Vibration of Visco-Elastic Parallelogram Plate with Thickness Variation Linearly in one Direction and Parabolic in another Direction

Arun Kumar Gupta^1, and Anuj Kumar¹

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

Cite this paper

Arun Kumar Gupta and Anuj Kumar. Vibration of Visco-Elastic Parallelogram Plate with Thickness Variation Linearly in one Direction and Parabolic in another Direction. American Journal of Applied Mathematics and Statistics. 2013; 1(5):103-109. doi: 10.12691/AJAMS-1-5-5

Abstract

The main objective of the present investigation is to study the vibration of visco-elastic parallelogram plate whose thickness varies bi-directionally. It is assumed that the plate is clamped on all the four edges and that the thickness varies linearly in one direction and parabolically in another direction. Using the separation of variables method and Rayleigh-Ritz technique with a two-term deflection function, the governing differential equation has been solved for vibration of visco-elastic parallelogram plate. For visco-elastic, the basic elastic and viscous elements are combined. We have taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here the elastic element means the spring and the viscous element means the dashpot. The assumption of small deflection is made. Visco-elastic of the plate is taken of the “Kelvin Type”. Time period and deflection function at different point for the first two modes of vibration are calculated for various values of taper constant, aspect ratio and skew angle and results are presented in tabular form. Alloy “Duralumin” is considered for all the material constants used in numerical calculations.

Keywords

vibration, parallelogram plate, visco-elastic mechanics, linear thickness variation, parabolic thickness variation, both directions

Copyright

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