Parametric model order reduction for acoustic metamaterials based on local thickness variations

The use of lightweight materials is obligatory in the design of economic structures, but with decreasing mass, the vibro-acoustic properties of the structures become unfavorable. Acoustic metamaterials based on the concept of acoustic black holes (ABH) can improve the vibrational behavior by adding local thickness variations to the host structure. To make computational models of metamaterials also valid for high frequencies, a fine discretization has to be used. This leads to high computation times. A parametric model order reduction (PMOR) approach is presented, which is able to create an efficient reduced model of ABHs. In the first step, one structure preserving reduced model for each parameter is generated using the iterative rational Krylov algorithm (IRKA). The transfer functions of all reduced models are used in the second step to create a single parametric model using the Loewner framework. The resulting model can be used to efficiently evaluate the frequency response of a structure equipped with ABHs for different parameter sets.