The effect of accuracy of the length scale parameter on natural frequencies of porous vibratory rectangular microplate

The length-scale parameter as a primary factor has an important role in approximation of natural frequencies of micro-structures. Applying the exact length scale parameters which are recently determined by researchers, natural frequencies of porous microstructures are determined. In view of the fact that assumption of constant length-scale parameter leads to deviation of natural frequencies from their exact value, this research applies a length scale parameter which is function of plate thickness and material. To model the porous structures of the plate, the proposed porous models including evenly porosity mode, unevenly symmetric porosity model, and unevenly asymmetric porosity model are employed. The micro-plate is assumed to be thin, and classical plate theory is applied to displacement field of the micro-plate. The modified stress couple theory is employed to approximate the behavior of the plate in micro-scale. The trial functions which satisfy the boundary conditions are taken as the polynomial form. Evaluating the energy values of the system, the Rayleigh-Ritz method is imposed to solve the governing equations of the system. Validated the solution procedure with data given in the literature search, effects of various parameters on natural frequency of the plate are studied in the form of tables and curves.