Analytic prediction of isolated forced response curves from spectral submanifolds

We show how spectral submanifold (SSM) theory can be used to provide analytic predictions for the response of periodically forced multi-degree-of-freedom mechanical systems. These predictions include an explicit criterion for the existence of isolated forced responses that will generally be missed b...

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Bibliographic Details
Published in:Nonlinear dynamics Vol. 98; no. 4; pp. 2755 - 2773
Main Authors: Ponsioen, S., Pedergnana, T., Haller, G.
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.12.2019
Springer Nature B.V
Subjects:
Algorithms
Automotive Engineering
Classical Mechanics
Control
Dynamical Systems
Engineering
Manifolds (mathematics)
Mechanical Engineering
Mechanical systems
Original Paper
Vibration
Vibration control
Model order reduction
Spectral submanifolds
Isolas
Forced response curves
ISSN:0924-090X, 1573-269X
Online Access:Get full text
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Summary:We show how spectral submanifold (SSM) theory can be used to provide analytic predictions for the response of periodically forced multi-degree-of-freedom mechanical systems. These predictions include an explicit criterion for the existence of isolated forced responses that will generally be missed by numerical continuation techniques. Our analytic predictions can be refined to arbitrary precision via an algorithm that does not require the numerical solutions of the mechanical system. We illustrate all these results on low- and high-dimensional nonlinear vibration problems. We find that our SSM-based forced response predictions remain accurate in high-dimensional systems, in which numerical continuation of the periodic response is becoming computationally expensive.
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ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-019-05023-4