TY - GEN
T1 - A global methodology for the modal reduction of large nonlinear systems containing quadratic and cubic nonlinearities
AU - Pesheck, E.
AU - Pierre, C.
N1 - Publisher Copyright:
© 1997 by ASME.
PY - 1997
Y1 - 1997
N2 - 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.
AB - 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.
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U2 - 10.1115/DETC97/VIB-3952
DO - 10.1115/DETC97/VIB-3952
M3 - Conference contribution
AN - SCOPUS:85051988545
T3 - Proceedings of the ASME Design Engineering Technical Conference
BT - 16th Biennial Conference on Mechanical Vibration and Noise
T2 - ASME 1997 Design Engineering Technical Conferences, DETC 1997
Y2 - 14 September 1997 through 17 September 1997
ER -