Energy equipartition and frequency distribution in complex attachments

Date
2009
Authors
Roveri, N.
Carcaterra, A.
Akay, A.
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Source Title
Journal of the Acoustical Society of America
Print ISSN
0001-4966
Electronic ISSN
Publisher
Acoustical Society of America
Volume
126
Issue
1
Pages
122 - 128
Language
English
Type
Article
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Abstract

As reported in several recent publications, an undamped simple oscillator with a complex attachment that consists of a set of undamped parallel resonators can exhibit unusual energy sharing properties. The conservative set of oscillators of the attachment can absorb nearly all the impulsive energy applied to the primary oscillator to which it is connected. The key factor in the ability of the attachment to absorb energy with near irreversibility correlates with the natural frequency distribution of the resonators within it. The reported results also show that a family of optimal frequency distributions can be determined on the basis of a variational approach, minimizing a certain functional related to the system response. The present paper establishes a link between these optimal frequency distributions and the energy equipartition principle: optimal frequency distributions are those that spread the injected energy as uniformly as possible over the degrees of freedom or over the modes of the system. Theoretical as well as numerical results presented support this point of view. © 2009 Acoustical Society of America.

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Keywords
Degrees of freedom, Energy equipartition, Energy sharings, Frequency distributions, Injected energy, Key factors, Numerical results, Optimal frequency, System response, Variational approaches, Oscillators (electronic), Resonators, Optimization
Citation
Published Version (Please cite this version)