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.

In this paper we study the bandgap properties of two-dimensional phononic crystals with cross-like holes using the finite element method. The influence of the geometry parameters of the holes on the bandgaps is discussed. In contrast to a system of square holes, which does not exhibits bandgaps if the symmetry of the holes is the same as that of the lattice, systems of cross-like holes show large bandgaps at lower frequencies. The bandgaps are significantly dependent upon the geometry (including the size, shape, and rotation) of the cross-like holes. The vibration modes of the bandgap edges are computed and analyzed in order to clarify the mechanism of the generation of the lowest bandgap. It is found that the generation of the lowest bangdap is a result of the local resonance of the periodically arranged lumps connected with narrow connectors. Spring-mass models are developed in order to predict the frequencies of the lower bandgap edges. The study in this paper is relevant to the optimal design of the bandgaps in light porous materials.

We theoretically and experimentally investigate a helical acoustic metasurface capable of providing a modulated sound-reflected wavefront and a continuously tunable broadband feature. Compared to existing metasurface designs, which mostly manipulate acoustic waves in a fixed or narrow frequency range, the matched screw-and-nut mechanism has added value and unusual properties, opening a realistic solution to achieve broadband tunability of acoustic metasurfaces with multifunctions. The conceived tunable metasurface is composed of identical units, which consist of matched screws rotated into helical channels from bottom to top to modulate the sound-reflected wavefront pattern. As a pragmatic example, we present the design details and functionalities of a flat metasurface operating at a wide working band. Then a sample of the metasurface is manufactured with the three-dimensional (3D)-printed cylindrical units to experimentally demonstrate the continuously tunable multifunction, including anomalous reflection, arbitrary focusing, and self-bending beams. All results are in good agreement. The proposed spiral matching concept could open up an alternative avenue for broadband tunable metasurfaces of reflected wavefront modulations and associated applications.

Propagation of elastic waves in acoustic metamaterials based on locally resonant viscoelastic phononic crystals is discussed. A variational formulation of the complex band structure for in-plane polarized waves is proposed and used to formulate a finite element model. Two different types of locally resonant band gaps are found for quasilongitudinal and quasishear waves, with distinct features in terms of complex bands and transmission bandwidth. The influence of viscosity on the complex band structure, transmission properties, and effective dynamic mass density of two-dimensional locally resonant metamaterials is further investigated. It is found that bands that were degenerate in the elastic case are separated when viscosity is introduced, and that sharp corners at high symmetry points become rounded. Transmission is generally worsened in passing bands, while it is enhanced inside locally resonant band gaps, contrary to what was observed previously for Bragg band gaps. All changes in the complex band structure and transmission spectra are solely due to the dispersive and dissipative effects of viscosity. It is also found that the negative mass density property may also disappear when viscosity is introduced. These results are relevant to practical applications of elastic and viscoelastic metamaterials.