Free Vibration Analysis of Orthotropic SSSS Non Homogeneous Parallelogram Plate with Varying Bi Dimensional Thickness and Thermal Effect

Abstract

Visco-elastic plates are widely used in various mechanical structures, aircrafts and industries. These plates are developed with an aim that scientists and design engineers can make a use of it with a practical approach. Therefore, study of effect of vibration is of immense importance. Visco-elastic plates may be regarded as an approximation to the wings, blades and variation in thickness may also lead to reduction in weight of structure of aircraft, space shuttle or satellite. In present scenario, plates of variable thickness are used in a wide variety of applications, which serve two fold purpose i.e. safety and economy. The plates of variable thickness are being mostly used in aerospace engineering, marine engineering, mechanical engineering, civil engineering, and nuclear power plants etc. An interest towards the effect of high temperatures on non-homogeneous plates of variable thickness is developed due to applications in various fields. The reason for these is that during heating up periods, structures are exposed to high intensity heat fluxes and material properties undergo significant changes; in particular the thermal effect cannot be taken as negligible. The information about first two modes of vibration is essential for construction engineer before finalizing a design. The vibration of plates of various shapes homogeneous and non homogeneous, orthotropic or isotropic with or without variation in thickness has been studied by lot of researchers with or without considering the effect of temperature. In present study five problems have been solved on the basis of classical plate theory of elasticity. newlineIn first problem, a simple model to study the effect of non-homogeneity on vibration of parallelogram plate with bi-linear thickness variation has been represented. Thermal induced vibration of these plates has been assumed as bi-linear temperature circulation. For non-homogeneity of the plate material density is taken to be linearly varying. The governing differential equation has been solved with the