Automatic model order reduction for systems with frequency-dependent material properties

The frequency response of vibro-acoustic systems can be improved by using various forms of damping materials. Their material properties are typically varying with the excitation frequency and are introduced by one or multiple complex-valued functions. Numerical models of such systems are typically large and require efficient solving strategies. In this contribution, a workflow to reduce the numerical complexity of systems containing frequency-dependent damping materials is presented. The functions modeling the material's frequency-dependent behavior are approximated in rational form and the resulting transfer function is used in a Krylov based moment matching method. The approximation is performed automatically using the adaptive Antoulas–Anderson algorithm. As robust and efficient automatic reduction algorithms are vital for an efficient design process of vibro-acoustic structures, we also show an adaptive procedure to automatically find a reasonably sized reduced model for a given system under a certain tolerance. The algorithms are tested for two forms of damping materials common in vibro-acoustic systems: poroelastic materials following the Biot theory and a constrained layer damping material.