Vibration isolation of two elastic structures using active compliance at the isolation mounts

A mathematical model of the vibration isolation of two elastically connected structures (via isolation mounts) employing active springs is presented. Two elastic structures are connected by an arbitrary number of springs, each made active by the inclusion of a piezoelectric pad at one of the spring and structure interfaces. Single-input–single-output feedback controllers at each spring support seek to minimize the force transmitted from one structure to the other. Solutions are based upon the formalism of Lagrange’s equations using the normal modes of the uncoupled structures as the generalized coordinates. The constraints by the springs and supports are enforced by Lagrange multipliers. A 2-D numerical example of two elastic beams is presented. One beam, driven by a harmonic disturbance force, is coupled to the second elastically supported beam through three active springs. A beam-relative displacement sensor colocated at each spring is the input to an arbitrary feedback filter which can incorporate practical amplifier characteristics and actuator dynamics. Results of the numerical simulation of the feedback control case are discussed.