WEAK NON-LINEARITY EFFECT ON STOCHASTIC PARAMETRIC RESONANCE
V. Kagalovsky2001, Journal of Sound and Vibration
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Abstract
The question of stability is one of the basic questions in the theory of oscillations. The in#uence of external forces or parametric perturbation of the system may lead to di!erent resonant phenomena . If the parameters of the system are #uctuating, the corresponding resonance is called a stochastic parametric resonance (SPR) [2}4]. It has to be distinguished from the phenomenon described in reference , where external forces cause resonant transitions between the neighboring potential wells. SPR manifests itself in the increase of the moments of higher orders with time, while the mean values of the system remain "nite. Then the question of stability of the corresponding oscillations is an important one in the investigation of di!erent technical devices. It is known that relaxation (linear friction) in the system leads to the appearance of the lower boundary for the value of #uctuation intensity necessary for a rise of SPR . Non-linear friction (velocity times the square of the co-ordinate) stabilizes SPR , that can be easily understood by simple consideration of energy conservation.
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