On wave propagation and free vibration of piezoelectric sandwich plates with perfect and porous functionally graded substrates

Abstract

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.

Vibration characteristics of FG saturated porous annular plates integrated by piezoelectric patches on visco‐Pasternak foundation

“…To describe the displacements of the under consideration annular plate, the cylindrical coordinate system is employed which its origin is rested at the center of the middle plane of the core. Therefore, and based on CPT which is on the basis of Love-Kirchhoff's hypothesis, the displacement components of the plate can be expressed as [45]:…”

“…To describe the displacements of the under consideration annular plate, the cylindrical coordinate system is employed which its origin is rested at the center of the middle plane of the core. Therefore, and based on CPT which is on the basis of Love–Kirchhoff's hypothesis, the displacement components of the plate can be expressed as [45]: $$$$\begin{eqnarray} U\left( {r,\theta ,z,t} \right) &=& u\left( {r,\theta ,t} \right) - z\frac{{\partial w\left( {r,\theta ,t} \right)}}{{\partial r}},\nonumber\\ V\left( {r,\theta ,z,t} \right) &=& v\left( {r,\theta ,t} \right) - z\frac{1}{r}\frac{{\partial w\left( {r,\theta ,t} \right)}}{{\partial \theta }},\nonumber\\ W\left( {r,\theta ,z,t} \right) &=& w\left( {r,\theta ,t} \right) \end{eqnarray}$$$$in which the radial, circumferential, and transverse displacements of each point of the annular plate are shown by U , V , and W , respectively. Also, those of the middle plane in the mentioned directions are presented by u , v , and w .…”

A Review of Piezoelectric Energy Harvesting: Materials, Design, and Readout Circuits

“…Substantial contributions to the development of optimal piezoelectric devices that use vibrational energy have been recognized in the literature [45,[162][163][164][165][166][167][168][169]. A cantilever beam has several advantages, including low resonance frequencies, high average strain for a given input force, and the ability to be easily generated through a microfabrication process due to its simple form.…”

The actuation performance of a piezoelectric laminated plate actuator via Galerkin method

“…Askari et al (2021) analyzed and numerical modeled a unimorph beam and a novel multi-beam vibration energy harvesting system with COMSOL, and presented extensive parametric studies. Askari et al (2022) developed analytical solutions for wave propagation and free vibration of perfect and porous functionally graded (FG) plate structures integrated with piezoelectric layers based on a four-variable higher-order theory. Zenkour and Aljadani (2020) analyzed the electro-mechanical buckling response for functionally graded piezoelectric plates applied voltage based on a quasi-3D refined plate theory.…”