Confidence intervals of energies predicted by MODal ENergy Analysis method. (29th September 2021) - Totaro, N.; Guyader, J.L.
Abstract: MODal ENergy Analysis (MODENA) was previously developed in the same framework as Statistical Energy Analysis (SEA) and Statistical modal Energy distribution Analysis (SmEdA) methods. It deals with energy exchanges between weakly coupled subsystems in vibro-acoustics. However, unlike SEA, MODENA is not a statistical method as it is based on deterministic structures and solved at pure tone. Compared to SmEdA, MODENA takes intrinsically into account couplings between non resonant modes and keeps information about resonance peaks. Consequently, it handles matrices of bigger size than SmEdA with the consequence of higher computation cost. MODENA was first based on the assumption of uncorrelated forces applied to two coupled oscillators. This assumption was fulfilled by considering a random phase between forces applied to oscillators. In the present article, this assumption is further investigated by considering the phase angle as a random variable with uniform distribution. The expressions for expectation and variance are then derived in this context. They allow estimating confidence intervals of energies predicted by MODENA method. Therefore, even if the assumption of random phase is not fulfilled, the solution should be included in the confidence interval. It is shown that confidence intervals of energies are rather null in case of two weakly coupled oscillators both excited by forces of equivalent level. The confidence intervals increase at some frequencies when the coupling strength is higher than the critical coupling or when the excitation level difference increases. In case of multi-modal coupling, two numerical test cases are investigated: a plate/cavity case and a cavity/plate/cavity case. In both cases, expectations and variances are computed using MODENA theory and are compared to deterministic responses of the subsystems computed using a finite element software.