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Dynamic stability of a nonlinear multiple-nanobeam system

Danilo Karlicic Orcid Logo, Milan Cajić, Sondipon Adhikari

Nonlinear Dynamics, Volume: 93, Issue: 3, Pages: 1495 - 1517

Swansea University Authors: Danilo Karlicic Orcid Logo, Sondipon Adhikari

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DOI (Published version): 10.1007/s11071-018-4273-3

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...

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Published in: Nonlinear Dynamics
ISSN: 0924-090X 1573-269X
Published: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa39986
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spelling 2023-02-14T15:36:48.0918441 v2 39986 2018-05-08 Dynamic stability of a nonlinear multiple-nanobeam system d99ee591771c238aab350833247c8eb9 0000-0002-7547-9293 Danilo Karlicic Danilo Karlicic true false 4ea84d67c4e414f5ccbd7593a40f04d3 Sondipon Adhikari Sondipon Adhikari true false 2018-05-08 EEN 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. Journal Article Nonlinear Dynamics 93 3 1495 1517 0924-090X 1573-269X Multiple-nanobeam system, Geometric nonlinearity, Nonlocal elasticity, Instability regions, IHB method, Floquet theory 31 12 2018 2018-12-31 10.1007/s11071-018-4273-3 COLLEGE NANME Engineering COLLEGE CODE EEN Swansea University 2023-02-14T15:36:48.0918441 2018-05-08T09:09:45.8452317 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering Danilo Karlicic 0000-0002-7547-9293 1 Milan Cajić 2 Sondipon Adhikari 3 0039986-08052018091210.pdf karlicic2018.pdf 2018-05-08T09:12:10.6300000 Output 7083532 application/pdf Version of Record true 2018-05-08T00:00:00.0000000 true eng
title Dynamic stability of a nonlinear multiple-nanobeam system
spellingShingle Dynamic stability of a nonlinear multiple-nanobeam system
Danilo Karlicic
Sondipon Adhikari
title_short Dynamic stability of a nonlinear multiple-nanobeam system
title_full Dynamic stability of a nonlinear multiple-nanobeam system
title_fullStr Dynamic stability of a nonlinear multiple-nanobeam system
title_full_unstemmed Dynamic stability of a nonlinear multiple-nanobeam system
title_sort Dynamic stability of a nonlinear multiple-nanobeam system
author_id_str_mv d99ee591771c238aab350833247c8eb9
4ea84d67c4e414f5ccbd7593a40f04d3
author_id_fullname_str_mv d99ee591771c238aab350833247c8eb9_***_Danilo Karlicic
4ea84d67c4e414f5ccbd7593a40f04d3_***_Sondipon Adhikari
author Danilo Karlicic
Sondipon Adhikari
author2 Danilo Karlicic
Milan Cajić
Sondipon Adhikari
format Journal article
container_title Nonlinear Dynamics
container_volume 93
container_issue 3
container_start_page 1495
publishDate 2018
institution Swansea University
issn 0924-090X
1573-269X
doi_str_mv 10.1007/s11071-018-4273-3
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering
document_store_str 1
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description 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.
published_date 2018-12-31T03:50:51Z
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