Eur. Phys. J. Plus (2022) 137: 5
https://doi.org/10.1140/epjp/s13360-021-02193-2

Regular Article

Size-dependent nonlinear free vibration of multilayer functionally graded graphene nanocomposite Timoshenko microbeam under different boundary conditions

¹ Department of Mechanical Engineering, Bijar Branch, Islamic Azad University, Bijar, Iran
² Department of Mechanical Engineering, Saghez Branch, Islamic Azad University, Saghez, Iran

^a F.allahkarami1366@gmail.com

Received: 25 September 2021
Accepted: 17 November 2021
Published online: 10 December 2021

Abstract

In the present study, nonlinear free vibration of functionally graded nanocomposite microbeam has been put forward. Estimating for effective elastic modulus of structure is carried out based upon the modified Halpin–Tsai micromechanics model. Three types of graphene platelets (GPLs) distribution patterns including U-pattern, X-pattern and O-pattern have been considered. The nonlinear motion equations and associated boundary conditions are extracted taking into account the Timoshenko beam model together with modified couple stress theory. Afterward, governing motion equations are solved through generalized differential quadrature method along with a standard iterative method. In order to confirm the correctness and validity of present model, a comparison between the natural frequency of structure and those published in the available literature is performed. Eventually, the manuscript attempts to scrutinize the influences of geometrical parameters of structure, GPLs patterns and their geometric, GPLs weight fraction and boundary conditions over both nonlinear frequency and frequency ratio of multilayer microbeam. It is revealed that the small-scale effect overshadows the impacts of GPLs weight fraction and GPLs geometric on frequency ratio, especially when thickness of microbeam tends to length scale parameter.