Eur. Phys. J. Plus (2020) 135: 905
https://doi.org/10.1140/epjp/s13360-020-00923-6

Regular Article

Vibration analysis of stress-driven nonlocal integral model of viscoelastic axially FG nanobeams

¹ School of Mechanical Engineering, Iran University of Science and Technology, 16846-13114, Narmak, Tehran, Iran
² Center of Excellence in Railway Transportation, Iran University of Science and Technology, 16846-13114, Narmak, Tehran, Iran

^* e-mail: fakher@mecheng.iust.ac.ir

Received: 13 July 2020
Accepted: 5 November 2020
Published online: 13 November 2020

Abstract

Finite element method (FEM) and generalized differential quadrature method (GDQM) are developed for damping vibration analysis of viscoelastic axially functionally graded (VAFG) nanobeams within the framework of stress-driven nonlocal integral model (SDM). The equivalent differential law of SDM and two constitutive non-classic boundary conditions (CBCs) are utilized to construct FE and GDQ models. In FEM, three different types of beam elements are derived: two different types for the both ends of the nanobeam and another type for elements located in the middle of nanobeam. Convergence and accuracy of the present FEM and GDQM are evaluated, and it is shown that the present results and formulations are efficient and reliable. Also, in the damping vibration analysis of VAFG nanobeams by SDM, variations of the mechanical properties are considered as a power-law function. After validation of present results and mathematical modeling, various benchmark results are presented to determine the influences of several parameters, such as nonlocal SDM parameter, FG index and damping factor on both parts of size-dependent complex frequencies of VAFG nanobeams with different boundary conditions.