Eur. Phys. J. Plus (2019) 134: 157
https://doi.org/10.1140/epjp/i2019-12510-9

Regular Article

Wave dispersion characteristics of heterogeneous nanoscale beams via a novel porosity-based homogenization scheme

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: 5 October 2018
Accepted: 15 January 2019
Published online: 16 April 2019

Abstract

The important effect of porosity on the mechanical behaviors of a continuum, makes it necessary to be accounted for while analyzing the structure. Motivated by this fact, a new porosity-dependent homogenization scheme is presented in this article to investigate the wave propagation responses of functionally graded (FG) nanobeams by considering the coupling effects between density and Young’s moduli in porous materials. In the introduced homogenization method, which is a modified form of the power-law model, dependency of effective Young’s modulus to the mass density is covered. Based on the Hamilton principle, the Navier equations are developed using the Euler-Bernoulli beam model. Thereafter, the constitutive equations are obtained employing the nonlocal elasticity theory of Eringen. Next, the governing equations are solved in order to reach the wave frequency. Once the validity of presented methodology is proved, a set of parametric studies are adopted to emphasize the role of each variant on the wave dispersion behaviors of porous FG nanobeams.