Active isolation of structural vibration on a multiple-degree-of-freedom system .1. The dynamics of the system

This paper is the first of two companion papers concerning the active control of structural vibration in an isolator system. A preparatory study is reported of the passive vibration transmission, which is evaluated in terms of power, considering a multi-mount and multi-degree-of-freedom isolator system with passive mounts. The modelling of the system is based on a matrix method which uses mobility or impedance representations of three separate elements: the source of vibration, the receiver and the mounting system which connects the source to the receiver. A detailed description of the mobility or impedance formulae is given for a rigid mass oscillating in a plane (the source), for a beam on which flexural and longitudinal waves propagate (the mounts) and for an infinite or finite plate in which in-plane shear and longitudinal and out-of-plane flexural waves propagate (the receiver). It is shown that at low frequencies any ''rigid body mode'' (axial-mode, transverse-mode, pitching-mode) is capable of transmitting considerable power to the receiving system, while the transmission of vibration at higher frequencies is mostly related to the dynamics of the distributed mounts or receiver. (C) 1997 Academic Press Limited.