Eur. Phys. J. Plus (2017) 132: 449
https://doi.org/10.1140/epjp/i2017-11694-2

Regular Article

Wave propagation analysis of embedded nanoplates based on a nonlocal strain gradient-based surface piezoelectricity theory

Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran

^* e-mail: febrahimy@eng.ikiu.ac.ir

Received: 31 July 2017
Accepted: 7 September 2017
Published online: 2 November 2017

Abstract

The present paper deals with the smart characteristics of waves propagating in a piezoelectric nanosize plate rested on an elastic medium whenever surface effects are included. A more realistic simulation about the elastic medium is presented by utilizing a three-parameter medium containing Winkler, Pasternak and damping coefficients. Furthermore, both of the decreasing and increasing impacts of small scale influences are covered in the framework of a nonlocal strain gradient theory (NSGT). The electric potential is approximated by a function possessing linear and trigonometric parts. Also, by developing the surface elasticity theory of Gurtin-Murdoch for piezoelectric solids, influences of surface layers are considered. Kinematic relations are derived employing the Kirchhoff plate theory. Afterwards, Hamilton’s principle is introduced in order to achieve Euler-Lagrange equations of piezoelectric nanoplates. The final part consists of an analytical approach to obtain the wave frequency value. The accuracy of the presented model is verified by organizing a comparison of the presented results with previous ones. Finally, some parametric case studies are rendered to clarify the influence of different parameters such as wave number, nonlocal and length scale parameters, foundation parameters and applied voltage.