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Simultaneous Resonance and Anti-Resonance in Dynamical Systems Under Asynchronous Parametric Excitation

Karev, Artem and Hagedorn, Peter (2020):
Simultaneous Resonance and Anti-Resonance in Dynamical Systems Under Asynchronous Parametric Excitation.
In: Journal of Computational and Nonlinear Dynamics, 15 (9), pp. 091001. American Society of Mechanical Engineers (ASME), ISSN 1555-1415,
DOI: 10.1115/1.4046499,
[Article]

Abstract

Since the discovery of parametric anti-resonance, parametric excitation has also become more prominent for its stabilizing properties. While resonance and anti-resonance are mostly studied individually, there are systems where both effects appear simultaneously at each combination resonance frequency. With a steep transition between them and a high sensitivity of their relative positions, there is a need for a concurrent study of resonance and anti-resonance. The semi-analytical method of normal forms is used to derive approximate analytical expressions describing the magnitude of the stability impact as well as the precise locations of stabilized and destabilized areas. The results reveal that the separate appearance of resonance and anti-resonance is only a special case occurring for synchronous parametric excitation. In particular, in circulatory systems the simultaneous appearance is expected to be much more common.

Item Type: Article
Erschienen: 2020
Creators: Karev, Artem and Hagedorn, Peter
Title: Simultaneous Resonance and Anti-Resonance in Dynamical Systems Under Asynchronous Parametric Excitation
Language: English
Abstract:

Since the discovery of parametric anti-resonance, parametric excitation has also become more prominent for its stabilizing properties. While resonance and anti-resonance are mostly studied individually, there are systems where both effects appear simultaneously at each combination resonance frequency. With a steep transition between them and a high sensitivity of their relative positions, there is a need for a concurrent study of resonance and anti-resonance. The semi-analytical method of normal forms is used to derive approximate analytical expressions describing the magnitude of the stability impact as well as the precise locations of stabilized and destabilized areas. The results reveal that the separate appearance of resonance and anti-resonance is only a special case occurring for synchronous parametric excitation. In particular, in circulatory systems the simultaneous appearance is expected to be much more common.

Journal or Publication Title: Journal of Computational and Nonlinear Dynamics
Journal volume: 15
Number: 9
Publisher: American Society of Mechanical Engineers (ASME)
Divisions: 16 Department of Mechanical Engineering
16 Department of Mechanical Engineering > Institute of Numerical Methods in Mechanical Engineering (FNB)
Date Deposited: 17 Aug 2020 07:22
DOI: 10.1115/1.4046499
Official URL: https://asmedigitalcollection.asme.org/computationalnonlinea...
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