Existence of quasi-periodic responses in quasi-periodically forced nonlinear mechanical systems
Open access
Author
Date
2021Type
- Journal Article
Abstract
Forced responses of mechanical systems are crucial design and performance criteria. Hence, their robust and reliable calculation is of vital importance. While numerical computation of periodic responses benefits from an extensive mathematical basis, the literature for quasi-periodically forced systems is limited. More specifically, the absence of applicable and general existence criterion for quasi-periodic orbits of nonlinear mechanical systems impedes definitive conclusions from numerical methods such as harmonic balance. In this work, we establish a general existence criterion for quasi-periodically forced vibratory systems with nonlinear stiffness terms. Our criterion does not rely on any small parameters and hence is applicable for large response and forcing amplitudes. On explicit numerical examples, we demonstrate how our existence criterion can be utilized to justify subsequent numerical computations of forced responses. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000500374Publication status
publishedExternal links
Journal / series
Nonlinear DynamicsVolume
Pages / Article No.
Publisher
SpringerSubject
Nonlinear oscillations; Steady-state response; Global analysis; Harmonic balance; Existence criterion; Quasi-periodic oscillationsOrganisational unit
03973 - Haller, George / Haller, George
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