Free vibration analysis of partially perforated circular plates

This paper presents free vibration analysis of partially perforated circular plates with a triangular hole pattern and clamped boundary condition. To reflect the effect of circular holes on natural frequencies of the perforated plate, the effective material properties based on the finite element analysis are introduced. The circular plates are divided into the solid annular and perforated central regions to estimate the theoretical natural frequencies of perforated circular plates using the Rayleigh-Ritz method based on minimizing the Rayleigh quotient of the ratio between the maximum potential energy and the total kinetic energy. In the theoretical calculation, the reduction of mass and stiffness in the perforated plate region are considered as a function of the ligament efficiency. The proposed theoretical method is verified by observing a good agreement with finite element analysis results based on the full and equivalent finite element models.