Efficient simulation of vibro-acoustic problems with poro-elastic damping using a Matrix-free Model Order Reduction scheme

摘要

Instigated by customer expectations and ever tightening regulations on noise emissions, the vibro-acoustic performance of products has become a key design feature. The fact that many products nowadays use various lightweight materials makes that it is often difficult to meet all these requirements. To ensure this, damping treatments – often multi-layered – are added, but almost always a posteriori.Predicting multi-layers in efficient simulations is essential in a modern design environment. These frequency dependent damping materials typically operate on a dynamic decoupling in order to dissipate energy more efficiently in the near-field. These effects make that the mesh should be sufficiently refined to capture the short wavelengths and high gradients. In order to alleviate long computation times, a variety of model order reduction (MOR) techniques have been developed. Typically, they can be divided into three groups, being modal-, Krylov- and truncation-based methods.Many of the available MOR techniques, however, still struggle when material properties are complex and especially when they have strong frequency dependency. Some attempts in the field of poro-elastic materials were made, especially for modal reduction techniques.However, all of these procedures are quite intrusive into the system matrices, which hampers general applicability and makes each of the methods dependent on the chosen method (e.g. Finite Element Method), the formulation for the poro-elastic problem (e.g. equivalent fluid, u-U, u-p, u-w, etc.) and the other physics involved (e.g. coupling to acoustics or structural vibrations). This contribution proposes a Krylov-based method which does not require knowledge on the underlying mathematical model, and can hence be considered “matrix-free”. This black box approach holds for both undamped and damped cases and can robustly cope with complex frequency dependency of the parameters.