Vibration analysis of irregular-shaped plates on simple supports

In this work, we propose a general perturbative approach for modal analysis of irregular-shaped plates uniform thickness with boundary conditions. Given plate irregular boundary, first, circular identical and area, centred at the centroid, is determined. The then treated as perturbation suitable smallness parameter, expressed generalized Fourier series. frequency shape function conditions are perturbed in terms parameter. homogeneous zeroth-order equation corresponds to plate, which exactly solvable. We show that inhomogeneous equations higher orders can also be solved using particular solution structure. construct exact up any order. proposed method demonstrated through simply supported super-circular plates. results validated numerical obtained from ANSYS ® , an excellent match. Interestingly, supposedly degenerate modes even number nodal diameters found split naturally.