Efficient dispersion curve computations for periodic vibro-acoustic structures using the (generalized) Bloch mode synthesis

Abstract

Periodic structures such as metamaterials and phononic crystals hold potential as promising compact and lightweight solutions for noise and/or vibration attenuation in targeted frequency ranges. The performance of these structures is usually investigated by means of dispersion curves. The input for dispersion curve computations is often a finite element model of the corresponding unit cell. Nowadays, the vibration and noise attenuation of the periodic structures are generally tackled as separate problems and their performance is investigated with either structural or acoustic dispersion curves, respectively. Recently, vibro-acoustic unit cell models have come to the fore which can exhibit simultaneous structural and acoustic stopbands. However, the vibro-acoustic coupling inside the unit cell is usually not taken into account during the dispersion curve computations. To consider this coupling during their performance assessment, the computation of vibro-acoustic dispersion curves is required. Although these dispersion curves provide valuable information, the associated computational cost rapidly increases with unit cell model size. Model order reduction techniques are important enablers to overcome this high cost. In this work, the Bloch mode synthesis (BMS) and generalized BMS (GBMS) unit cell model order reduction techniques are extended to be applicable for 2D and 3D periodic vibro-acoustic systems. Through a verification case, the methodologies are shown to enable a strongly reduced dispersion curve calculation time while maintaining accurate predictions.