On the vibration analysis of coupled transverse and shear piezoelectric functionally graded porous beams with higher-order theories

Abstract

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.

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

“…Thus, the modified rule of mixture is used here to describe and approximate the effective material properties of the porous FGM substrate. In this regard, two types of porosity distribution, namely Even and Uneven patterns (see Figure 2), are considered; therefore, equation (4) is modified and changed to the following relations for a porous FGM domain (Askari et al, 2021; Wang et al, 2017):…”

“…They showed that the undesired micro voids can affect the mechanical behavior of FGM structures significantly. Nevertheless, only a few studies have investigated this critical issue and included the effect of porosities in their respective analysis (Askari et al, 2021; Cuong-Le et al, 2021; Moradi-Dastjerdi and Behdinan, 2021; Phung-Van et al, 2019; Thanh et al, 2019). For instance, very recently, Askari et al (2021) developed an analytical work to study the free vibration problem of a simply supported porous FGM beam integrated with thickness-poled and length-poled piezoelectric layers in both SC and OC electrical conditions.…”

“…Nevertheless, only a few studies have investigated this critical issue and included the effect of porosities in their respective analysis (Askari et al, 2021; Cuong-Le et al, 2021; Moradi-Dastjerdi and Behdinan, 2021; Phung-Van et al, 2019; Thanh et al, 2019). For instance, very recently, Askari et al (2021) developed an analytical work to study the free vibration problem of a simply supported porous FGM beam integrated with thickness-poled and length-poled piezoelectric layers in both SC and OC electrical conditions. It was concluded from their work that the free vibration response of the smart piezoelectric FGM beam is highly influenced by porosity parameter as well as the type of distribution of internal pores in the FGM core.…”

A new higher-order beam theory for buckling and free vibration responses of laminated composite and functionally graded porous beams

“…Although the elasticity theory describes the beam's responses precisely, it is computationally complex and difficult to apply to arbitrary boundary conditions or complicated geometries. As a result, several alternative methods have been proposed, including layer-wise theories, 10,11 equivalent single-layer theories (ESLT), [12][13][14][15] zig-zag theories, [16][17][18][19] and Carrera's Unified Formulation. 20,21 Among these theories, the ESLT is widely utilised due to its formulation simplicity and programming ease.…”

On the Vibration Analysis of Rotating Piezoelectric Functionally Graded Beams Resting on Elastic Foundation with a Higher-Order Theory

“…A functionally graded porous piezoelectric sandwich nanobeam reinforced by graphene platelets was investigated by Chen et al [11] using the Euler-Bernoulli beam theory and a differential quadrature technique in order to capture the effect of flexoelectricity on the vibration responses of the nanobeam. Askari and colleagues [12] used the classical, first-order, and higher-order beam theories to analyze the natural frequencies of FG porous beams combined with transverse and shear piezoelectric layers under electrical conditions of short circuit and open circuit.…”