Influence of Crandall lines on ergodic billard in SEA
Résumé
The main relationship of statistical energy analysis is the so-called coupling power proportionality (CPP) which states that the mean power exchanged between two subsystems is proportional to the difference of their modal energies. A very important condition for the validity of CPP is that the vibra- tional field must be perfectly diffuse in all subsystems. This is a special state of vibration for which the vibrational energy is homogeneously and isotropically distributed. There are two ways to obtain a diffuse fifield. Firstly, if the excitation is composed of many uncorrelated forces on the whole plate (like rain-on-the-roof), then the fifield is forced to be diffuse. Secondly, if the excitation is a single point force and the geometry of subsystem is an ergodic billiard, then homogeneity and isotropy of the vibrational fifield are a priori enforced. However, even when diffuseness of the fifield is enforced by ergodicity, certain special lines called Crandall lines present a higher level of energy. On these lines, rays interfere constructively, leading to an enhancement of the vibrational energy. We show that if the coupling between the two plates is fixed on one of these lines of high energy, the CPP slightly differs from the theorical value predicted by SEA. Numerical simulations are provided to support these results.
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