Abstract
In this paper, we analytically study vibration of functionally graded piezoelectric (FGP) nanoplates based on the nonlocal strain gradient theory. The top and bottom surfaces of the nanoplate are made of PZT-5H and PZT-4, respectively. We employ Hamilton’s principle and derive the governing differential equations. Then, we use Navier’s solution to obtain the natural frequencies of the FGP nanoplate. In the first step, we compare our results with the obtained results for the piezoelectric nanoplates in the previous studies. In the second step, we neglect the piezoelectric effect and compare our results with those obtained for the functionally graded (FG) nanoplates. Finally, the effects of the FG power index, the nonlocal parameter, the aspect ratio, and the side-tothickness ratio, and the nanoplate shape on natural frequencies are investigated.
Highlights
In the past four decades, microelectromechanical systems have been widely used in engineering
Despite some recent investigations on vibration behaviors of functionally graded piezoelectric (FGP) nanoplates, this problem based on the nonlocal strain gradient theory has not been studied so far
We have considered an FGP nanoplate consisting of two-phase graded piezoelectric materials such as PZT-4 and PZT-5H
Summary
In the past four decades, microelectromechanical systems have been widely used in engineering. The problem of predicting mechanical properties of nano/micro structures is an important subject in physics and engineering due to their potential applications. Li et al.[9] used nonlocal strain gradient models in examining the sizedependent effects on the static and dynamical behaviors of micro/nano structures. There are several methods to study the size-dependent mechanical properties of micro/nanoscale structures. We can use various continuum theories to study physical properties of piezoelectric materials. Despite some recent investigations on vibration behaviors of functionally graded piezoelectric (FGP) nanoplates, this problem based on the nonlocal strain gradient theory has not been studied so far. We study the free vibration of an FGP nanoplate based on the nonlocal strain gradient theory. We solve analytically the equations and determine the natural frequency of the FGP nanoplate
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