| Power flow transmission characteristics and vibration control in flexible isolation system are the key research subjects in the vibration-engineering field. Decomposing and integrating methods are the main instruments to study the complicated coupled system. The results of above modeling techniques combined with the progress of computer application will have far-reaching effects. Based on the above viewpoint, supported by the project of National Nature Science Foundation of China(NSFC) "Optimum control of complicated mechanical system's dynamic of flexible foundation"(No. 59575023) and the project of china state shipbuilding corporation(CSCC) in the Ninth five-year Plane "Investigation and result evaluation of power flow method in transmission characteristics of the floating raft system"(No. 10.6.2.2), aimed at the gearbox-liked system which is the representative of rotational machinery, the thesis is concentrates on modeling of multi-dimensional compliant coupled system used for analysis of structure-borne and air-borne sound , analysis of dynamics, characteristics of power flow transmissio, etc.Firstly, combined the methods of mobility and mode synthesize, a new model is developed to describe the compliant coupled system and the power flow transmission characteristics,. With the abilities of both tow methods the established model can be use to in more widely range of vibration control problem. Developed general mobility matrixes formula are ready to deal with multi-dimensional coupled system. The model of path between source and receiver subsystem with all parameters of mass, stiffness and damping is established. As the dimensions of mobility matrixes have relationship only with the number of subsystem's interfaces but not with that of the summing modes, the truncation problem in large system modeling would be avoided, and higher frequency analysis results can be obtained. The subsystem's mode parameters can be obtained from experiment , FEA, etc, with these information how the modification of subsystem affects the characteristics of power flow transmission of coupled system can be evaluated.Furthermore, a new source subsystem mobility matrix formula is established which is suitable to multi-substructure coupled and multi-excitation condition source subsystem. With this model and aimed at floating raft system, the mobility matrix of "machine-isolator-raft" source subsystem model and "raft-isolator-base' receiver subsystem model is developed, which are subjected a floating raft system , and the characteristics of power flow transmission is investigated. The results show that the characteristics of the system at low frequency mainlyaffected by rigid modes of system when raft and baseplate are both stiffened, but with asymmetrically installed or combined excitation the rotating rigid modes and flexible modes of raft and baseplate will be excited, which caused the increasing of power flow transmission. The characteristics of the system at middle and high frequency mainly affected by th flexible modes of both raft and baseplate. The stiffened raft and baseplate will help to decrease the power flow put into the base. Changes in the stiffness parameters of isolators' mainly affect the lower frequency characteristics of the system. Decreasing in up-isolator's stiffness some like increasing the source flexibility will companied with decreased transmission of power flow for all subsystem. Decreasing in down-isolator's stiffness some like increasing the receiver flexibility will make the decreasing of transmission power flow to the baseplate.Then a model of structure-borne sound transmission characteristics of power flow aimed at gearbox system is established. A multi-dimensional and compliant path model is developed aimed at the bearing that is the representative of joint path in rotational machinery. Combined with the developed source mobility matrix, description of gearbox-like system characteristics of power flow transmission is established. Which is subjected to a gearbox-like system and the effects of subsystem parameters to the characteristics of power flow transmission into the casing plate is investigated. The results show that in-plane power flow is dominating at lower frequency range, while out-plane power flow increasing at middle and high frequency range and then exceeds the former. For the out-plane power flow is the main energy source of vibration and noise in casing plate, the established model is suitable to reveal the mechanism of power flow transmission in gearbox-like system we studied. Properly decreasing bearing stiffness will help to reduce the structure-borne noise transmission from rotating source to stationary casing plate. The effects of bearing damping is efficiency at higher frequency range. Increasing bearing damping makes the resonant peaks smoothly at higher frequencies, and make the energy put into the system spread around from resonant frequency range. As the dissipation power flow at path damping is increased that effectively reduced the power flow transmission into the casing plate. That is increasing path damping will help to reduce the structure-borne noise transmission.After developing the formula describing energy transmission between subsystems, and formula for calculating parameters of established subsystem, a SEA model of air-borne sound transmission aimed at gearbox is established ,which is subject to two excitation patterns, and some frequency distributing rules are obtained. The results show that the established model can reveal the vibration rules of coupled system that will help to design the isolation system.
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