Free Vibration of a Simply-supported Rectangular Plate with a Straight Through-notch

Abstract

Free vibration of a simply-supported rectangular plate having a straight notch simulating a through-crack in the plate is analyzed to obtain its eigenvalues and the dynamic stress concentration in the front of the notch. That is, the plate is divided into two parts along the notch and then, Fredholm integral equations of the first kind are derived for the internal moment and shearing force, using Green functions satisfying the boundary conditions of each part and continuity conditions of deflection and deflection angle of the original plate. The integral equations are transformed into the algebraic equations by the numerical integration and subdomain method, to calculate the eigenvalues and the moment and shearing force distributions. They are numerically calculated with regard to the lower four modes and the effects of the aspect ratio of the plate and the length and location of the notch on them are discussed in detail.