Auto-parametric semi-trivial and post-critical response of a spherical pendulum damper

The pendulum vibration damper modelled as a two degree of freedom strongly non-linear auto-parametric system is investigated. A kinematic external excitation in the suspension point is applied. The excitation is considered to be horizontal and harmonically variable in time. A semi-trivial solution a...

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Bibliographic Details
Published in:Computers & structures 2009-10, Vol.87 (19), p.1204-1215
Main Authors: Náprstek, Jiří, Fischer, Cyril
Format: Article
Language:English
Subjects:
Asymptotic methods
Auto-parametric systems
Bifurcation points
Dynamic stability
Non-linear vibration
Spherical pendulum
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Summary:The pendulum vibration damper modelled as a two degree of freedom strongly non-linear auto-parametric system is investigated. A kinematic external excitation in the suspension point is applied. The excitation is considered to be horizontal and harmonically variable in time. A semi-trivial solution and its stability are analyzed. Special attention is paid to the resonance domain. In certain domains of pendulum and excitation parameters the semi-trivial solution does not exist in this domain and various post-critical three-dimensional regimes occur. Some of them are non-stationary despite the harmonic excitation. Three different types of the resonance domain are investigated. Their main properties depend significantly on dynamic parameters of the pendulum and of the external excitation amplitude. An analytical and numerical study brings forth several recommendations for designers of these devices. Their aim is to avoid any post-critical response regimes endangering the pendulum functionality.
ISSN:0045-7949
1879-2243
DOI:10.1016/j.compstruc.2008.11.015