[Truncated abstract] Shipbuilding is fast becoming a priority industry in Australia. With increasing demands to build fast vessels of lighter weight, shipbuilders are more concerned with noise and vibration problems in ships than ever. The objective of this thesis is to study the vibration response of coupled structures, in the hope that the study may shed some light in understanding the general features of ship vibration. An important feature characterizing the vibration in complex structures is the input mobility, as it describes the capacity of structures in accepting vibration energy from sources. The input mobilities of finite ribbed plate and plate/plate coupled structures are investigated analytically and experimentally in this study. It is shown that the input mobility of a finite ribbed plate is bounded by the input mobilities of the uncoupled plate and beam(s) that form the ribbed plate and is dependent upon the distance between the source location and the stiffened beam(s). Off-neutral axis loading on the beam (point force applied on the beam but away from the beam’s neutral axis) affects the input power, kinetic energy distribution in the component plates of the ribbed plate and energy flow into the plates from the beam under direct excitation ... solutions were then used to examine the validity of statistical energy analysis (SEA) in the prediction of vibration response of an L-shaped plate due to deterministic force excitations. It was found that SEA can be utilized to predict the frequency averaged vibration response and energy flow of L-shaped plates under deterministic force (moment) excitations providing that the source location is more than a quarter of wavelength away from the plate edges. Furthermore, a simple experimental method was developed in this study to evaluate the frequency dependent stiffness and damping of rubber mounts by impact test. Finally, analytical methods developed in this study were applied in the prediction of vibration response of a ship structure. It was found that input mobilities of ship hull structures due to machinery excitations are governed by the stiffness of the supporting structure to which the engine is mounted. Their frequency averaged values can be estimated from those of the mounting structure of finite or infinite extents. It was also shown that wave propagation in ship hull structures at low frequencies could be attenuated by irregularities imposed to the periodic locations of the ship frames. The vibration at higher frequencies could be controlled by modifications of the supporting structure.