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Abstract
A simple model presented here is to study the thermal effect on vibration of non-homogeneous orthotropic visco-elastic rectangular plate of parabolically varying thickness having clamped boundary conditions on all the four edges. For non-homogeneity of the plate material, density is assumed to vary linearly in one direction. Using the separation of variables method, the governing differential equation has been solved for vibration of non-homogeneous orthotropic viscoelastic rectangular plate. An approximate frequency equation is derived by using Rayleigh-Ritz technique with a two-term deflection function. Results are calculated for time period and deflection at different points, for the first two modes of vibration, for various values of temperature gradients, non-homogeneity constant, taper constant and aspect ratio and shown by graphs.
Highlights
In modern technology an interest towards the effect of high temperatures on non-homogeneous plates of variable thickness is developed due to applications in various engineering branches such as nuclear, power plants, aero-nautical, chemical etc. where metals and their alloys exhibits visco-elastic behavior
A simple model presented here is to study the thermal effect on vibration of non-homogeneous orthotropic visco-elastic rectangular plate of parabolically varying thickness 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 non-homogeneous orthotropic visco-elastic rectangular plate
Summary
In modern technology an interest towards the effect of high temperatures on non-homogeneous plates of variable thickness is developed due to applications in various engineering branches such as nuclear, power plants, aero-nautical, chemical etc. where metals and their alloys exhibits visco-elastic behavior. Johri and Vats [3] have discussed the thermal effect on vibration of non- homogeneous orthotropic rectangular plate having bi- directional parabolically varying thickness. Gupta and Khanna [9] have studied the effect of linearly varying thickness in both directions on vibration of visco-elastic rectangular plate. Gupta and Singhal [12] discussed the effect of non-homogeneity on thermally induced vibration of orthotropic visco-elastic rectangular plate of linearly varying thickness. The object of the present study is to determine the thermal effect on vibration of non-homogeneous orthotropic visco-elastic rectangular plate of parabolically varying thickness. It is clamped supported on all the four edges. Time period and deflection for the first two modes of vibration are calculated for the various values of thermal gradients, non-homogeneity constant, aspect ratio and taper constant
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