Abstract
In this paper, the stability of vehicle concerning the slow-varying sprung mass is analyzed based on two degrees of freedom quarter-car model. A mathematical model of vehicle is established, the nonlinear vibration caused by sprung mass vibration is solved, and frequency curve is obtained. The characteristics of a stable solution and the parameters affecting the stability are analyzed. The numeric solution shows that a slow-varying sprung mass is equivalent to adding a negative damping coefficient to the suspension system, making the effective damping coefficient change from negative to positive. Such changing parameters lead to Hopf bifurcation and a shrinking limit cycle. The simulation results indicate the existence of static as well as dynamic bifurcation and the result is a change in the final stable vibration of the suspension. Even the tiny vibration of the sprung mass will lead to amplitude mutation, leading to the sprung mass instability.
Highlights
The stability and bifurcation of a nonlinear system are closely related. Bifurcations that include both static and dynamic bifurcations affect the stability of the system. Static bifurcation such as saddle node bifurcation occurs mainly due to the nonlinear stiffness, discussed in vibration absorbers [1, 2]
Dynamic bifurcation such as Hopf bifurcation occurs due to the parameter variations, reported in induction motor drive system [3] and circuit system [4]
In the range l1 < 0, the initial amplitude inside the limit cycle increases and that outside the limit cycle reduces, all converging in the stable limit cycle in the end. This process leads to change in the static bifurcation nature of some initial values after they go through the dynamic bifurcation, destroying the system stability
Summary
The stability and bifurcation of a nonlinear system are closely related. Bifurcations that include both static and dynamic bifurcations affect the stability of the system. The stability of the rotational motion is studied in [15,16,17], of which the work presented in [16] analyzed an asymmetric rotation movement and found that both the Hopf bifurcation and the saddle node bifurcation will occur when the damping coefficient or the speed reaches a certain value. Different from that, the sprung mass is usually considered as constant It decreases slowly, adding a slowly varying parameter to a suspension system, which changes the form of the equations. A controller considering actuator time delay is presented in [28, 29] They focus only on the control of nonlinear suspension and time delay, ignoring the slowly changing parameters, especially the variations in sprung mass. 2. Governing Equation for Nonlinear Suspension with Slowly Varying Sprung Mass under Forced Vibration.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
