Virtual Mechanical System control law for vibration mitigation in a system with arctangent nonlinearity

This study investigates a one-degree-of-freedom (DOF) system with softening stiffness, modelled with an arctangent characteristic, and subjected to impulsive excitation. The goal is to free the host system from vibrations by transferring the vibration energy from this system to an active controller. To this end, a Virtual Mechanical System (VMS) control law is implemented. This law is characterised by controller dynamics, which describe the behaviour of a mechanical system coupled to the host system skew-symmetrically in the velocities and having identical stiffness to the host system. The hypothesis is that the similarity facilitates energy transfer. By using the Complexification-Averaging (CxA) technique and examining the slow flow dynamics wrt. fixed points, bifurcations and impulsive orbits, the conditions for energy transfer are uncovered.