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Shock and Vibration
Volume 2014 (2014), Article ID 392325, 6 pages
Research Article

Free Transverse Vibration of Orthotropic Thin Trapezoidal Plate of Parabolically Varying Thickness Subjected to Linear Temperature Distribution

Department of Mathematics, M.S. College, Saharanpur 247001, India

Received 21 October 2013; Revised 4 March 2014; Accepted 20 March 2014; Published 3 April 2014

Academic Editor: Anindya Ghoshal

Copyright © 2014 Arun Kumar Gupta and Shanu Sharma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The present paper deals with the free transverse vibration of orthotropic thin trapezoidal plate of parabolically varying thickness in x-direction subjected to linear temperature distribution in x-direction through a numerical method. The deflection function is defined by the product of the equations of the prescribed continuous piecewise boundary shape. Rayleigh-Ritz method is used to evaluate the fundamental frequencies. The equations of motion, governing the free transverse vibrations of orthotropic thin trapezoidal plates, are derived with boundary condition CSCS. Frequency corresponding to the first two modes of vibration is calculated for the orthotropic thin trapezoidal plate having CSCS edges for different values of thermal gradient, taper constant, and aspect ratio. The proposed method is applied to solve orthotropic thin trapezoidal plate of variable thickness with C-S-C-S boundary conditions. Results are shown by figures for different values of thermal gradient, taper constant, and aspect ratio for the first two modes of vibrations.