A global methodology for the modal reduction of large nonlinear systems containing quadratic and cubic nonlinearities

E. Pesheck, C. Pierre

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations

Abstract

A methodology is presented for the systematic modal reduction of structural systems which contain quadratic and cubic nonlinearities in displacement. The procedure is based on the center manifold approach for describing individual nonlinear modes, but it has been extended to account for simultaneous motion within several chosen modal coordinates. Motions of the reduced system are constrained to lie on high-dimensional manifolds within the phase space of the original system. Polynomial approximations of these manifolds are obtained through third order for arbitrary system parameters. Algorithms have been developed for automation of this procedure, and they are applied to an example system. Free and forced responses of the reduced system are discussed and compared to responses reduced through simple modal truncation. A more rigorous treatment of harmonic forcing is proposed, which will allow for the production of high-dimensional, time-dependent manifolds through a simple adaptation of the unforced procedure.

Original languageEnglish
Title of host publication16th Biennial Conference on Mechanical Vibration and Noise
ISBN (Electronic)9780791880401
DOIs
StatePublished - 1997
EventASME 1997 Design Engineering Technical Conferences, DETC 1997 - Sacramento, United States
Duration: 14 Sep 199717 Sep 1997

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume1A-1997

Conference

ConferenceASME 1997 Design Engineering Technical Conferences, DETC 1997
Country/TerritoryUnited States
CitySacramento
Period14/09/9717/09/97

Fingerprint

Dive into the research topics of 'A global methodology for the modal reduction of large nonlinear systems containing quadratic and cubic nonlinearities'. Together they form a unique fingerprint.

Cite this