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

The analysis presented here is to study the effect of linear thickness variations in both directions on vibration of visco-elastic rectangular plate having clamped boundary conditions on all the four edges. Using the separation of variables method, the governing differential equation has been solved for vibration of visco-elastic rectangular plate. An approximate but quite convenient frequency equation is derived by using Rayleigh–Ritz technique with a two-term deflection function. Logarithmic decrement, time period and deflection at different points for the first two modes of vibration are calculated for various values of taper constants and aspect ratio.