An effective finite-element-based method for the computation of nonlinear normal modes of nonconservative systems

Ludovic Renson; Geoffrey Deliege; Gaetan Kerschen

doi:10.1007/s11012-014-9875-3

An effective finite-element-based method for the computation of nonlinear normal modes of nonconservative systems

Ludovic Renson, Geoffrey Deliege, Gaetan Kerschen

Department of Engineering Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

26 Citations (Scopus)

328 Downloads (Pure)

Abstract

This paper addresses the numerical computation of nonlinear normal modes defined as two-dimensional invariant manifolds in phase space. A novel finite-element-based algorithm, combining the streamline upwind Petrov–Galerkin method with mesh moving and domain prediction–correction techniques, is proposed to solve the manifold-governing partial differential equations. It is first validated using conservative examples through the comparison with a reference solution given by numerical continuation. The algorithm is then demonstrated on nonconservative examples.

Original language	English
Pages (from-to)	1901-1916
Number of pages	16
Journal	Meccanica
Volume	49
Issue number	8
Early online date	24 Jan 2014
DOIs	https://doi.org/10.1007/s11012-014-9875-3
Publication status	Published - Aug 2014

Keywords

Nonlinear normal modes
Invariant manifolds
Nonconservative systems
Modal analysis
Finite element method

Access to Document

10.1007/s11012-014-9875-3

Full-text PDF (accepted author manuscript)
This is the accepted author manuscript (AAM). The final published version (version of record) is available online via Springer Verlag at DOI: 10.1007/s11012-014-9875-3 . Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 2.73 MB

Cite this

@article{7cc0aece657640df83d0ebf98e349e84,

title = "An effective finite-element-based method for the computation of nonlinear normal modes of nonconservative systems",

abstract = "This paper addresses the numerical computation of nonlinear normal modes defined as two-dimensional invariant manifolds in phase space. A novel finite-element-based algorithm, combining the streamline upwind Petrov–Galerkin method with mesh moving and domain prediction–correction techniques, is proposed to solve the manifold-governing partial differential equations. It is first validated using conservative examples through the comparison with a reference solution given by numerical continuation. The algorithm is then demonstrated on nonconservative examples.",

keywords = "Nonlinear normal modes, Invariant manifolds, Nonconservative systems, Modal analysis, Finite element method",

author = "Ludovic Renson and Geoffrey Deliege and Gaetan Kerschen",

year = "2014",

month = aug,

doi = "10.1007/s11012-014-9875-3",

language = "English",

volume = "49",

pages = "1901--1916",

journal = "Meccanica",

issn = "0025-6455",

publisher = "Springer Netherlands",

number = "8",

}

TY - JOUR

T1 - An effective finite-element-based method for the computation of nonlinear normal modes of nonconservative systems

AU - Renson, Ludovic

AU - Deliege, Geoffrey

AU - Kerschen, Gaetan

PY - 2014/8

Y1 - 2014/8

N2 - This paper addresses the numerical computation of nonlinear normal modes defined as two-dimensional invariant manifolds in phase space. A novel finite-element-based algorithm, combining the streamline upwind Petrov–Galerkin method with mesh moving and domain prediction–correction techniques, is proposed to solve the manifold-governing partial differential equations. It is first validated using conservative examples through the comparison with a reference solution given by numerical continuation. The algorithm is then demonstrated on nonconservative examples.

AB - This paper addresses the numerical computation of nonlinear normal modes defined as two-dimensional invariant manifolds in phase space. A novel finite-element-based algorithm, combining the streamline upwind Petrov–Galerkin method with mesh moving and domain prediction–correction techniques, is proposed to solve the manifold-governing partial differential equations. It is first validated using conservative examples through the comparison with a reference solution given by numerical continuation. The algorithm is then demonstrated on nonconservative examples.

KW - Nonlinear normal modes

KW - Invariant manifolds

KW - Nonconservative systems

KW - Modal analysis

KW - Finite element method

U2 - 10.1007/s11012-014-9875-3

DO - 10.1007/s11012-014-9875-3

M3 - Article (Academic Journal)

VL - 49

SP - 1901

EP - 1916

JO - Meccanica

JF - Meccanica

SN - 0025-6455

IS - 8

ER -

An effective finite-element-based method for the computation of nonlinear normal modes of nonconservative systems

Abstract

Keywords

Access to Document

Fingerprint

Cite this