A scaling approach for the vibro-acoustic analysis of a complex system in the mid-frequency region

According to the dynamic properties of its components, a complex system can be partitioned into a deterministic subsystem and many coupled statistical subsystems. Each statistical subsystem bears a direct and a reverberant field and its reverberant loading can be described by a diffusive field reciprocity relationship. To reduce computational complexity, each statistical subsystem is replaced by a scaled subsystem with a lower modal density and assembled to the rest of the system through an adapter structure. It is proved by using the hybrid FEA-SEA formulation that the scaled system has the same governing equations as those of the original system. Due to their dynamic similitude, the vibro-acoustic responses of the original system can be obtained by analyzing the scaled system. In practice, the simplified problem is solved by a Monte-Carlo simulation of an ensemble of randomized scaled systems. Its applicability is illustrated by a mid-frequency analysis of two plate structures, and benchmark comparisons are made with the full Monte Carlo simulations on the original systems.