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.
