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Resonance in the Oscillation of Linear Systems under the Action of an Almost Periodic Parametric Perturbation

  • V. N. Fomin
Part of the Problems in Mathematical Analysis / Problemy Matematicheskogo Analiza / Πроблемы Математического Анализа book series (PMA)

Abstract

The phenomenon of parametric resonance is well known — the study of the conditions for its occurrence is one of the central problems of the theory of stability of elastic systems [1–4]. The case of periodic loading has been studied in sufficient detail [1–10]: Formulas for the effective calculation of the resonance frequencies of the perturbation, and the determination of the domains of dynamic instability adjoining them have been obtained and other problems of the theory of parametric resonance have been solved. The present article represents an attempt to develop the analogous theory in the case of systems subject to the action of an almost-periodic parametric perturbation. The latter is a more substantial case inasmuch as there are effects which do not have an analog in the periodic case. The existence of these effects prevents us from developing the theory as fully as could be expected at first sight. However, the basic results of the theory of parametric resonance can be extended to systems of the type under investigation.

Keywords

Operator Function Imaginary Axis Parametric Resonance Hamiltonian Equation Elastic System 
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Copyright information

© Consultants Bureau, New York 1971

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  • V. N. Fomin

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