Resonant frequencies of perforated plates with rectangular slots

Most previous work on perforated plates employed elasticity theory to determine equivalent material properties that make the deflection of the solid plate identical to that of the perforated plate. However, it will be inaccurate to utilize the proposed elastic properties to predict the natural frequencies of a perforated plate. In this paper, the free vibrations of perforated plates with rectangular slots and rectangular slot-patterns are examined using theoretical and finite-element methods. The natural frequencies are obtained for various cases of perforations. An explicit expression is obtained for the equivalent elastic properties using the regression analysis method. These effective material properties are used in a solid-plate model to predict the natural frequencies of the corresponding perforated plate. To validate the theoretical analysis, the effective resonant frequencies are compared with the exact natural frequencies of the perforated plates. Parametric studies are conducted to examine the effect of both parallel and perpendicular ligament efficiencies on the resonant frequencies