Vibration of visco-elastic parallelogram plate with linearly thickness variations in both directions

Abstract

An analysis for free transverse vibrations of visco-elastic parallelogram plate whose thickness varies linearly in both directions is presented. Using the separation of variables method and Rayleigh-Ritz technique with a two-term deflection function, the governing differential equation has been solve for vibration of visco-elastic parallelogram plate. For the visco-elastic case, the basic elastic and viscous elements are combined. The Kelvin model for visco-elasticity that is a combination of the elastic and viscous elements in parallel is taken. Here the elastic element means the spring and the viscous element means the dashpot. Time period and deflection function at different point for the first two modes of vibration for various values of taper constant, aspect ratio & skew angle are obtained and shown in tabular form.

Keywords: Vibration, visco-elastic, parallelogram plate, linear thickness variation, both directions.