Nonlinear normal modes of nonconservative systems

L. Renson; G. Kerschen

doi:10.1007/978-1-4614-6570-6_17

Nonlinear normal modes of nonconservative systems

L. Renson^*, G. Kerschen

^*Corresponding author for this work

Department of Engineering Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

4 Citations (Scopus)

Abstract

Linear modal analysis is a mature tool enjoying various applications ranging from bridges to satellites. Nevertheless, modal analysis fails in the presence of nonlinear dynamical phenomena and the development of a practical nonlinear analog of modal analysis is a current research topic. Recently, numerical techniques (e.g., harmonic balance, continuation of periodic solutions) were developed for the computation of nonlinear normal modes (NNMs). Because these methods arc limited to conservative systems, the present study targets the computation of NNMs for nonconservative systems. Their definition as invariant manifolds in phase space is considered. Specifically, a new finite element technique is proposed to solve the set of partial differential equations governing the manifold geometry.

Original language	English
Title of host publication	Conference Proceedings of the Society for Experimental Mechanics Series
Pages	189-202
Number of pages	14
Volume	1
DOIs	https://doi.org/10.1007/978-1-4614-6570-6_17
Publication status	Published - 2013
Event	31st IMAC, A Conference on Structural Dynamics, 2013 - Garden Grove, CA, United States Duration: 11 Feb 2013 → 14 Feb 2013

Conference

Conference	31st IMAC, A Conference on Structural Dynamics, 2013
Country/Territory	United States
City	Garden Grove, CA
Period	11/02/13 → 14/02/13

Keywords

Invariant manifold
Nonconservative systems
Nonlinear modal analysis
Nonlinear normal modes

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title = "Nonlinear normal modes of nonconservative systems",

abstract = "Linear modal analysis is a mature tool enjoying various applications ranging from bridges to satellites. Nevertheless, modal analysis fails in the presence of nonlinear dynamical phenomena and the development of a practical nonlinear analog of modal analysis is a current research topic. Recently, numerical techniques (e.g., harmonic balance, continuation of periodic solutions) were developed for the computation of nonlinear normal modes (NNMs). Because these methods arc limited to conservative systems, the present study targets the computation of NNMs for nonconservative systems. Their definition as invariant manifolds in phase space is considered. Specifically, a new finite element technique is proposed to solve the set of partial differential equations governing the manifold geometry.",

keywords = "Invariant manifold, Nonconservative systems, Nonlinear modal analysis, Nonlinear normal modes",

author = "L. Renson and G. Kerschen",

year = "2013",

doi = "10.1007/978-1-4614-6570-6_17",

language = "English",

isbn = "9781461465690",

volume = "1",

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T1 - Nonlinear normal modes of nonconservative systems

AU - Renson, L.

AU - Kerschen, G.

PY - 2013

Y1 - 2013

N2 - Linear modal analysis is a mature tool enjoying various applications ranging from bridges to satellites. Nevertheless, modal analysis fails in the presence of nonlinear dynamical phenomena and the development of a practical nonlinear analog of modal analysis is a current research topic. Recently, numerical techniques (e.g., harmonic balance, continuation of periodic solutions) were developed for the computation of nonlinear normal modes (NNMs). Because these methods arc limited to conservative systems, the present study targets the computation of NNMs for nonconservative systems. Their definition as invariant manifolds in phase space is considered. Specifically, a new finite element technique is proposed to solve the set of partial differential equations governing the manifold geometry.

AB - Linear modal analysis is a mature tool enjoying various applications ranging from bridges to satellites. Nevertheless, modal analysis fails in the presence of nonlinear dynamical phenomena and the development of a practical nonlinear analog of modal analysis is a current research topic. Recently, numerical techniques (e.g., harmonic balance, continuation of periodic solutions) were developed for the computation of nonlinear normal modes (NNMs). Because these methods arc limited to conservative systems, the present study targets the computation of NNMs for nonconservative systems. Their definition as invariant manifolds in phase space is considered. Specifically, a new finite element technique is proposed to solve the set of partial differential equations governing the manifold geometry.

KW - Invariant manifold

KW - Nonconservative systems

KW - Nonlinear modal analysis

KW - Nonlinear normal modes

UR - http://www.scopus.com/inward/record.url?scp=84880542488&partnerID=8YFLogxK

U2 - 10.1007/978-1-4614-6570-6_17

DO - 10.1007/978-1-4614-6570-6_17

M3 - Conference Contribution (Conference Proceeding)

AN - SCOPUS:84880542488

SN - 9781461465690

VL - 1

SP - 189

EP - 202

BT - Conference Proceedings of the Society for Experimental Mechanics Series

T2 - 31st IMAC, A Conference on Structural Dynamics, 2013

Y2 - 11 February 2013 through 14 February 2013

ER -

Nonlinear normal modes of nonconservative systems

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