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Analytical estimates of the effect of nonlinear damping in some nonlinear oscillators. (English) Zbl 0999.70021
Under the assumption that general nonlinear damping terms are proportional to a power of velocity, the authors investigate the nonlinearly damped Duffing oscillator and nonlinearly damped simple pendulum. The critical parameters are provided in terms of damping coefficients and damping exponents. The authors also consider generalized nonlinear damped systems which may contain several nonlinear damping terms. Using the idea of Melnikov equivalence, the authors show that the effect of nonlinear dissipation can be equivalently described by a linearly damped nonlinear oscillator with modified damping coefficient.

MSC:
70K40 Forced motions for nonlinear problems in mechanics
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