Non-linear modal analysis of the forced response of structural systems

Nicolas Boivin, Christophe Pierre, Steven W. Shaw

Research output: Contribution to conferencePaper

2 Citations (Scopus)

Abstract

A non-linear modal analysis procedure is presented for the forced response of non-linear structural systems. It utilizes the notion of invariant manifolds in the phase space, which was recently used to define non-linear normal modes and the corresponding non-linear modal analysis for unforced vibratory systems. For harmonic forcing, a similar procedure could be formulated, simply by augmenting the size of the free vibration problem. However, in order to accommodate general, non-harmonic external excitations, the invariant manifolds associated with the unforced system are used herein for the forced response analysis. The procedure allows one to generate reduced-order models for the forced analysis of structural systems. Although strictly speaking the invariance property is violated, good results are obtained for the case study considered. In particular, it is found that fewer non-linear modes than linear modes are needed to perform a forced modal analysis with the same accuracy. For systems with small and/or diagonal damping, approximate invariant manifolds are determined, which are shown to yield good results for both the unforced and forced responses.

Original languageEnglish (US)
Pages385-405
Number of pages21
DOIs
StatePublished - Jan 1 1996
EventAIAA Dynamics Specialists Conference, 1996 - Salt Lake City, United States
Duration: Apr 18 1996Apr 19 1996

Other

OtherAIAA Dynamics Specialists Conference, 1996
CountryUnited States
CitySalt Lake City
Period4/18/964/19/96

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Modal analysis
Invariance
Damping

Cite this

Boivin, N., Pierre, C., & Shaw, S. W. (1996). Non-linear modal analysis of the forced response of structural systems. 385-405. Paper presented at AIAA Dynamics Specialists Conference, 1996, Salt Lake City, United States. https://doi.org/10.2514/6.1996-1250
Boivin, Nicolas ; Pierre, Christophe ; Shaw, Steven W. / Non-linear modal analysis of the forced response of structural systems. Paper presented at AIAA Dynamics Specialists Conference, 1996, Salt Lake City, United States.21 p.
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Boivin, N, Pierre, C & Shaw, SW 1996, 'Non-linear modal analysis of the forced response of structural systems' Paper presented at AIAA Dynamics Specialists Conference, 1996, Salt Lake City, United States, 4/18/96 - 4/19/96, pp. 385-405. https://doi.org/10.2514/6.1996-1250

Non-linear modal analysis of the forced response of structural systems. / Boivin, Nicolas; Pierre, Christophe; Shaw, Steven W.

1996. 385-405 Paper presented at AIAA Dynamics Specialists Conference, 1996, Salt Lake City, United States.

Research output: Contribution to conferencePaper

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Boivin N, Pierre C, Shaw SW. Non-linear modal analysis of the forced response of structural systems. 1996. Paper presented at AIAA Dynamics Specialists Conference, 1996, Salt Lake City, United States. https://doi.org/10.2514/6.1996-1250