Modeling the effect of the inclination angle on the dynamic response of a biaxially pre-stressed plate

Abstract

In this study, I report on an investigation of the forced vibrations procured by an arbitrary angled time-harmonic loading from a plate based on a rigid foundation. The study was formulated according to the three-dimensional linearized theory of elasticity for solids under initial stress (TLTESIS). It was assumed throughout the investigation that there is a rigid clamped state between the system and the rigid ground; further, it was assumed that the plate was exposed to biaxially static initial stresses. Given this, a mathematical model was developed, and then solved using a three-dimensional finite element method (3D-FEM). Presented are numerical investigations that illustrate the influence of changes in the inclination of the force, as well as other important factors such as dimensionless frequency parameters, on the dynamic behavior of the system. In particular, the results indicate that the effect the initial stresses have on the dynamic stress distribution character increases with the aspect ratio but decreases with the thickness ratio.