,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.
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