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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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This paper aims to develop analytical solutions for wave propagation and free vibration of perfect and porous functionally graded (FG) plate structures integrated with piezoelectric layers. The effect of porosities, which occur in FG materials, is rarely reported in the literature of smart FG plates but included in the present modeling. The modified rule of mixture is therefore considered for variation of effective material properties within the FG substrate. Based on a four-variable higher-order theory, the electromechanical model of the system is established through the use of Hamilton’s principle, and Maxwell’s equation. This theory drops the need of any shear correction factor, and results in less governing equations compared to the conventional higher-order theories. Analytical solutions are applied to the obtained equations to extract the results for two investigations: (I) the plane wave propagation of infinite smart plates and (II) the free vibration of smart rectangular plates with different boundary conditions. After verifying the model, extensive numerical results are presented. Numerical results demonstrate that the wave characteristics of the system, including wave frequency and phase velocity along with the natural frequencies of its bounded counterpart, are highly influenced by the plate parameters such as power-law index, porosity, and piezoelectric characteristics.

The aim of this study is developing an analytical solution for the free vibration of piezoelectric bimorph and unimorph doubly curved panels with a porous substrate. The panel is assumed to be relatively thick, and the effects of its shear deformation are taken into account. Nonlinear models are considered to describe the variation of mechanical properties and of the electric potential within porous host and piezoelectric layers, respectively. Furthermore, short and open circuit electrical conditions are studied to predict the frequency response for sensing and actuation applications. Employing the first-order shear deformation theory (FSDT), in conjunction with the Hamilton’s variational principle and Maxwell’s equation allows deriving six highly coupled partial differential equations to describe the system dynamics under electromechanical coupling. After analytically solving those equations for simply supported panels, the system frequency response is investigated, for various values of design parameters such as porosity, electrical boundary conditions, and geometry. Moreover, some types of smart panels, including bimorphs and unimorphs layouts, are analyzed. The analysis confirms that the above-mentioned parameters play major roles in the natural frequency response of this system and must be carefully considered in the mechatronic design of this smart structure, although they allow to tailor the system behaviour to the selected application.

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