Analytical and Numerical Investigation on the Duffing Oscilator Subjected to a Polyharmonic Force Excitation

Abstract

Abstract. An analytical solution for a specific case of the forced Duffing oscillator is proposed. The excitation force contains two harmonics with significant difference frequencies. This case corresponds to a presence of a defect in the machinery and is in the art of the machinery vibration diagnostics. The results obtained show an amplitude modulation. Therefore, the presence of an amplitude modulation in the vibration signal may be used as an indicator for a malfunction. Analytical solution derived clarifies how the amplitude modulation occurs. Also, a numerical solution is realized and compared with the analytical one. For this, the Duffing equation is solved numerically and then, the spectrograms of vibrations are obtained through a Discrete-time Fourier Transform.

Dynamic Smoothing Effect in Non-Linear Dynamic System under Polyharmonic External Excitation

“…The faster the frequency rate increases, the lower down are the peak shifts in the resonance frequencies and the less are the maximum oscillation amplitudes. This researches [ 4,5] prove the plausible existence of a number of additional local maxima of amplitudes in the linear systems under conditions of the rapidly changing frequencies of the external excitation.…”

“…At present, from a practical perspective, the problem of determining the stability of the oscillation modes in a system is of primary concern inasmuch as an unknown analytical solution based on a certain approximation has to ensure a complete validity of the conclusions on the system stability [4,5,9].…”

Influence of the Nonlinear Stiffness Parameter of the Vibratory Stress Relief Device on Strong Nonlinear Superharmonic Resonance

“…Compared with the strong nonlinear calculation method used in reference [13], the same parameters are used for the calculation and numerical solution [22], as shown in Fig. 5.…”