Dynamic stability of a nonlinear multiple-nanobeam system

Karličić, D., Cajić, M. and Adhikari, S. (2018) Dynamic stability of a nonlinear multiple-nanobeam system. Nonlinear Dynamics, 93(3), pp. 1495-1517. (doi: 10.1007/s11071-018-4273-3)

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Abstract

We use the incremental harmonic balance (IHB) method to analyse the dynamic stability problem of a nonlinear multiple-nanobeam system (MNBS) within the framework of Eringen’s nonlocal elasticity theory. The nonlinear dynamic system under consideration includes MNBS embedded in a viscoelastic medium as clamped chain system, where every nanobeam in the system is subjected to time-dependent axial loads. By assuming the von Karman type of geometric nonlinearity, a system of m nonlinear partial differential equations of motion is derived based on the Euler–Bernoulli beam theory and D’ Alembert’s principle. All nanobeams in MNBS are considered with simply supported boundary conditions. Semi-analytical solutions for time response functions of the nonlinear MNBS are obtained by using the single-mode Galerkin discretization and IHB method, which are then validated by using the numerical integration method. Moreover, Floquet theory is employed to determine the stability of obtained periodic solutions for different configurations of the nonlinear MNBS. Using the IHB method, we obtain an incremental relationship with the frequency and amplitude of time-varying axial load, which defines stability boundaries. Numerical examples show the effects of different physical and material parameters such as the nonlocal parameter, stiffness of viscoelastic medium and number of nanobeams on Floquet multipliers, instability regions and nonlinear amplitude–frequency response curves of MNBS. The presented results can be useful as a first step in the study and design of complex micro/nanoelectromechanical systems.

Item Type:Articles
Additional Information:This research was supported by the project of the Ministry of Education, Science and Technological Development of the Republic of Serbia under the Grant No. OI 174001.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Adhikari, Professor Sondipon
Authors: Karličić, D., Cajić, M., and Adhikari, S.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Nonlinear Dynamics
Publisher:Springer Nature
ISSN:0924-090X
ISSN (Online):1573-269X
Published Online:26 April 2018
Copyright Holders:Copyright © The Author(s) 2018
First Published:First published in Nonlinear Dynamics 93:1495–1517
Publisher Policy:Reproduced under a Creative Commons licence

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