INFLUENCE OF THE LOGARITHMIC DECREMENT BASE ON THE ACCURACY OF APPROXIMATING AMPLITUDE CHARACTERISTICS OF OSCILLATIONS

Résumé fourni par la source

The stage of identifying nonlinear force characteristics of oscillatory systems based on the transition from a discrete description of a dynamic process by sequences of oscillation amplitudes and periods to analytical dependencies for amplitude and phase is considered. Based on the realization of free damped oscillations, sequences of peak-to-peak amplitudes and periods were determined, the dependence of the logarithmic decrement on amplitude was constructed, and its approximation by polynomials of various degrees was performed. The influence of amplitude measurement errors on the approximation accuracy was investigated. It is shown that at an amplitude measurement noise level of 0.2%, the approximation error of the classical decrement increases to 43–98% depending on the polynomial degree, whereas transitioning to a generalized decrement with a base of k=5…10 reduces the error to 5–11%. The use of a generalized logarithmic decrement with an extended calculation base is proposed. It is shown that increasing the decrement base significantly enhances the noise immunity of the procedure for constructing the logarithmic decrement dependence and allows for a substantial reduction in the approximation error.

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