On the Use of Greatest Integer Function to Express Material Property Variation in Free Vibration Problem of Simply Supported Square Plates with Square Array of Circular Perforations

In this work vibration analysis of thin square plates with circular perforations arranged in square pattern is studied. The boundary condition for all the four edges is simply supported. The analytical approach presented here is based on Rayleigh's formulation. The deflection of the plate is represented by a simple function satisfying all the boundary conditions. In analytical modeling circular holes are replaced by equivalent square hole and variation of material properties such as density and modulus of elasticity is expressed using greatest integer function. The fundamental frequency of vibration is determined numerically for plates of different sizes. The results of the proposed method are validated using finite element method (FEM) modal analysis. The results obtained by the proposed approach are found to be in good agreement with the results of FEM.