Journal of Applied and Computational Mechanics

Nonlinear Dynamic Response of Functionally Graded Porous Plates on Elastic Foundation Subjected to Thermal and Mechanical Loads

Document Type : Research Paper

Authors

1 Advanced Materials and Structures Laboratory, VNU-Hanoi - University of Engineering and Technology (UET), Hanoi, 100000, Vietnam

2 Infrastructure Engineering Program -VNU-Hanoi, Vietnam-Japan University (VJU), Hanoi, 100000, Vietnam

3 Department of Civil and Environmental Engineering, Sejong University, 98 Gunja Dong, Gwangjin Gu, Seoul, 143-747, South Korea

Abstract

In this paper, the first-order shear deformation theory is used to derive theoretical formulations illustrating the nonlinear dynamic response of functionally graded porous plates under thermal and mechanical loadings supported by Pasternak’s model of the elastic foundation. Two types of porosity including evenly distributed porosities (Porosity-I) and unevenly distributed porosities (Porosity-II) are assumed as effective properties of FGM plates such as Young’s modulus, the coefficient of thermal expansion, and density. The strain-displacement formulations using Von Karman geometrical nonlinearity and general Hooke’s law are used to obtain constitutive relations. Airy stress functions with full motion equations which is employed to shorten the number of governing equations along with the boundary and initial conditions lead to a system of differential equations of the nonlinear dynamic response of porous FGM plates. Considering linear parts of these equations, natural frequencies of porous FGM plates are determined. By employing Runge-Kutta method, the numerical results illustrate the influence of geometrical configurations, volume faction index, porosity, elastic foundations, and mechanical as well as thermal loads on the nonlinear dynamic response of the plates. Good agreements are obtained in comparison with other results in the literature.

Keywords

Main Subjects

[1] Wang, Z.X., Shen, H.S., Nonlinear dynamic response of sandwich plates with FGM face sheets resting on elastic foundations in thermal environments, Ocean Engineering, 57, 2013, 99–110.
[2] Han, S.C., Park, W.T., Jung, W.Y., A four-variable refined plate theory for dynamic stability analysis of S-FGM plates based on physical neutral surface, Composite Structures, 131, 2015, 1081-1089.
[3] Duy, H.T., Noh, H.C., Analytical solution for the dynamic response of functionally graded rectangular plates resting on elastic foundation using a refined plate theory, Applied Mathematical Modelling, 39(20), 2015, 6243-6257.
[4] Cong, P.H., Anh, V.M., Duc, N.D., Nonlinear dynamic response of eccentrically stiffened FGM plate using Reddy’s TSDT in thermal environment, Journal of Thermal Stresses, 40(6), 2016, 704-732.
[5] Hosseini-Hashemi, Sh., Rokni Damavandi Taher, H., Akhavan, H., Omidi, M., Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory, Applied Mathematical Modelling, 34, 2010, 1276-1291.
[6] Zhao, X., Lee, Y.Y., Liew, K.M., Free vibration analysis of functionally graded plates using the element-free kp-Ritz method, Journal of Sound and Vibration, 319, 2009, 918-939.
[7] Wang, Y.Q., Zu, J.W., Nonlinear dynamic thermoelastic response of rectangular FGM plates with longitudinal velocity, Composites Part B, 117 2017, 74-88.
[8] Thom, D.V., Kien, N.D., Duc, N.D., Duc, H.D., Tinh, Q.B., Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory, Thin-Walled Structures, 119, 2017, 687–699.
[9] Duc, N.D., Tuan, N.D., Tran, P., Quan, T.Q., Nonlinear dynamic response and vibration of imperfect shear deformable functionally graded plates subjected to blast and thermal loads, Mechanics of Advanced Materials and Structures, 24(4), 2017, 318-329.
[10] Duc, N.D., Cong, P.H., Tuan, N.D., Tran, P., Anh, V.M, Quang, V.D., Nonlinear vibration and dynamic response of imperfect eccentrically stiffened shear deformable sandwich plate with functionally graded material in thermal environment, Journal of Sandwich Structures and Materials, 18(4), 2016, 445-473.
[11] Duc, N.D., Cong, P.H., Nonlinear dynamic response of imperfect symmetric thin S-FGM plate with metal-ceramic-metal layers on elastic foundation, Journal of Vibration and Control, 21(4), 2015, 637-646.
[12] Duc, N.D., Cong, P.H., Nonlinear vibration of thick FGM plates on elastic foundation subjected to thermal and mechanical loads using the first-order shear deformation plate theory, Cogent Engineering, 2, 2015, 1045222.
[13] Duc, N.D., Cong, P.H., Quang, V.D., Thermal stability of eccentrically stiffened FGM plate on elastic foundation based on Reddy’s third-order shear deformation plate theory, Thermal Stresses, 39(7), 2016, 772-794.
 [14] Piazza, D., Capiani, C., Galassi, C., Piezoceramic material with anisotropic graded porosity, Journal of the European Ceramic Society, 25, 2005, 3075–3078.
[15] Rad, A.B., Shariyat, M., Three-dimensional magneto-elastic analysis of asymmetric variable thickness porous FGM circular plates with non-uniform tractions and Kerr elastic foundations, Composite Structures, 125, 2015, 558-574.
[16] Ebrahimi, F., Zia, M., Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities, Acta Astronautica, 116, 2015, 117-125.
[17] Zhou, W., Zhou, H.,  Zhang, R.,  Pei, Y., Fang, D., Measuring residual stress and its influence on properties of porous ZrO2/(ZrO2+Ni) ceramics, Materials Science & Engineering A, 622, 2015, 82–90.
[18] Zhou, W., Zhang, R., Ai, S., He, R., Pei, Y., Fang, D., Load distribution in threads of porous metal–ceramic functionally graded composite joints subjected to thermomechanical loading, Composite Structures, 134, 2015, 680–688.
[19] Wattanasakulpong, N., Ungbhakorn, V., Nonlinear vibration of a coating-FGM-substrate cylindrical panel subjected to a temperature gradient, Computer Methods in Applied Mechanics and Engineering, 195, 2006, 007-1026.
[20] Ghadiri, M., SafarPour, H., Free vibration analysis of size-dependent functionally graded porous cylindrical microshells in thermal environment, Journal of Thermal Stresses, 40, 2017, 55-71.
[21] Jahwari, F. A., Naguib, H. E., Analysis and Homogenization of Functionally Graded Viscoelastic Porous Structures with a Higher Order Plate Theory and Statistical Based Model of Cellular Distribution, Applied Mathematical Modelling, 40(3), 2015, 2190-2205.
[22] Mechab, B., Mechab, I., Benaissa, S., Ameri, M., Serier, B., Probabilistic analysis of effect of the porosities in functionally graded material nanoplate resting on Winkler–Pasternak elastic foundations, Applied Mathematical Modelling, 40, 2015, 1–12.
[23] Torres, Y., Trueba, P., Pavon, J.J., Chicardi, E., Kamm, P., Garcıa-Moreno, F., Rodrıguez-Ortiz, J.A., Design, processing and characterization of titanium with radial graded porosity for bone implants, Materials & Design, 110, 2016, 179-187.
[24] Shafei, N., Mousavi, A., Ghadiri, M., On size-dependent nonlinear vibration of porous and imperfect functionally graded tapered microbeams, International Journal of Engineering Science, 106, 2016, 42–56.
[25] Shafei, N., Kazemi, M., Buckling analysis on the bi-dimensional functionally graded porous tapered nano-/ micro-scale beams, Aerospace Science and Technology, 66, 2017, 1-11.
[26] Shafei, N., Mirjavadi, S.S., MohaselAfshari, B., Rabbly, S., Kazemi, M., Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams, Computer Methods in Applied Mechanics and Engineering, 322, 2017, 615-632.
[27] Barati, M.R., Shahverdi, H., Aero-hygro-thermal stability analysis of higher-order refined supersonic FGM panels with even and uneven porosity distributions, Journal of Fluids and Structures, 73, 2017, 125–136.
[28] Chen, D., Yang, J., Kitipornchai, S., Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams, Composites Science and Technology, 142, 2017, 235-245.
[29] Ebrahimi, F., Jafari, A., Barati, M.R., Vibration analysis of magneto-electro-elastic heterogeneous porous material plates resting on elastic foundations, Thin-Walled Structures, 119, 2017, 33–46.
[30] Şimşek, M., Aydın, M., Size-Dependent Forced Vibration of an Imperfect Functionally Graded (FG) Microplate with porosities Subjected to a moving load using the modified couple stress theory, Composite Structures, 160, 2016, 408-421.
[31] Shahverdi, H., Barati M.R., Vibration analysis of porous functionally graded nanoplates, International Journal of Engineering Science, 120, 2017, 82–99.
[32] Akbaş, S.D., Vibration and static analysis of functionally graded porous plates, Journal of Applied and Computational Mechanics, 3(3), 2017, 199-207.
[33] Shojaeefard, M.H., Googarchin, H. S., Ghadiri, M., Mahinzare, M., Micro temperature-dependent FG porous plate: Free vibration and thermal buckling analysis using modified couple stress theory with CPT and FSDT, Applied Mathematical Modelling, 50, 2017, 366-355.
[34] Wang, Y.Q., Wan, Y.H., Zhang, Y.F., Vibrations of longitudinally traveling functionally graded material plates with porosities, European Journal of Mechanics / A Solids, 66, 2017, 55-68.
[35] Wang, Y., Wu, D., Free vibration of functionally graded porous cylindrical shell using a sinusoidal shear deformation theory, Aerospace Science and Technology, 66, 2017, 83-91.
[36] Ziane, N., Meftah, S.A., Ruta, G., Tounsi, A., Thermal effects on the instabilities of porous FGM box beams, Engineering Structures, 134, 2017, 150–158.
[37] Duc, N.D., Nonlinear Static and Dynamic Stability of Functionally Graded Plates and Shells, Vietnam National University Press, Hanoi, Vietnam, 2014.
[38] Reddy, J.N., Mechanics of laminated composite plates and shells: theory and analysis, Boca Raton, CRC Press, 2004.
Journal of Applied and Computational Mechanics
Volume 4, Issue 4
October 2018
Pages 245-259