The equivalent impedance of power-minimising vibration controllers on plates

Strategies for the suppression of plate vibration are investigated by considering the equivalent impedance of power-minimising vibration controllers. The total power transmitted to a plate by both a primary and secondary point forces is used as a function to be minimised. If the system is linear, then the total power has a known minimum value that is associated with an optimal solution for the secondary force. This minimum power, applied to infinite and finite plates, has been compared to the power reduction that can be achieved with passive vibration treatments. The ratio of the optimal secondary force and the resultant velocity at the secondary force location is termed the equivalent impedance of the active control system, and if only a single primary source is present, this equivalent impedance is entirely reactive but generally unrealisable.The approximation of the equivalent impedance by lumped parameter systems is considered. In particular, passive controllers, based on springs and dampers, have been analysed, although, in many practical applications, a rigid ground is not available to react these components off. The importance of this work lies in the practical approximation of these equivalent impedances with realisable passive systems.