Affiliations: Department of Mathematics, M.S. College, Saharanpur,
Pin-247001, (U. P.), India | Mathematics Department, S.I.E.T. Gangoh, Saharanpur,
Pin-247001, (U. P.), India
Abstract: 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.
Keywords: Visco-elastic, rectangular plate, vibration and parabolic variation
