In linear dynamical analysis of complex mechanical systems, the structural fuzzy is defined as the set of minor subsystems that are connected to the master structure but are not accessible by classical modeling. The notion of master structure is presently extended to others elements such as an external dense compressible fluid strongly coupled with the primary structure. For the low-frequency (LF) dynamical analysis, the modeling of the structural fuzzy is commonly made with a system of masses. If the LF modeling of the structural fuzzy is applied in the medium-frequency (MF) domain, there are some large differences between calculations and experiment. It is therefore necessary to take into account internal degrees of freedom of the structural fuzzy. A global probabilistic modeling of the structural fuzzy is proposed to improve the calculated estimates of the MF vibrations into the master structure and of the far field radiated by itself in or out of context of the acoustic scattering. This paper reviews the author’s previous work and introduces the type II probabilistic constitutive law. In this paper: (1) a probabilistic modeling of the structural fuzzy is presented, (2) two probabilistic constitutive laws of the structural fuzzy are constructed, (3) the modeling in the MF range for vibroacoustic predictions using theory of structural fuzzy is developed, (4) the fuzzy solution in the MF range is studied, and (5) numerical simulations on standard structures and on a submerged complex industrial structure are shown.
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Christian Soize (1993) studied this question.