Ji L., Mace B.

This paper concerns the higher frequency vibrations of built-up structures and in particular systems comprising two subsystems connected via an arbitrary interface. The individual subsystems are analysed using free-interface component mode synthesis. Analytical expressions are developed which represent the dynamic couplings between the sets of subsystem modes. These expressions explicitly include the effects of uncertainty in the parameters of the subsystems, the uncertainty being introduced into the modal properties of the subsystems. The general aims are to predict ensemble mean and variance of the subsystem energy. The dynamic coupling between the two subsystems is seen to fall into three categories: (1) strongly connected, (2) weakly connected, and (3) weakly coupled. Effective mass and damping are introduced to account for the dynamic influence on a particular subsystem mode of the remaining modes after the subsystems are coupled. It is seen that for weak connection/coupling, the inter-modal coupling relations reduce to those of two sets of stiffness-coupled oscillators (with modified damping values, if appropriate). As a result, the model can be accommodated within a recently developed theory for the prediction of the ensemble mean and variance of the energy response of coupled oscillator sets. This provides an approach to the analysis of complex, built-up systems in a more systematic way than conventional SEA. Numerical examples are given for two point-coupled plates. The present theory is seen to give good predictions for weak connection/coupling when compared with Monte Carlo simulations, if the statistical overlap of the system is sufficiently large. The approach helps to give insight into the physics of the coupling mechanism of subsystem modes. It also has the potential for forming SEA-like models of the system and predicting energy response and variance directly from coupled FE models of the individual subsystems, without the need for solution of the global eigenvalue problem.