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

Abstract

This paper presents methods for determining resonant and parametric excitation frequencies in a nonlinear two-degree-of-freedom dynamic system. It is clarified that in order to determine the resonant frequencies in the system, it must be divided into two subsystems. The results show that in nonlinear dynamic system there are nine 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 for determining the parametric frequencies must not be divided into subsystems. It is clarified that the system generated a very wide spectrum of parametric excitation frequencies, and when they coincide with the resonant frequency, the level of system vibrations increases significantly. It has been found that vibrations at high amplitude resonant frequency also become generators of parametric vibrations in a nonlinear dynamic system. By setting the parameters of the system (stiffness, mass, damping, etc.), we determine its resonant frequencies; however, the magnitude of the parametric vibration frequency and their number 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 paper was verified by numerical calculations.