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

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

Wave Motion in Periodic Flexural Beams and Characterization of the Transition Between Bragg Scattering and Local Resonance

Phononic crystals (PCs) and metamaterials (MMs) can exhibit abnormal properties, even far beyond those found in nature, through artificial design of the topology or ordered structure of unit cells. This emerging class of materials has diverse application potentials in many fields. Recently, the concept of tunable PCs or MMs has been proposed to manipulate a variety of wave functions on demand. In this review, we survey recent developments in tunable and active PCs and MMs, including bandgap and bandgap engineering, anomalous behaviors of wave propagation, as well as tunable manipulation of waves based on different regulation mechanisms: tunable mechanical reconfiguration and materials with multifield coupling. We conclude by outlining future directions in the emerging field.

Tunable and Active Phononic Crystals and Metamaterials

Broadband locally resonant beams containing multiple periodic arrays of attached resonators

FSI research in pipeline systems – A review of the literature

Propagation of flexural wave in periodic beam on elastic foundations

Dynamic Stability of Periodic Pipes Conveying Fluid

The vibrational properties of a periodic composite pipe in 3D space

Utilizing the coordinate transformation method, together with exchange of variables between Maxwell’s equations and the acoustic equations with axial-invariance in cylindrical coordinates, the acoustic parameters (anisotropic density and scalar bulk modulus) for an ideal cloak and an ideal anti-cloak are obtained. An anti-cloak allows the inside object to ‘see’ outside, but to be invisible from outside; whereas a cloak is invisible from outside, but ‘blind’ from inside. Utilizing a scattering algorithm developed in this paper, the pressure field calculation of the cloak/anti-cloak is performed and the concepts and characteristics of the acoustic cloak/anti-cloak are revisited. To be more easily achievable experimentally, a multilayered cloak/anti-cloak model with homogeneous isotropic materials is introduced, and its corresponding pressure distributions are calculated. Also, the total scattering cross-section curves for the multilayered cloak and anti-cloak over a certain frequency range are presented and compared. Finally, an active acoustic metamaterial made up of piezo-diaphragm cavity arrays is designed for the cloak/anti-cloak. Taking into account the coupling between adjacent cavity cells, a multi-control strategy for piezo-diaphragm cavity arrays is exploited, rendering possible wide ranges of effective densities and effective bulk moduli (or acoustic speeds), or even double-negative transformation medium (i.e. both density and bulk modulus parameters are negative). With such sets of active acoustic metamaterials, the cloak and anti-cloak may become both theoretically and experimentally realizable. (Some figures may appear in colour only in the online journal)

https://iopscience.iop.org/article/10.1088/0022-3727/45/28/285401/pdf

Huijie Shen

Papers

Propagation of flexural wave in periodic beam on elastic foundations

Dynamic Stability of Periodic Pipes Conveying Fluid

The vibrational properties of a periodic composite pipe in 3D space

Acoustic cloak/anti-cloak device with realizable passive/active metamaterials

Control of sound and vibration of fluid-filled cylindrical shells via periodic design and active control