Fast Computation of Steady-State Response for Nonlinear Vibrations of High-Degree-of-Freedom Systems

Abstract

We discuss an integral equation approach that enables fast computation of the response of nonlinear multi-degree-of-freedom mechanical systems under periodic and quasi-periodic external excitation. The kernel of this integral equation is a Green's function that we compute explicitly for general mechanical systems. We derive conditions under which the integral equation can be solved by a simple and fast Picard iteration even for non-smooth mechanical systems. The convergence of this iteration cannot be guaranteed for near-resonant forcing, for which we employ a Newton--Raphson iteration instead, obtaining robust convergence. We further show that this integral-equation approach can be appended with standard continuation schemes to achieve an additional, significant performance increase over common approaches to computing steady-state response.

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Cited by in corpus (6)

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• Nonlinear analysis of forced mechanical systems with internal resonance using spectral submanifolds, Part II: Bifurcation and quasi-periodic response
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• Using Spectral Submanifolds for Optimal Mode Selection in Model Reduction
• Integral Equations & Model Reduction For Fast Computation of Nonlinear Periodic Response
• Exact Model Reduction and Fast Forced Response Calculation in High-Dimensional Nonlinear Mechanical Systems