Eur. Phys. J. Plus (2019) 134: 112
https://doi.org/10.1140/epjp/i2019-12464-x

Regular Article

Application of the nonlocal strain gradient elasticity on the wave dispersion behaviors of inhomogeneous nanosize beams

¹ Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran
² School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

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

Received: 10 September 2018
Accepted: 10 December 2018
Published online: 21 March 2019

Abstract

In this article, the wave dispersion analysis of heterogeneous functionally graded (FG) nanosize beams is undertaken in the framework of a nonlocal strain gradient higher-order beam theory. Shear deformation effects are completely included free from any additional shear correction coefficient by the means of a refined sinusoidal beam theorem. Furthermore, the small scale effects are covered based on the nonlocal strain gradient elasticity theory. This is proven that the aforementioned theory is powerful enough to guesstimate the behavior of the nanostructures better than formerly presented ones. In fact, both stiffness-softening and -hardening characteristics of nanosize elements are coupled together in this theory. On the other hand, the equivalent material properties are achieved utilizing the rule of mixture. The motion equations are derived extending the dynamic version of the principle of virtual work. Thereafter, the size-dependent partial differential equations of the problem are solved based on an exponential solution function to reach the circular wave frequency. Next, some graphical examples are presented to investigate the influences of various parameters on the wave propagation behaviors of FG nanobeams.