46: 131-150.
5
[6] Daux C., Moës N., Dolbow J., Sukumar N., Belytschko T., 2000, Arbitrary branched and intersecting cracks with the extended finite element method, International Journal for Numerical Methods in Engineering 48: 1741-1760.
6
[7] Sukumar N., Moës N., Moran B., Belytschko T., 2000, Extended finite element method for three-dimensional crack modelling, International Journal for Numerical Methods in Engineering 48: 1549-1570.
7
[8] Dolbow J., Moës N., Belytschko T., 2000, Modelling fracture in Mindlin–Reissner plates with the extended finite element method, International Journal of Solids and Structures 37: 7161-7183.
8
[9] Dolbow J., Moës N., Belytschko T., 2001, An extended finite element method for modeling crack growth with frictional contact, Computer Methods in Applied Mechanics and Engineering 190: 6825-6846.
9
[10] Areias P., Belytschko T., 2005, Analysis of three-dimensional crack initiation and propagation using exteneded finite element method, International Journal for Numerical Methods in Engineering 63: 760-788.
10
[11] Nagashima T., Omoto Y., Tani S., 2003, Stress intensity factor analysis of interface cracks using X-FEM, International Journal of Numerical Methods in Engineering 56: 1151-1173.
11
[12] Liu X. Y., Xiao Q. Z., Karihaloo B. L., 2004, XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi-materials, International Journal of Numerical Methods in Engineering 59: 1113-1118.
12
[13] Sukumar N., Chopp D. , Moes N., Belytschko T., 2001, Modelling holes and inclusions by level sets in the extended finite element method, Computer Methods in Applied Mechanics and Engineering 190: 6183-6200.
13
[14] Alves M., Rossi R., 2003, A modidied element-free galerkin method with essential boundary conditions enforced by an extended partition of unity finite element weight function, International Journal for Numerical Methods in Engineering 57 : 1523-1552.
14
[15] Sukumar N., Prévost J. H., 2003, Modelling quasi-static crack growth with the extended finite element method Part I: Computer implementation, International Journal of Solids and Structures 40: 7513-7537.
15
[16] Huang R., Sukumar N., Prévost J. H. , 2003, Modeling quasi-static crack growth with the extended finite element method Part II: Numerical applications, International Journal of Solids and Structures 40: 7539-7552.
16
[17] Zi G., Belytschko T., 2003, New crack-tip elements for XFEM and applications to cohesive cracks, International Journal for Numerical Methods in Engineering 57: 2221-2240.
17
[18] Mergheim J., Kuhl E., Steinmann P., 2005, A finite element method for the computational modelling of cohesive cracks, International Journal for Numerical Methods in Engineering 63: 276-289.
18
[19] Sukumar N., Huang Z. Y., Prévost J. H., Suo Z., 2004, Partition of unity enrichment for bimaterial interface cracks, International Journal for Numerical Methods in Engineering 59: 1075-1102.
19
ORIGINAL_ARTICLE
Response of GN Type II and Type III Theories on Reflection and Transmission Coefficients at the Boundary Surface of Micropolar Thermoelastic Media with Two Temperatures
In the present article, the reflection and transmission of plane waves at the boundary of thermally conducting micropolar elastic media with two temperatures is studied. The theory of thermoelasticity with and without energy dissipation is used to investigate the problem. The expressions for amplitudes ratios of reflected and transmitted waves at different angles of incident wave are obtained. Dissipation of energy and two temperature effects on these amplitude ratios with angle of incidence are depicted graphically. Some special and particular cases are also deduced.
http://jsm.iau-arak.ac.ir/article_514614_8a65a9dac6fd112c58d2c204b590f67d.pdf
2014-12-30T11:23:20
2019-10-20T11:23:20
422
440
Micropolar thermoelastic media
Two temperatures
Reflection and transmission coefficients
Amplitude ratios
Energy Dissipation
R
Kumar
rajneesh_kuk@rediffmail.com
true
1
Department of Mathematics, Kurukshetra University, Kurukshetra
Department of Mathematics, Kurukshetra University, Kurukshetra
Department of Mathematics, Kurukshetra University, Kurukshetra
AUTHOR
M
Kaur
mandeep1125@yahoo.com
true
2
Department of Applied Sciences, Guru Nanak Dev Engineering College, Ludhiana
Department of Applied Sciences, Guru Nanak Dev Engineering College, Ludhiana
Department of Applied Sciences, Guru Nanak Dev Engineering College, Ludhiana
LEAD_AUTHOR
S.C
Rajvanshi
true
3
Department of Applied Sciences, Gurukul Vidyapeeth Institute of Engineering and Technology, Sector-7, Banur, District Patiala
Department of Applied Sciences, Gurukul Vidyapeeth Institute of Engineering and Technology, Sector-7, Banur, District Patiala
Department of Applied Sciences, Gurukul Vidyapeeth Institute of Engineering and Technology, Sector-7, Banur, District Patiala
AUTHOR
[1] Eringen A.C., 1966, Linear theory of micropolar elasticity, Journal of Applied Mathematics and Mechanics 15:909-923.
1
[2] Eringen A.C., 1970, Foundations of Micropolar Thermoelasticity, International Centre for Mechanical Science, Springer-Verlag, Berlin.
2
[3] Nowacki W., 1986, Theory of Asymmetric Elasticity, Oxford, Pergamon.
3
[4] Dost S., Taborrok B., 1978, Generalized micropolar thermoelasticity, International Journal of Engineering Science 16:173-178.
4
[5] Chandrasekharaiah D.S., 1986, Heat flux dependent micropolar thermoelasticity, International Journal of Engineering Science 24:1389-1395.
5
[6] Boschi E., Iesan D., 1973, A generalized theory of linear micropolar thermoelasticity, Meccanica 7:154-157.
6
[7] Boley B. A., Tolins I. S., 1962, Transient coupled thermoelastic boundary value problems in the half-space, Journal of Applied Mechanics 29: 637-646.
7
[8] Chen P.J., Gurtin M.E., Williams W.O., 1968, A note on non simple heat conduction, Zeitschrift für Angewandte Mathematik und Physik 19:960-970.
8
[9] Chen P.J., Gurtin M.E., Williams W.O., 1969, On the thermoelastic material with two temperatures, Zeitschrift für Angewandte Mathematik und Physik 20:107-112.
9
[10] Boley M., 1956, Thermoelastic and irreversible thermodynamics, Journal of Applied Physics 27:240-253.
10
[11] Warren W.E., Chen P.J., 1973,Wave propagation in the two temperature theory of thermoelasticity, Acta Mechanica 16:21-23.
11
[12] Youssef H.M., 2006, Theory of two temperature generalized thermoelasticity, Journal of Applied Mathematics 71:383-390.
12
[13] Kumar R., Mukhopadhyay S., 2010 , Effect of thermal relaxation time on plane wave propagation under two temperature thermoelasticity, International Journal of Engineering Science 48:128-139.
13
[14] Kaushal S., Sharma N., Kumar R., 2010, Propagation of waves in generalized thermoelastic continua with two temperature, International Journal of Applied Mechanics and Engineering 15:1111-1127.
14
[15] Ezzat M.A., Awad E.S., 2010, Constitutive relations, uniqueness of solution and thermal shock application in the linear theory of micropolar generalized thermoelasticity involving two temperatures, Journal of Thermal Stresses 33:226-250.
15
[16] Kaushal S., Kumar R., Miglani A., 2011, Wave propagation in temperature rate dependent thermoelasticity with two temperatures, Mathematical Sciences 5:125-146.
16
[17] El-Karamany A.S., Ezzat M.A. ,2011, On the two-temperature green–naghdi thermoelasticity theories, Journal of Thermal Stresses 34: 1207-1226.
17
[18] Banik S., Kanoria. M., 2013, Study of two-temperature generalized thermo-piezoelastic problem, Journal of Thermal Stresses 36: 71-93.
18
[19] Kumar R., Abbas I. A., 2013, Deformation due to thermal source in micropolar thermoelastic media with thermal and conductive temperatures, Journal of Computational and Theoretical Nanoscience 10: 2241-2247.
19
[20] Youssef H. M., 2013, State-space approach to two-temperature generalized thermoelasticity without energy dissipation of medium subjected to moving heat source, Applied Mathematics and Mechanics 34: 63-74.
20
[21] Ailawalia P., Lotfy K.H. , 2014,Two temperature generalized magneto-thermoelastic interactions in an elastic medium under three theories, Applied Mathematics and Computation 227: 871-888.
21
[22] Green A.E., Naghdi P.M., 1991, A re-examination of the basic postulates of thermomechanics, Proceedings of the Royal Society of London A 357:253-270.
22
[23] Green A.E., Naghdi P.M., 1992, On undamped heat waves in an elastic solid, Journal of Thermal Stresses 15:253-264.
23
[24] Green A.E., Naghdi P.M., 1993, Thermoelasticity without energy dissipation, Journal of Elasticity 31:189-209.
24
[25] Taheri H., Fariborz S., Eslami M.R., 2004, Thermoelasticity solution of a layer using the Green-Naghdi model, Journal of Thermal Stresses 27:795-809.
25
[26] Mukhopadhyay S., Kumar R., 2008, A problem on thermoelastic interactions in an infinite medium with a cylindrical hole in generalized thermoelasticity III, Journal of Thermal Stresses 31:455-475.
26
[27] Mohamed N.A., Khaled A.E., Ahmed E.A., 2009, Electromagneto-thermoelastic problem in a thick plate using Green and Naghdi theory, International Journal of Engineering and Science 47:680-690.
27
[28] Chirita S., Ciarletta M., 2010, On the harmonic vibrations in linear thermoelasticity without energy dissipation, Journal of Thermal Stresses 33:858-878.
28
[29] Chirita S., Ciarletta M., 2011, Several results in uniqueness and continous dependence in thermoelasticity of type III, Journal of Thermal Stresses 34:873-889.
29
[30] Passarella F., Zampoli V., 2011, Reciprocal and variational principles in micropolar thermoelasticity of type II, Acta Mechanica 216:29-36.
30
[31] Abbas I.A. ,2013, A GN model for thermoelastic interaction in an unbounded fiber-reinforced anisotropic medium with a circular hole, Applied Mathematics Letters 26: 232-239.
31
[32] Ailawalia P., Budhiraja S., Singla A., 2014, Dynamic problem in green-naghdi (Type III) thermoelastic half-space with two temperature, Mechanics of Advanced Materials and Structures 21: 544-552.
32
[33] Das P., Kar A., Kanoria M., 2013, Analysis of magneto-thermoelastic response in a transversely isotropic hollow cylinder under thermal shock with three-phase-lag effect, Journal of Thermal Stresses 36: 239-258.
33
[34] Kothari S., Mukhopadhyay S., 2013, Some theorems in linear thermoelasticity with dual phase-lags for an anisotropic medium, Journal of Thermal Stresses 36: 985-1000.
34
[35] Othman M.I.A., Atwa S.Y., Jahangir A., Khan A. , 2013, Generalized magneto-thermo-microstretch elastic solid under gravitational effect with energy dissipation, Multidiscipline Modeling in Materials and Structures 9:145-176.
35
[36] Fahmy M.A., 2013, A three-dimensional generalized magneto-thermo-viscoelastic problem of a rotating functionally graded anisotropic solids with and without energy dissipation, International Journal of Computation and Methodology 63: 713-733.
36
[37] El-Karamany A.S., Ezzat M.A., 2014, On the dual-phase-lag thermoelasticity theory, Meccanica 49: 79-89.
37
[38] Guo F.L., Song J., Wang G.Q., Zhou Y.F. , 2014, Analysis of thermoelastic dissipation in circular micro-plate resonators using the generalized thermoelasticity theory of dual-phase-lagging model, Journal of Sound and Vibration 333: 2465-2474.
38
[39] Eringen A.C., 1984, Plane waves in non local micropolar elasticity, International Journal of Engineering Science 22:1113-1121.
39
[40] Dhaliwal R.S., Singh A., 1980, Dynamic Coupled Thermoelasticity, Hindustan Publication Corporation, New Delhi, India.
40
[41] Gauthier R.D., 1982, Experimental Investigations on Micropolar Media, World Scientific, Singapore.
41