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Parametric Random Excitation of a Damped Mathieu Oscillator
Author(s) -
Ariaratnam S. T.,
Tam D. S. F.
Publication year - 1976
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19760561102
Subject(s) - excitation , parametric statistics , mathieu function , parametric oscillator , moment (physics) , harmonic oscillator , white noise , physics , mathematics , instability , stability (learning theory) , statistical physics , mathematical analysis , classical mechanics , quantum mechanics , statistics , machine learning , computer science
The effect of parametric random excitation on the moment stability of a damped Mathieu oscillator is investigated. Conditions for stability of the first and second moments of the response are obtained when the harmonic excitation lies in the neighbourhood of twice the natural frequency of the oscillator. It is found that the presence of the additional parametric random excitation can cause either a stabilizing or a destabilizing effect depending on the values of certain parameters of the random excitation. In particular, it is shown that parametric excitation by white noise has no effect on the first moments of the response but has a destabilizing effect on the second moments. For the case of exponentially correlated noise, regions of instability are shown in graphical form.