Clamped-Free Non Homogeneous Magneto Electro Elastic Plate of Polygonal Cross-Sections with Hydrostatic Stress and Gravity

Document Type: Research Paper


1 Department of Science and Humanities, Sri Krishna College of Engineering and Technology, Coimbatore-641008, Tamil Nadu, India

2 Department of Mathematics, Karunya University, Coimbatore-641114, Tamil Nadu, India



In this article, the influence of hydrostatic stress and gravity on a clamped- free non homogeneous magneto electro elastic plate of polygonal cross sections is studied using linear theory of elasticity. The equations of motion based on two-dimensional theory of elasticity are applied under the plane strain assumption of prestressed and gravitated magneto electro elastic plate of polygonal cross-sections composed of non homogeneous isotropic material. The frequency equations are obtained by satisfying the boundary conditions along the irregular surface of the polygonal plate using Fourier expansion collocation method. The complex roots of the frequency equations are obtained by secant method. The numerical computations are carried out for triangular, square, pentagon and hexagon cross sectional plates. Graphical representation is given for the various physical variables via gravity and different edge boundaries and its characteristics are discussed. This result can be applied for optimum design of concrete plates with polygonal cross sections.


[1] Akbarzadeh A.H., Pasini D., 2014, Multiphysics of multilayered functionally graded cylinders under prescribed hygrothermoagnetoelectro-mechanical loading, Journal of Applied Mechanics 81: 041018-1-13.
[2] Arefi M., Koohi Faegh R., Loghman A., 2016, The effect of axially variable thermal and mechanical loads on the 2D thermoelastic response of FG cylindrical shell, Journal of Thermal Stresses 39: 1539-1559.
[3] Khoshgoftar M., Rahimi G.H., Arefi M., 2013, Exact solution of functionally graded thick cylinder with finite length under longitudinally non-uniform pressure, Mechanics Research Communications 51: 61-66.
[4] Arefi M,, Rahimi G.H., 2012, The effect of non homogeneity and end supports on the thermo elastic behaviour of a clamped –clamped FG cylinder under mechanical and thermal loads, International Journal of Pressure Vessels and Piping 96: 30-37.
[5] Arefi M., 2013, Nonlinear thermoelastic analysis of thick-walled functionally graded piezoelectric cylinder, Acta Mechanicca 11: 2771-2783.
[6] Loghman A., Nasr M., Arefi M., 2017, Nonsymmetric thermo mechanical analysis of a functionally graded cylinder subjected to mechanical, thermal and magnetic loads, Journal of Thermal Stresses 40: 765-782.
[7] Rahimi G.H., 2011, Application and analysis of functionally graded piezoelectrical rotating cylinder as mechanical sensor subjected to pressure and thermal loads, Applied Mathematics and Mechanics 32: 997-1008.
[8] Nagaya K., 1981, Dispersion of elastic waves in bars with polygonal cross section, Journal of Acoustical Society of America 70: 763-770.
[9] Hutchinson J.R., 1979, Axisymmetric flexural vibrations of a thick free circular plate, Journal of Applied Mechanics 46: 139-144.
[10] Arefi M., Allam M.N.M., 2015, Nonlinear responses of an arbitrary FGP circular plate resting on the Winkler-Pasternak foundation, Smart Structures and Systems 16: 81-100.
[11] Nagaya K., 1980, Method for solving vibration problems of a plate with arbitrary shape, The Journal of the Acoustical Society of America 67: 2029-2033.
[12] Arefi M., 2015, Nonlinear electromechanical analysis of a functionally graded square plate integrated with smart layers resting on Winkler-Pasternak foundation, Smart Structures and Systems 16: 195-211.
[13] Chakraverty S., Jindal R., Agarwal V.K., 2005, Flexural vibrations of non-homogeneous elliptic plates, Indian Journal of Engineering and Materials Sciences 12: 521-528.
[14] Tanigawa Y., 1995, Some basic thermoelastic problems for nonhomogeneous structural materials, Applied Mechanics Reviews 48: 287-300.
[15] Annibale F.D., 2014, Linear stability of piezoelectric controlled discrete mechanical system under non constructive positional forces, Meccanica 50: 1-15.
[16] Selvamani R., 2015, Wave propagation in a rotating disc of polygonal cross section immersed in an inviscid fluid, Cogent Engineering 2(1): 1-20.
[17] Bin W., Jiangong J., Cunfu H., 2008, Wave propagation in non-homogeneous magneto-electro-elastic plates, Journal of Sound and Vibrations 317: 250-264.
[18] Chen W.Q., Lee K.Y., Ding H.J., 2005, On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plate, Journal of Sound and Vibration 279: 237-251.
[19] Li J.Y., 2000, Magneto electro elastic multi-inclusion and inhomogeneity problems and their applications in composite materials, International Journal of Engineering Science 38: 1993-2011.
[20] Kong T., Li D.X., Wang X., 2009, Thermo-magneto-dynamic stresses and perturbation of magnetic field vector in non-homgeneous hollow cylinder, Applied of Mathematical Modelling 33: 2939-2950.
[21] Kumar R., Sharma P., 2016, Variational principle, uniqueness and reciprocity theorems in porous magneto thermo elastic medium, Cogent Mathematics 3(1): 1-25.
[22] Pan E., 2001, Exact solution for simply supported and multilayered magneto-electro-elastic plates,transactions of the ASME, Journal of Applied Mechanics 68: 608-618.
[23] Pan E., Heyliger P.R., 2002, Free vibration of simply supported and multilayered magneto-electro-elastic plates, Journal of Sound and Vibrations 252: 429-442.
[24] Pan E., Han F., 2005, Exact solution for functionally graded and layered magneto-electro-elastic plates, International Journal of Engineering and Sciences 43: 321-339.
[25] Feng W.J., Pan E., 2008, Dynamic fracture behavior of an internal interfacial crack between two dissimilar magneto-electro-elastic plates, Engineering Fracture Mechanics 75: 1468-1487.
[26] Kumar R., 1998, Wave propagation in a generalized thermo microstretch elastic solid, International Journal of Engineering Sciences 36: 891-912.
[27] Selim M., 2007, Waves propagation in an initially stressed dissipative cylinder, Applied Mathematical Sciences 1: 1419-1427.
[28] Kumar R., 2011, Wave propagation in transversely isotropic generalized thermo elastic half space with voids under initial stress, Multidiscipline Modelling in Materials and Structures 7: 440-468.
[29] Akbarov S.D., 2011, Tortional wave dissipation in a finitely pre-strained hollow sandwich circular cylinder, Journal of Sound and Vibration 330: 4519-4537.
[30] Kakar R., 2013, Magneto elastic torsional surface waves in prestressed fiber reinforced medium, International Journal of Mathematical Mechanics 9: 1-19.
[31] Kakar R., 2013, Wave propagation in compressed materials with reinforcement in preferred direction subjected to gravity and initial compression, Journal of Chemical Biological and Physicsl Sciences 3(2):1468-1481.
[32] Kumari N., 2015, Edge waves in initially stressed visco elastic plate, Journal of Physics: Conference Series-International Conference of Vibration Problems 662: 012011.
[33] De S.N., 1974, Influence of gravity on wave propagation in an elastic cylinder, Journal of Acoustical Society of America 55: 919-921.
[34] Dey S., 1992, Tortional wave propagation in an initially stressed cylinder, Proceedings of the Indian National Science Academy 58: 425-429.
[35] Chen W.Q., 2012, Waves in pre stretched incompressible soft electro active cylinders: Exact Solution, Acta Mechanica 25: 530-541.
[36] Wilson A.J., 1977, Wave propagation in thin pre-stressed elastic plates, International Journal of Engineering Science 15: 245-251.
[37] Zhang X.M., YU J.G., 2013, Effects of initial stresses on guided waves in unidirectional plates, Archives of Mechanics 65: 3-26.
[38] Lotfy K.H., 2019, Magneto rotation fibre-reinforced thermoelastic gravity and energy dissipation, International Journal for Computational Methods in Engineering Science and Mechanics 1550: 2287-2295.
[39] Ahmed S.H., 1999, Influence of gravity on the propagation of waves in granular medium, Applied Mathematics and Computation 101: 269-280.
[40] Hou P.F., Andrew Y.T., Leung Ding H.J., 2008, Point heat source on the surface of a semi-infinite transversely isotropic electro-magneto-thermo-elastic material, International Journal of Engineering Sciences 46: 273-285.
[41] Chen J., Chen H., Pan E., 2006, Free vibration of functionally graded,magneto-thermo-electro-elastic and multilayered plates, Act Mechanica Solida Sinica 19: 60-66.