An investigation of the effect of the coupling value and the structural perturbation parameter is conducted on coupled systems. The analysis of a coupled pendulums system results in the analytical expression of the natural frequencies of the system. The response of the system for harmonic excitation and random input is developed.

Two single Euler-Bemouilli beams coupled by a torsional spring constitute the multi degree of freedom extension of the study. Special care is given to show the variation of the natural frequencies \with the two parameters and modal overlapping is shown. The study of the response to harmonic excitation makes the localization phenomenon apparent. For the special case where one of the beam is excited by a rain-on-the roof load, the estimates of the amplitude for each beam and the power flow between the beams are analytically expressed. The power flow is proved to be concentrated around the natural frequencies, stronger for a tuned system and sensitive to the number of modes, especially v:hen modal overlapping occurs. A Monte Carlo simulation considering the perturbation parameter as a Gaussian random variable points out that the mean value of the power decreases rapidly with higher frequency. The power flow is also calculated using the theory of the Statistical Energy Analysis.