Free vibration analysis of a composite elliptical plate made of a porous core and two piezoelectric layers

Abstract

Porous materials are used extensively to manufacture beams, plates, and shells, and have been studies from different perspectives. Composite porous plates in various shapes and dimensions have numerous industrial applications. The vibration behaviors of rectangular and circular plates have been previously studied; however, less attention has been paid to the analysis of complex configuration, such as elliptical plates. We analyzed the free vibration of composite elliptical plates, consisting of a porous core and two piezoelectric layers. The governing equations were based on the classical plate theory and Rayleigh–Ritz’s energy method. The properties of porous materials with varying thickness of the core and porosity distributions continuously undergo changes due to the intended applications and functions. The proposed theoretical functions satisfy the boundary conditions in simple and clamped forms, and with a high degree of accuracy in the frequencies. Finally, we investigated the effects of important variables, such as geometric parameters and material specifications on the natural frequencies. The results of our analyses were consistent with the findings of previous studies. Based on our vibration analyses, the most crucial factors in composite elliptical plates are geometrical parameters, material specifications, and their effects on the vibration frequencies of the proposed model.