Methods for determining resonant and parametric excitation frequencies of nonlinear dynamic systems

Abstract

This paper presents methods for determining resonant and parametric excitation frequencies in a nonlinear single-degree-of-freedom dynamic system. The results show that in nonlinear dynamic system there are four groups of resonant frequencies, which are defined by energy, force, stiffness connection peculiarities, as well as the total stiffness of the system. The results also demonstrate that the system generates a very wide spectrum of parametric excitation frequencies, such that when they coincide with the resonant frequency the level of system vibrations increases significantly. By setting the parameters of the system (stiffness, mass, damping, etc.), we determine its resonant frequencies, however the frequency and number of parametric vibrations of a dynamic system depend on the level of nonlinearity of the system. Thus, the frequency of parametric vibration is independent of their amplitude. The certainty of the analytical methods presented in the article was verified by numerical calculations.