A deterministic energy method for predicting the response of coupled finite structures

The forced response of finite, thin rectangular plates coupled by a line joint can be predicted using well-established analytical methods. However, such methods become difficult to implement for thick panels coupled by complex joints. In these cases, the finite element (FE) method and conventional statistical energy analysis (SEA) are viable alternatives. However, the FE method can be time-consuming at mid/high frequencies while SEA involves various approximations and assumptions. This paper develops a deterministic energy method for predicting the forced response of coupled complex panels based on a hybrid finite element/wave finite element (WFE) method, modelling the panels as coupled wave-bearing subsystems. The method involves meshing only a small segment of the panel and the joint using finite elements, and is able to model complex structures such as laminated panels and joints with low computational cost. Excitations of the structure by a time-harmonic point force and the rain-on-the-roof excitations are both considered. The wave subsystem energy and power flow formulations corresponding to these excitations are derived to be the sum of wave components. The energy/power formulations are then used for establishing an SEA-like model for predicting the coupling data between the subsystems. Numerical examples of two thin, rectangular plates coupled by an “L” shaped joint and coupled practical cross-laminated-timber (CLT) panels connected by L-shaped joints with/without an elastic layer are presented to illustrate this method. Wave subsystem energy and power transmission between subsystems are calculated for the coupled structures. The normalised energy responses of the coupled CLT panels are also calculated and compared with measurements. Good agreement between the predictions and the measurements is achieved.