Free vibration of stiffened rectangular plates using Green's functions and integral equations

Abstract

A new method for the free-vibration analysis of stiffened rectangular plates based on the use of Green's functions and the solution of a system of Fredholm integral equations of the second kind is demonstrated. The lateral forces and twisting moments of constraint between the plate and beam stiffeners are accounted for. For plates with simply supported edges perpendicular to the stiffeners the integral equations are solved exactly to yield the characteristic equations for the natural frequencies. The characteristic equations are then solved to yield the exact natural frequencies (within the context of the mathematical model chosen). The pertinent parameters of the problem all appear explicitly in the characteristic equation which then has implications for its use as a mathematical design tool. The exact natural modes can be calculated and the orthogonality relation for the natural modes is given which implies that the forced response of the stiffened plate, including the effects of damping, can be determined by modal analysis. As an example, a table and figures show the natural frequencies for a stiffened simply supported rectangular plate with a single stiffener.