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An Analytical Approach on Thermally Induced Vibrations of Nonhomogeneous Tapered Plate

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  • Anupam Khanna
  • Ashish Singhal

Abstract

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.

Suggested Citation

  • Anupam Khanna & Ashish Singhal, 2013. "An Analytical Approach on Thermally Induced Vibrations of Nonhomogeneous Tapered Plate," Journal of Mathematics, Hindawi, vol. 2013, pages 1-6, May.
    • Handle: RePEc:hin:jjmath:721868
    DOI: 10.1155/2013/721868
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