Vibrational power-flow analysis of a MIMO system using the transmission matrix approach

The transmission matrix approach is employed in this paper for the vibrational power-flow analysis of a multiple-input/multiple-output (MIMO) system. The substructures in each subsystem are modelled as a group of general MIMO transmission elements, which are described in terms of discrete or distributed properties. The global transmission matrix of the system is formed by assembling the transmission matrices together. Using the proposed approach, the output variables of any subsystem can be expressed in terms of the input state variables of that subsystem. Hence, the proposed approach is very systematic in analysing the dynamic behaviour of a complex system with a group of elements. In the numerical example, the power flow of a multi-mount system is modelled analytically. The transmission of vibratory power flow from the vibrating rigid body into a simply supported plate through elastic mounts is studied in detail. The effects on the power flows of various factors, such as the plate thickness, loading type, mounting locations, and mass and damping properties of the mounts, are addressed.