MODal ENergy analysis

Abstract

Energy methods like Statistical Energy Analysis (SEA) or Statistical modal Energy distribution Analysis (SmEdA), based on the well-known equations of two coupled oscillators, are both limited when non-resonant contributions of modes are not negligible (typically in the case of cavity/structure/cavity coupling). In SEA, this non-resonant contribution can be taken into account introducing indirect coupling between subsystems. In SmEdA, the non-resonant contribution is more difficult to estimate as indirect coupling is not allowed. However, this issue can be a matter of importance to compute Transmission Loss (TL) of highly damped structures for example.The present work deals with an energy method, developed within the framework of SmEdA, which solves the system of equations of two coupled oscillators at pure tone, taking thus intrinsically into account the non-resonant contributions of oscillators. As in SEA or SmEdA, the net exchanged power between two coupled oscillators is proportional to the weighted difference of total energies of oscillators. The expression of a critical coupling strength is also proposed and may be related to classical weak coupling criterion of SEA.Extending equations obtained for two coupled sets of oscillators to the case of two linear continuous subsystems, one can compute easily frequency dependent modal energies of modes, total energies of subsystems, power transmitted between two modes and power dissipated.The theoretical bases and assumptions of the proposed MODal ENergy Analysis (MODENA) are first exposed and the case of two coupled oscillators is addressed. Then, plate/cavity and cavity/plate/cavity systems are treated with MODENA and compared to an exact solution. Finally, it is demonstrated that the non-resonant contribution of a highly damped plate is correctly represented by MODENA.