Journal
JOURNAL OF SOUND AND VIBRATION
Volume 468, Issue -, Pages -Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jsv.2019.115039
Keywords
Spectral submanifolds; Lyapunov subcenter manifold; Model-order reduction; Nonlinear normal modes; Structural dynamics; Backbone curves; Forced-response curves
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For general nonlinear mechanical systems, we derive closed-form, reduced-order models up to cubic order based on rigorous invariant manifold results. For conservative systems, the reduction is based on Lyapunov Subcenter Manifold (LSM) theory, whereas for damped-forced systems, we use Spectral Submanifold (SSM) theory. To evaluate our explicit formulas for the reduced model, no coordinate changes are required beyond an initial linear one. The reduced-order models we derive are simple and depend only on physical and modal parameters, allowing us to extract fundamental characteristics, such as backbone curves and forced-response curves, of multi-degree-of-freedom mechanical systems. To numerically verify the accuracy of the reduced models, we test the reduction formulas on several mechanical systems, including a higher-dimensional nonlinear Timoshenko beam. (C) 2019 Elsevier Ltd. All rights reserved.
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