Non-Homogeneous Effect on Vibration of Visco-Elastic Rectangular Plate Having Parabolically Varying Thickness in Both Directions

Abstract

At present the vibration theory has become significant in every sphere of applied sciences. In the advance time, the plates of variable thickness are widely used in civil, aeronautical, mechanical, electronics and marine structures like jet engines designing, space crafts, gas turbines, nuclear power projects etc. The effect of variation of non-homogeneity on vibration of visco-elastic rectangular plate with parabolically varying thickness in both directions is presented in this paper. The non-homogeneity of the plate is characterized by taking a linear variation in the density of the material and effect of temperature on young modulus. 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 graphical form.