A hybrid mid-frequency formulation for vibro-acoustic predictions

Predicting the acoustic behavior of a complex structure in the mid-frequency range is a challenging task due to the complexity of the structure and the involved physical phenomena. In this frequency field, the structure-borne noise is predominant for numerous mechanical structures, and the details of the structures need to be taken into account. In other respect, this frequency field is characterized by high modal densities, leading to huge computational time when trying to solve the problem with conventional numerical methods. In this context, the authors are developing a formulation based on a hybrid representation of the structure. The stiff members are modeled using deterministic BEM or FEM descriptions, and randomness is introduced to the geometry of the soft members whose vibrational behaviors are very sensitive to any perturbation of their physical parameters when the modal density increases. It is shown that the significant unknowns of the formulation are the expectations of the square kinematic unknowns. These variables describe accurately the responses of the structures; the modes due to the stiff members are precisely described whereas the strongly oscillating response due to the soft members is smoothed. The formulation is established for isolated and assembled one and two-dimensional structures. Numerical applications illustrate the effectiveness of the method.