Recent investigations have shown theoretically and experimentally that the transient vibrations of a lightly damped system can be suppressed or even stabilized by a time-periodic open-loop control of one of its system parameters. 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 to extract vibration energy from the system and to increase the effective damping of transient vibrations. At this specific operation the system is tuned at parametric anti-resonance.
The beneficial interaction of damping and time-periodicity was first formulated by A. Tondl in 1998. His pioneering work deals with stabilizing self-excited vibrations. It was proven by F. Dohnal in 2005 that the vibrations of a general lightly damped system (not necessarily unstable) can be reduced by parametric anti-resonance, too. A physical interpretation of the parametric anti-resonance is related to the coupling of vibration modes of the underlying system with constant coefficients. This interpretation leads intuitively to the calculation of the energy flow of each vibration mode and leads to clear physical insight of how parametric anti-resonances work. This interpretation of mode coupling is developed further resulting in an approximate analytical expression for the effective damping of a system driven at parametric anti-resonance. This expression allows the statement of the maximum effective damping achievable by this method. The discussion of the energy flow of a linear, lightly damped system possessing a time-periodic stiffness coefficient its physical and modal displacements highlights the coupling of vibration modes of the underlying system with constant coefficients.