Using Time-Periodicity for Inducing Energy Transfer Between Vibration Modes

Introducing time-periodicity in system parameters may lead, in general, to a dangerous and well-known parametric resonance. In contrast to such a resonance, a properly tuned time-periodicity is capable of transferring energy between vibration modes. Time-periodicity in combination with system damping is capable of efficiently extracting vibrational energy from the system and of amplifying the existing damping affecting transient vibrations. Operating the system at such a specific time-periodicity, the system is tuned at a parametric anti-resonance. The basic principle of this concept has been studied theoretically and was proven experimentally. The physical interpretation of this concept was proposed in “Damping by Parametric Stiffness Excitation: Resonance and Anti-Resonance”, Journal of Vibration and Control, 2008, for a multiple degrees of freedom system. The present contribution highlights those findings on a multiple degrees of freedom system. It is illustrated that a parametric anti-resonance is connected to inducing an energy transfer between two of the many vibration modes of the underlying system with constant coefficients. The induced energy transfer can be utilized to transfer the vibration energy from low frequency to high frequency or vice versa or, in case of system damping, to a more efficient dissipation of vibrational energy. The achievable energy dissipation is most significant if an energy transfer is induced between a lightly damped mode and a strongly damped mode.