The damping of plate vibrations by means of multiple active control systems

Abstract

In the first of these two companion papers a description has been given of the essential features of an active system for deriving specific control of plate motions in the interests of damping the vibrations of a lightweight acoustical barrier, or reinforcing those of an enclosure. A single control unit was analysed for the feedback of energy via a corrective point force derived from local sensed motion of the plate. Conditions for the maintenance of stability over a wide frequency range depend on the restriction of phase variation between those plate points on the closed loop at which the motion sensor and control force are applied. In accordance with a varying sign of modal symmetry linking these points the stability requirements can be contravened except in the “simple” case where coincidence between these points is arranged. The present analysis shows that the characteristics of multiple and single systems are essentially similar, and is concerned with four basic arrangements of motion sensors and force actuators designed to improve efficiency by utilizing the ability of a multiple system to act selectively on specific modes. Particularized optimum forward gains may be applied. Again stability depends on preservation of like transfer symmetry between sensing and forcing points. On these terms, only the one “multiple simple system” is preferred, being inherently stable over a wide frequency band, whereby each single unit may then act independently on modes in groups, of either symmetry, chosen from known or ascertained responses of the plate. In the case where the control force generator is supported on the plate by a damped spring system, two purely mechanical properties of the associated passive damper unit are isolated as design parameters.