1 Department of Mechanical Engineering, Technical University of Denmark2 Department of Applied Mathematics and Computer Science, Technical University of Denmark3 Dynamical Systems, Department of Applied Mathematics and Computer Science, Technical University of Denmark4 Mathematics, Department of Applied Mathematics and Computer Science, Technical University of Denmark5 Solid Mechanics, Department of Mechanical Engineering, Technical University of Denmark6 IT Service, Administration, Technical University of Denmark7 Dynamical systems, Department of Mathematics, Technical University of Denmark
We propose and investigate three different methods for assessing stability of dynamical equilibrium states during experimental bifurcation analysis, using a control-based continuation method. The idea is to modify or turn off the control at an equilibrium state and study the resulting behavior. As a proof of concept the three methods are successfully implemented and tested for a harmonically forced impact oscillator with a hardening spring nonlinearity, and controlled by electromagnetic actuators. We show that under certain conditions it is possible to quantify the instability in terms of finite-time Lyapunov exponents. As a special case we study an isolated branch in the bifurcation diagram brought into existence by a 1:3 subharmonic resonance. On this isola it is only possible to determine stability using one of the three methods, which is due to the fact that only this method guarantees that the equilibrium state can be restored after measuring stability.
Journal of Sound and Vibration, 2014, Vol 333, Issue 21