Determination of the Steady-State Response of Viscoelastically Supported Rectangular Orthotropic Mass Loaded Plates by an Energy-Based Finite Difference Method

Abstract

A method based on a variational procedure in conjunction with a finite difference method is used to examine the free vibration characteristics and steady-state response to a sinusoidally varying force applied orthotropic elastic rectangular plate carrying masses. Using the energy-based finite difference method, the problem reduced to the solution of a system of algebraic equations. Due to the significance of the fundamental natural frequency of the plate, its variation is investigated with respect to the mechanical properties of the plate material, the translational spring coefficient of the supports, the mass distribution, the mass locations and the quantity of mass. The steady-state response of the viscoelastically supported plates was also investigated numerically for the damping coefficient of the supports and the force distribution in addition to the characteristics of the plate system. Many new results are presented and the validity of the present approach is demonstrated by comparing the results with other solutions based on the Kirchhoff-Love plate theory.