Vibration of Non-Homogeneous Visco-Elastic Rectangular Plate Having Linearly Varying Thickness in Both Directions with Thermal Gradient Effect

Abstract

In the modern time, there is extensive use of the plates of variable thickness in the field of engineering such as jet engines designing, space crafts, gas turbines, nuclear power projects etc. The effect of variation of non-homogeneity on visco-elastic rectangular plate with linearly varying thickness in both directions together thermal gradient in one direction is presented in this paper. The non-homogeneity of the plate is characterized by taking a linear variation in the density of the material. Plates are considered to be having clamped boundary conditions on all the four edges. Basic elastic and viscous elements are combined to make visco-elastic materials. We have taken Kelvin model for visco-elasticity, which is a combination of elastic and viscous elements connected in parallel. Using the separation of variable method, the governing differential equation has been solved and Rayleigh-Ritz technique has been used to get the required frequency equation. In the present research, the deflection and time period of vibration of a clamped rectangular plate on the first two modes of vibration are calculated to see the effects of various factors like non-homogeneity constant, taper constants, aspect ratio and thermal gradient. Results are presented in the tabular form.

How to cite this article:

Gupta AK, Aggarwal S. Vibration of Non-Homogeneous Visco-Elastic Rectangular Plate Having Linearly
Varying Thickness in Both Directions with Thermal Gradient Effect. J Adv Res Appl Math Stat 2018; 3(1&2): 19-28.