Locally resonant effective phononic crystals for subwavelength vibration control of torsional cylindrical waves

Locally resonant materials allow for wave propagation control in the sub-wavelength regime. Even though these materials do not need periodicity, they are usually designed as periodic systems since this allows for the application of the Bloch theorem and analysis of the entire system based on a single unit cell. However, geometries that are invariant to translation result in equations of motion with periodic coefficients only if we assume plane wave propagation. When wave fronts are cylindrical or spherical, a system realized through tessellation of a unit cell does not result in periodic coefficients and the Bloch theorem cannot be applied. Therefore, most studies of periodic locally resonant systems are limited to plane wave propagation. In this paper, we address this limitation by introducing a locally resonant effective phononic crystal composed of a radially-varying matrix with attached torsional resonators. This material is not geometrically periodic but exhibits effective periodicity, i.e. its equations of motion are invariant to radial translations, allowing the Bloch theorem to be applied to radially propagating torsional waves. We show that this material can be analyzed under the already developed framework for metamaterials. To show the importance of using an effectively periodic system, we compare its behavior to a system that is not effectively periodic but has geometric periodicity. We show considerable differences in transmission as well as in the negative effective properties of these two systems. Locally resonant effective phononic crystals open possibilities for subwavelength elastic wave control in the near field of sources.

Silencer for high-frequency turbocharger compressor noise via an acoustic straightener

Decades of successful research and development on automotive silencers for engine breathing systems have brought about significant reductions in emitted engine noise. A majority of this research has pursued airborne noise at relatively low frequencies, which typically involve plane wave propagation. However, with the increasing demand for downsized turbocharged engines in passenger cars, high-frequency compressor noise has become a challenge in engine induction systems. Elevated frequencies promote multi-dimensional wave propagation rendering at times conventional silencer treatments ineffective due to the underlying assumption of one-dimensional wave propagation in their design. The present work focuses on developing a high-frequency silencer that targets tonal noise at the blade-pass frequency within the compressor inlet duct for a wide range of rotational speeds. The approach features a novel "acoustic straightener" that creates exclusive plane wave propagation near the silencing elements. An analytical treatment is combined with a three-dimensional acoustic finite element method to guide the early design process. The effects of mean flow and nonlinearities on acoustics are then captured by three-dimensional computational fluid dynamics simulations. The configuration developed by the current computational effort will set the stage for further refinement through future experiments.