A Multi-Level Wave Based Method to predict the dynamic response of 2D poroelastic materials containing holes or inclusions

Invited paper

Elke Deckers

KU Leuven

Tuesday 2 june, 2015, 14:20 - 14:40

0.7 Lisbon (47)

Poroelastic materials are often applied as effective noise measures. They are, however, most effective at higher frequencies. A lot of research has been performed to increase absorption also at lower frequencies. A solution is to add inhomogeneities to the foams, being inclusions or perforations. Recently, a Wave Based Method was developed to predict the dynamic response of poroelastic materials, described by the theory of Biot. The method is based on a Trefftz approach; it uses exact solutions of the governing partial differential equations to describe the field variables. Specifically for Biot models, the method explicitly accounts for the three different wave types that exist in this class of materials. As compared to standard element based techniques, the inclusion of a priori known information on the physics of the problem in the model leads to a more efficient solution. The main drawback of the method is that it is limited to geometrically simple problems. A sufficient condition for the method to converge is that the considered problem domain is convex. Non-convex domains have to be partitioned into convex subdomains. Consequently, domains with circular inclusions cannot be accurately accounted for with the Wave Based Method. To overcome this constraint, the so-called Multi-Level Wave Based Method has been introduced for acoustic and structural dynamic problems. It combines solutions of the bounded domain and outgoing solutions exterior to the inclusions to describe the dynamic fields. This paper extends the Multi-level approach for poroelastic materials. Unbounded wave functions are defined that are exact solutions of an unbounded poroelastic domain exterior to a circular truncation. The known bounded wave functions and novel unbounded wave functions are combined in a Multi-Level framework. The method is validated through comparison to the Finite Element Method for different configurations.

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