Eur. Phys. J. Plus (2017) 132: 167
https://doi.org/10.1140/epjp/i2017-11441-9

Regular Article

Small-scale effects on the dynamic response of inhomogeneous nanobeams on elastic substrate under uniform dynamic load

Aerospace Engineering Department & Center of Excellence in Computational Aerospace, University of Technology, 15875-4413, Tehran, Iran

^* e-mail: h_shahverdi@aut.ac.ir

Received: 5 December 2016
Accepted: 7 March 2017
Published online: 13 April 2017

Abstract

In this article, forced vibration and resonance frequencies of functionally graded (FG) nanobeams resting on Winkler-Pasternak foundation are investigated employing a higher-order refined beam theory which captures shear deformation influences without the need for any shear correction factor. The nanobeam is subjected to a uniform dynamic load with a finite length. The two-parameter elastic medium consists of parallel springs and a shear layer. Gradation of the material properties of the nanobeam is described via the Mori-Tanaka distribution model. The governing equations of embedded higher-order FG nanobeams under dynamic loading are obtained by employing Eringen’s elastic differential law and Hamilton’s principle. These equations are solved for simply-supported-simply-supported (S-S) and clamped-clamped (C-C) boundary conditions. It is indicated that forced vibration characteristics and resonance frequencies of embedded FG nanobeams are significantly influenced by material composition, nonlocality, foundation parameters and boundary conditions. A nonlocal FG beam has lower resonance frequency compared with a local beam. However, the presence of elastic foundation leads to a significant delay in the occurrence of resonance frequencies.