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This talk introduces the UMP (Unified Multi-Phase) modeling method, recently developed for the streamlined analysis and systematic design of complex vibro-acoustic systems. The main difference between the conventional method and the UMP method is that the latter uses the same governing equations for all acoustic components while the former, different equations for different acoustic components. The UMP approach also treats all interface conditions by a unified formulation unlike the conventional approach. Consequently, physically different components and various interface conditions are treated by a unified multi-phase model along with unified interface conditions. The key in this approach is to realize that Biot’s equations for poroelastic media can degenerate to the Helmholtz equation or the elastodynamic equations if some of poroelastic material coefficients are properly controlled and that the interface conditions for poroelastic-poroelastic media can also degenerate to those for interfaces of any similar/dissimilar media. Since any reduction in the degrees of primary field variables in degenerated systems can cause numerical singularity, some of the poroelastic coefficients are slightly perturbed from the exact limit values in representing the degenerated systems. The unified approach becomes extremely useful when an iterative design process requiring interface evolutions at every iteration step is implemented as in the topology optimization of complex vibro-acoustic systems.

Unified Multi-Phase Modeling and Topology Optimization for Complex Vibro-Acoustic Systems consisting of Acoustic, Elastic and Poroelastic Media