Analytic upper and lower bounds for the period of nonlinear oscillators

We show that analytic expressions for the frequency of second-order nonlinear oscillations can be obtained from dual variational principles. At each amplitude two analytic expressions can be constructed which constitute upper and lower bounds to the exact value of the frequency. The results are accu...

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Bibliographic Details
Published in:Journal of sound and vibration 2009-12, Vol.328 (3), p.338-344
Main Authors: Depassier, M.C., Haikala, V.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Physics
Solid mechanics
Structural and continuum mechanics
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
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Summary:We show that analytic expressions for the frequency of second-order nonlinear oscillations can be obtained from dual variational principles. At each amplitude two analytic expressions can be constructed which constitute upper and lower bounds to the exact value of the frequency. The results are accurate at small and large amplitude and compare well with the perturbative approach.
ISSN:0022-460X
1095-8568
DOI:10.1016/j.jsv.2009.08.019