Stability and Hopf Bifurcation of Impact Dynamics Considering Delay in a Semi-Active Energy Absorbing Suspension System

In a crash event, such as the crash of an aircraft or the collision of two ground vehicles, the impact dynamics are a function of the impact velocity and payload mass. A typical bumper system on a ground vehicle has passive viscous energy absorbers (PVEAs) that are optimally designed for a specific impact velocity and payload, so that off-design performance may be suboptimal, and may even be unacceptable for large perturbations in sink rate and payload mass from the designed values. This is because the load-stroke profile of the energy absorbing suspension system (EASS) is passive in that spring stiffness and damping of the energy absorbers is fixed. Therefore, in this study, the PVEA in an EASS is replaced by an active or semi-active energy absorber (SAEA), and the effects of time delay in achieving controllable semi-active damping is analyzed in the context of impact dynamics. To accomplish this, a three degree-of-freedom dynamic model of an EASS is presented, and the effect of the time delay in commanding the controllable force of the EA is analyzed. The asymptotic stability and Hopf bifurcation of the trivial steady state response are analyzed for a range of time delay. A technique to stabilize the impact dynamic is developed, and it is shown that the impact dynamics can be stabilized using appropriate feedback control.