When does a periodic response exist in a periodically forced multi-degree-of-freedom mechanical system?
Open access
Date
2019-11Type
- Journal Article
Abstract
While periodic responses of periodically forced dissipative nonlinear mechanical systems are commonly observed in experiments and numerics, their existence can rarely be concluded in rigorous mathematical terms. This lack of a priori existence criteria for mechanical systems hinders definitive conclusions about periodic orbits from approximate numerical methods, such as harmonic balance. In this work, we establish results guaranteeing the existence of a periodic response without restricting the amplitude of the forcing or the response. Our results provide a priori justification for the use of numerical methods for the detection of periodic responses. We illustrate on examples that each condition of the existence criterion we discuss is essential. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000392054Publication status
publishedExternal links
Journal / series
Nonlinear DynamicsVolume
Pages / Article No.
Publisher
SpringerSubject
Nonlinear oscillations; Periodic response; Global analysis; Harmonic balance; Existence criterionOrganisational unit
03973 - Haller, George / Haller, George
Notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.More
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