Accelerated dispersion curve calculations for periodic vibro-acoustic structures

Abstract

Over the years, metamaterials have shown their potential in a wide range of different disciplines, e.g. optics, electromagnetics, dynamics etc. Metamaterials are, often periodic, engineered structures made of conventional materials but which exhibit properties not encountered in nature. In the field of noise and vibration, metamaterials have received increasing interest since they can obtain frequency ranges of high noise and vibration attenuation, called stop bands. Their performance is often investigated by means of dispersion curves, which are calculated based on a single unit cell and assuming a structure of infinite periodic extent. Nowadays, the attenuation of acoustic and structural waves is commonly tackled as two separate problems, whereby either acoustic or structural dispersion curves are used. Recently, vibro-acoustic unit cell designs have come to the fore which can exhibit appealing characteristics, such as simultaneous structural and acoustic stop bands. To consider the vibro-acoustic coupling in these unit cell designs during the performance predictions, vibro-acoustic dispersion curve calculations are thus required. However, these computations are typically cumbersome to perform due to the associated high computational cost and therefore, often, uncoupled dispersion curves are used during the performance assessment. Although several unit cell model order reduction approaches have recently been proposed to accelerate the dispersion curve computations, such as the Bloch mode synthesis (BMS) and Generalized Bloch mode synthesis (GBMS), they are not readily applicable to vibro-acoustic unit cells. To accelerate vibro-acoustic dispersion curve calculations, this work extends the BMS and GBMS techniques towards 2D and 3D periodic vibro-acoustic systems. To balance accuracy versus speed, the extended BMS reduction basis is constructed using a split set of vibro-acoustic coupled modes, while the extended GBMS reduction basis uses the uncoupled modes. Several verification cases demonstrate that strongly accelerated vibro-acoustic dispersion curve computations are achieved whereby the vibro-acoustic coupling inside the unit cell is accurately accounted for.