Free vibration of clamped visco-elastic rectangular plate having bi-direction exponentially thickness variations

Free vibration of a clamped visco-elastic rectangular plate having bi-direction exponentially varying thickness has been analysed on the basis of classical plate theory. For visco-elastic materials, basic elastic and viscous elements are combined. We have assumed the Kelvin model for visco-elasticity, which is a combination of elastic and viscous elements connected in parallel. Here, the elastic element is constituted by a spring and the viscous one is a dashpot. An approximate but quite convenient frequency equation is derived by using the Rayleigh-Ritz technique. Logarithmic decrement, time period and deflection (at two different instant of time) for the first two modes of vibration and for various values of the taper constants and aspect ratio are calculated. Comparison studies have been carried out with bi-linearly thickness variation to establish the accuracy and versatility of the method.