A unified approach for predicting the free vibration of an elastically restrained plate with arbitrary holes

This paper proposes a unified approach to study the free vibration of elastically restrained plate with holes. The hole is treated as a virtual plate in which the mass density and the Young's modulus is set to zero. Therefore, the free vibration problem of a plate with holes can be translated into the free vibration problem of the equivalent rectangular plate with non-uniform thickness. The model is derived based on the so-called Spectro-Geometric Method (SGM) in which the displacement of the plate including the holes is invariably expressed as a modified Fourier series expansion. The proposed model allows considering the edges of the plate elastically restrained against both deflection and rotation. The accuracy of the method is validated against the results obtained by the finite element method. Some numerical solutions including the plates with triangular, rectangular holes are investigated.