Vibration of Non-Homogeneous Rectangular Plate Having Parabolically Varying Thickness in Both Directions with Exponentially Temperature Distribution

Arun Kumar Gupta¹ and Vaibhav Panwar^2,

¹Department of Mathematics, M. S. College, Saharanpur, U.P., India

²Department of MCA, Institute of Management Studies, Dehradun, India

Cite this paper:
Arun Kumar Gupta and Vaibhav Panwar. Vibration of Non-Homogeneous Rectangular Plate Having Parabolically Varying Thickness in Both Directions with Exponentially Temperature Distribution. Applied Mathematics and Physics. 2013; 1(4):94-102. doi: 10.12691/amp-1-4-2

Abstract

An analysis is presented for frequencies of non-homogeneous rectangular plates of bi-parabolically thickness variation with exponentially temperature distribution on the basis of classical plate theory. An approximate but quiet convenient frequency equation is derived by using Rayleigh-Ritz technique with a two term deflection function. Effect of non-homogeneity together with taper constants and thermal gradient on the natural frequencies of vibration of a clamped rectangular plate on the first two modes of vibration have been analysed. Results are presented in tabular and graphical form both.

Keywords:
vibration bi-parabolically thickness variation exponentially thermal non-homogeneous rectangular plate

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