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The eigenvibration characteristics of a smart plate with piezoelectric layers and porous-cellular core are investigated in the present article. The core plate is assumed to be composed of materials that contain pores and the porosities may be distributed according to different mathematical rules. Variational principle is applied in order to derive the continuous system equations on the basis of Mindlin plate theory. A highly efficient analytical modeling for eigenfrequency analysis of the smart plate is presented under the assumption that both Skempton’s pore pressure coefficient and normal elongation through the thickness are negligible. Unlike numerical methods that require huge computational cost, this approach enables us to find the system’s response for rectangular plates with arbitrary dimensions. To examine the validity of the present framework, multiple comparison studies are made between the extracted results and those available in the literature. It is shown that the type of porosity distribution influences strongly on the way that frequency changes. Furthermore, it is found out that it is necessary to consider electrical effects for plates with open circuit condition unlike the other electrical condition.

This investigation aims to perform a detailed natural frequency analysis of functionally graded porous beams integrated with transverse ( d31) and shear ( d15) piezoelectric layers under short circuit and open circuit electrical conditions. It is assumed that the core layer is made of functionally graded materials containing porosities. Due to the existence of internal pores, the mechanical properties of functionally graded materials are considered according to the modified power-law rule which includes the effect of porosity. The distribution of electric potential within the d31 and d15 piezoelectric layers is modeled based on nonlinear variation for both short circuit and open circuit conditions. Employing the classical, the first-order, and the higher-order beam theories incorporated with the virtual work principle as well as Maxwell’s equation, the electromechanical equations of motion are derived. The governing equations are then solved analytically for simply supported boundary condition and a parametric study is presented. After validation of the results, some new interesting conclusions covering the effects of porosity volume fraction, porosity distribution, various piezoelectricity modes, power-law index, and the beam theories on short circuit and open circuit resonance frequencies are reported. It is believed that the presented numerical results could provide a benchmark to check the accuracy of the approximated approaches.

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