Nonlinear vibration characteristics and bifurcation control of a class of piecewise constrained systems with dynamic clearances

Considering the mass block system under Piecewise nonlinear constraint, the vibration dynamic model of the system is established according to the generalized dissipative Lagrange principle, and the average method is used to solve the amplitude-frequency response of the vibration system. The influence of system parameters on vibration characteristics is analyzed with amplitude-frequency characteristics, phase plane characteristics, frequency characteristics, bifurcation characteristics ,and so on. The results show that: 1) the reverse of the rate of change of Piecewise nonlinear elastic force will destroy the stability of the system and obtain the relationship of the constraint parameters that need to be satisfied when the system is stable at the piecewise critical point. 2) With the increase in the number of nonlinear constraints, the vibration displacement of the system tends to be chaotic, and the frequency composition becomes more complex and variable, prone to resonance behavior. 3) As the static gap decreases and the dynamic gap amplitude and frequency increase, the unstable frequency range of the system will increase, and the vibration behavior will become chaotic and difficult to predict. 4) The design of a differential sliding mode controller can effectively control the bifurcation behavior of the system.