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.