Vibration analysis of decoupling nonlinear systems with cubic terms

Based on the common phenomenon of vibration decoupling caused by hard supports in engineering cases such as aviation, automobiles, and machinery, a three degree of freedom nonlinear system model with a cubic term is proposed. Representative vibration parameters of different stages of the system are introduced, and the dynamic response of each degree of freedom is analyzed from phase diagrams and Poincare section characteristics. It is explained that as the vibration progresses from weak to strong, the system changes from single cycle to multi period. Subsequently, the nonlinear behavior has evolved from multi period to bifurcation chaos indicating direct perception of system environmental parameters. This provides a good theoretical basis for online monitoring of such engineering vibrations.