Free vibration analysis of non-homogeneous visco-elastic circular plate with varying thickness subject to thermal gradient

摘要

The analysis of free vibration of non-homogeneous visco-elastic circular plate with varying thickness in the radial direction subjected to thermal gradient is performed. The effect of linear temperature variation on Young's modulus and Shear's modulus is considered only in radial direction. The thickness of circular plate varies parabolically in radial direction. For non-homogeneity of the circular plate material, density is assumed to vary linearly in radial direction. To solve the governing differential equation the method of separation of variables is applied. An approximate but quite convenient frequency equation is derived by using Rayleigh-Ritz technique with a three-term deflection function. Yet the method used for the solution of the problem provides an approximate solution but it is quite convenient and authentic. Deflection (at two different instant of time), time period and logarithmic decrement for the first two modes of vibration are computed for a non-homogeneous visco-elastic circular plate of parabolically varying thickness with clamped edge conditions for various values of non-homogeneity constant, taper constant and temperature gradients, and these are shown graphically for the Voigt-Kelvin model.