An analytical model to determine fundamental frequency of rectangular plate having rectangular array of circular perforations

In the current study an analytical model to determine fundamental frequency of perforated plate with circular perforation is formulated. Circular holes are replaced by equivalent square hole and non homogeneity in Young's modulus and density due to equivalent square perforation is expressed by using unit step functions. Analytical formulation is based on Rayleigh-Ritz method. In present study boundary condition considered is clamped at all edges. The deflected middle surface of the plate is approximated by a function which satisfies the boundary conditions. Proposed approach is validated by comparing numerical analysis results with Finite Element Method (FEM) modal analysis results.