Modulation of vibrations in a resonant system with variable own frequency

Abstract

Introduction. The absence of the calculated formulas for calculating the modulation coefficient in amplitude modulation, the deviation of the phase of oscillation in phase modulation and the deviation of the frequency of oscillations in frequency modulation in resonant systems, the model of which can be a linear oscillator with attenuation. Purpose. Determination of the basic relations between the effects of amplitude and phase modulation of oscillations. Methods. The problem of oscillations of the resonance system under the action of harmonic inducing force in conditions of harmonic change of one of the parameters of the resonance system is approximately solved by the method of slowly variable amplitudes. Results. Simple and convenient formulas for engineering calculations are obtained for the modulation coefficient in amplitude modulation and deviation of the phase of oscillations in phase modulation, and the conditions of their applications are specified. Conclusion . The solution of the problem of oscillations of a resonant system describes a stationary oscillation process and includes transitional attenuation oscillations. If the parameters of the resonance system are unchanged, and the inducing force is frequently-modulated then there is a transformation of the type of modulation in the resonant system: at optimal values of the resonant upset FM is converted into AM, and in the absence of the upset, FM is converted into PM. Since the phase and frequency modulations are connected, the regularities of phase modulation established by us allow us to find the relations of frequency modulation.