Parametric Model Order Reduction for Vibroacoustic Metamaterials Based on Modal Superposition

• Main Authors: Droste, Marvin, Hülsebrock, Moritz, Stoll, Georg, Atzrodt, Heiko
• Format: Report
• Language: English
• ISSN: 0148-7191; 2688-3627
• DOI: 10.4271/2022-01-0943

Vibroacoustic Metamaterials (VAMM) have recently shown great potential in the elimination of noise and vibration in targeted and tunable frequency regions. The so-called stop band behavior is mainly driven by small resonance structures on a subwavelength scale. Due to the complex material and geometry composition, stochastic methods for uncertainty quantification, model updating, and optimization are necessary in the design and validation process of VAMM. Those methods require to repeatedly solve Finite Element (FE) models with slightly changed parameters and can become computationally challenging for large numerical models. Hence, the need for Parametric Model Order Reduction (PMOR) techniques arise to reduce the computational burden. For VAMM, consisting of many substructures, common PMOR methods based on Component Mode Synthesis (CMS) can become cumbersome to set up and numerically challenging. In this work, a promising method for PMOR, based on modal superposition, is applied to a VAMM demonstrator. The method is extended to FRF damped systems by deriving the damping matrix in the reduced order subspace based on material dependent damping ratios. The RMS-averaged Frequency Response Functions (FRF) of the system are analyzed for four update scenarios. The FRF of the PMOR system are compared to the FRF of the Full model by means of the Frequency Response Assurance Criterion (FRAC) and the Cross Signature Scale Factor (CSSF). The implemented PMOR model allows an accurate approximation of the dynamic system behavior. For investigated parameter changes up to 20% the accuracy mainly depends on the magnitude of the updating parameters as well as the choice of updating parameters themselves.