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Journal of Mathematics
Volume 2013, Article ID 721868, 6 pages
Research Article

An Analytical Approach on Thermally Induced Vibrations of Nonhomogeneous Tapered Plate

1Department of Mathematics, Maharishi Markandeshwar University, Mullana, Haryana, Ambala 133203, India
2Department of Mathematics, KIIT College of Engineering, Haryana, Gurgaon 122001, India

Received 10 January 2013; Accepted 21 April 2013

Academic Editor: Harold Benson

Copyright © 2013 Anupam Khanna and Ashish Singhal. 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.


A mathematical model to control the vibrations of a rectangular plate is constructed with an aim to assist engineers in designing and fabrication of various structures used in the field of science and technology, mostly used in satellite and aeronautical engineering. The present study is related to the analysis of free vibrations of nonhomogeneous rectangular plate clamped at all the four edges. Authors studied the bilinear effect of thickness as well as temperature variations in both and directions. Variation in Poisson's ratio is also considered linearly in -direction due to nonhomogeneity. Rayleigh-Ritz method is used to analyze the frequencies for the first two modes of vibrations for different values of thermal gradient, nonhomogeneity constant, taper constants and aspect ratio. All the numerical computations have been performed for an alloy of aluminum, that is, duralumin. All the results are presented in the form of graphs.