Analytical model to determine fundamental frequency of free vibration of perforated plate by using unit step functions to express non-homogeneity

In the current study an analytical model to determine fundamental frequency of perforated plate is formulated. Non-homogeneity in Young’s modulus and density due to perforation is expressed by using unit step function in Rayleigh’s Quotient. In the present analysis the boundary condition considered is clamped at all edges. Perforated plate is considered as plate with uniformly distributed mass and holes are considered as nonhomogeneous patches. The deflected middle surface of the plate is approximated by a function which satisfies the boundary conditions. The proposed approach is validated by comparing results with finite element method modal analysis.