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Shock and Vibration
Volume 15 (2008), Issue 6, Pages 713-723

Vibration of Clamped Visco-Elastic Rectangular Plate with Parabolic Thickness Variations

A.K. Gupta1 and Anupam Khanna2

1Department of Mathematics, M.S. College, Saharanpur, Pin-247001, (U. P.), India
2Mathematics Department, S.I.E.T. Gangoh, Saharanpur, Pin-247001, (U. P.), India

Received 25 September 2006; Revised 14 September 2007

Copyright © 2008 Hindawi Publishing Corporation. 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.


Most of the machines and engineering structures experience vibration and their design generally requires consideration for their dynamic behavior. Due to this, the study of vibration, as it deals with the vibratory behavior of bodies, is acquiring increasingly importance in several engineering applications, nuclear reactor technology and aeronautical field etc. Most of the work has been done in the field of elastic and non-elastic behavior of the bodies but a very little work is done in the field of visco-elastic bodies with varying thickness. The analysis presented here is to study the effect of taper constants on free vibration of a clamped visco-elastic rectangular plate with parabolically varying thickness. The two-dimensional thickness variation is taken as the Cartesian product of parabolic variations along the two concurrent edges of the plate. Using Rayleigh-Ritz method, frequency equation derives. Logarithmic decrement, time period and deflection for the first two modes of vibration are calculated for various values of taper constants and aspect ratio.