Free vibration analysis of functionally graded porous plates based on a new generalized single-variable shear deformation plate theory

A generalized single-variable shear deformation plate theory (GSSDPT) is proposed. Compared with other single-variable vibration theories, GSSDPT discards the assumption that the shear component has zero effect on the bending moment. This makes the simplification process more reasonable. GSSDPT takes into account the inhomogeneous distribution of material properties, which makes it suitable for many new composite materials, such as functionally graded materials. Compared with higher-order shear deformation plate theories and first-order shear deformation plate theory, GSSDPT has only one governing equation, which significantly simplifies the calculation. GSSDPT takes into account the parabolic distribution of shear stress in the thickness direction. Therefore, it does not require shear correction. In this paper, the free vibration behavior of functionally graded plates under three pore distribution forms is investigated. The convenience and effectiveness of GSSDPT are verified by comparing it with existing literature. In addition, the effects of the porosity parameter, side-to-thickness ratio, aspect ratio, power-law index, and pore distribution forms are investigated based on GSSDPT.