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

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

36 Citations (Scopus)

437 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

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10.1007/s11012-014-9875-3

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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.",

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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)

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EP - 1916

JO - Meccanica

JF - Meccanica

IS - 8

ER -

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

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Keywords

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