Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook

Nonlinear Oscillations: Exact Solutions and their Approximations

The Journal of the Acoustical Society of America

The study of classical wave physics has been reinvigorated by incorporating the concept of the geometric phase, which has its roots in optics, and topological notions that were previously explored in condensed matter physics. Recently, sound waves and a variety of mechanical systems have emerged as excellent platforms that exemplify the universality and diversity of topological phases. In this Review, we introduce the essential physical concepts that underpin various classes of topological phenomena realized in acoustic and mechanical systems: Dirac points, the quantum Hall, quantum spin Hall and valley Hall effects, Floquet topological phases, 3D gapless states and Weyl crystals. This Review describes topological phenomena that can be realized in acoustic and mechanical systems. Methods of symmetry breaking are described, along with the consequences and rich phenomena that emerge.

Topological phases in acoustic and mechanical systems

Two-dimensional phononic crystals: Examples and applications

The lumped-mass method is applied to study the propagation of elastic waves in two-dimensional binary periodic systems, i.e., periodic soft rubber/epoxy and vacuum/epoxy composites, for which the conventional methods fail or converge very slowly. A comprehensive study is performed for the two-dimensional binary locally resonant phononic crystals, which are composed of periodic soft rubber cylinders immersed in epoxy host. Numerical simulations predict that subfrequency gaps also appear because of the high contrast of mass density and elastic constant of the soft rubber. The locally resonant mechanism in forming the subfrequency gaps is thoroughly analyzed by studying the two-dimensional model and its quasi-one-dimensional mechanical analog. The rule used to judge whether a resonant mode in the phononic crystals can result in a corresponding subfrequency gap or not is found.

Two-dimensional locally resonant phononic crystals with binary structures.

The authors study the propagation of flexural waves in a locally resonant (LR) thin plate made of a two-dimensional periodic array of spring–mass resonators attached on a thin homogeneous plate. The well-known plane wave expansion method is extended to deal with such a plate system with a periodic array of lumped resonant elements. Explicit matrix formulations are developed for the calculation of complex band structures, in which the imaginary parts of Bloch wave vectors are displayed to quantify the wave attenuation performance of band gaps. It is found that resonance-type and Bragg-type band gaps coexist in the LR plate, and the bandwidth of these gaps can be dramatically affected by the resonant frequency of local resonators. In particular, a super-wide pseudo-directional gap can be formed by a combination of the resonance gap and Bragg gap; inside such a pseudo-gap, only a very narrow pass band exists. An explicit formula is further developed to facilitate the design of such a pseudo-gap. Finally, vibration transmission in finite LR plates is calculated using the finite element method. Vibration transmission gaps are observed, and the results are in good agreement with the band gap properties predicted by the complex band structures.

https://iopscience.iop.org/article/10.1088/0022-3727/45/19/195401/pdf

Jihong Wen

Papers

Two-dimensional locally resonant phononic crystals with binary structures.

Flexural wave band gaps in locally resonant thin plates with periodically attached spring-mass resonators

Flexural wave propagation in beams with periodically attached vibration absorbers: Band-gap behavior and band formation mechanisms

Sound transmission loss of metamaterial-based thin plates with multiple subwavelength arrays of attached resonators

Vibration reduction by using the idea of phononic crystals in a pipe-conveying fluid