Three-dimensional Acoustic Metamaterial Research Articles

Novel three-dimensional acoustic metamaterials with low-frequency bandgap and strong vibration and noise attenuation

The suppression of low-frequency vibration and noise has been the research focus of acoustic metamaterials. Based on the local resonance effect of the subwavelength structure, two new topology optimization methods are proposed in this paper, and two new three-dimensional single-phase material structures are obtained. Based on Bloch theorem and lattice theory, finite element simulations of the single cells with different structures are carried out to analyze and explore the bandgap properties and opening mechanism of the structures. The frequency response spectra are obtained by vibrational transport simulation of the finite-period structures. The results show that both novel metamaterial structures have good bandgap properties, the widest first bandgap width within 2000 Hz reaches 809 Hz, and the total bandgap width percentage reaches 52.7 %, and the main vibration forms of opening the bandgap are rotational and offset resonance of the internal structure and torsional resonance of part of the structure.

Three-dimensional acoustic metamaterials with topological states of different orders and multidirectional waveguiding

Three-dimensional acoustic metamaterials with topological states of different orders and multidirectional waveguiding

Coexisting hinge and vertical disclination states in a higher-order acoustic Dirac semimetal

The concept of crystalline disclinations in solid-state physics has gained attention in recent years, particularly with a focus on two-dimensional ${C}_{n}$-symmetric topological crystalline insulators. Research in this area has revealed novel topological phases different from the traditional bulk-boundary correspondence, expanding the topological material family. However, there remains a need to investigate the bulk-disclination correspondence in three-dimensional topological semimetals. We present an example of a higher-order Dirac semimetal in acoustic crystals with central disclinations. Our simple model not only exhibits hinge modes in the vertical direction but also supports a robust one-dimensional disclination hinge state along the central bulk-hollow path. Simulations demonstrate that our structure is capable of realizing backscatter-free disclination and higher-order hinge waves under the same architecture. Our findings offer insight for potential applications in acoustic devices for sound wave propagation and manipulation, as well as for exploring more exotic high-performance three-dimensional acoustic metamaterials.

Numerical Investigation of Discrepancies Between Two-Dimensional and Three-Dimensional Acoustic Metamaterials

In order to get insight information of the band structure of acoustic metamaterials (AMMs) in condensed matter, periodic lattice structures are analyzed using Bloch’s theorem. Typical approaches of the band structure computation methods, topology optimization, and tunable abilities cannot overcome the gap between the two-dimensional (2D) AMMs theoretical and three-dimensional (3D) specimens’ experimental data yet. In this work, the variation in the results of the band structure obtained from the 2D mathematical model computed with respect to the 3D experimental models, and related cause of the variation is explored. The band structures and mode shapes of the 2D AMMs, quasi-2D models, and 3D specimen models are followed to reveal the boundary conditions and source for the observed differences in band structures. The cause for the discrepancies is verified by using the finite element method (FEM) with corresponding boundary conditions. It is found that outcomes from computational data of the 2D AMMs model are diverted significantly by means of bandgap, band structure, and stress distribution in counterparts of the 3D specimen model. This approach can provide assistance for computing the band structure of 2D AMMs for practical applications.

Observation of an acoustic octupole topological insulator

Berry phase associated with energy bands in crystals can lead to quantised observables like quantised dipole polarizations in one-dimensional topological insulators. Recent theories have generalised the concept of quantised dipoles to multipoles, resulting in the discovery of multipole topological insulators which exhibit a hierarchy of multipole topology: a quantised octupole moment in a three-dimensional bulk induces quantised quadrupole moments on its two-dimensional surfaces, which in turn induce quantised dipole moments on one-dimensional hinges. Here, we report on the realisation of an octupole topological insulator in a three-dimensional acoustic metamaterial. We observe zero-dimensional topological corner states, one-dimensional gapped hinge states, two-dimensional gapped surface states, and three-dimensional gapped bulk states, representing the hierarchy of octupole, quadrupole and dipole moments. Conditions for forming a nontrivial octupole moment are demonstrated by comparisons with two different lattice configurations having trivial octupole moments. Our work establishes the multipole topology and its full hierarchy in three-dimensional geometries.

Demonstration of a third-order hierarchy of topological states in a three-dimensional acoustic metamaterial.

Classical wave systems have constituted an excellent platform for emulating complex quantum phenomena, such as demonstrating topological phenomena in photonics and acoustics. Recently, a new class of topological states localized in more than one dimension of a D-dimensional system, referred to as higher-order topological (HOT) states, has been reported, offering an even more versatile platform to confine and control classical radiation and mechanical motion. Here, we design and experimentally study a 3D topological acoustic metamaterial supporting third-order (0D) topological corner states along with second-order (1D) edge states and first-order (2D) surface states within the same topological bandgap, thus establishing a full hierarchy of nontrivial bulk polarization-induced states in three dimensions. The assembled 3D topological metamaterial represents the acoustic analog of a pyrochlore lattice made of interconnected molecules, and is shown to exhibit topological bulk polarization, leading to the emergence of boundary states.

Higher-order topological states in a three-dimensional acoustic metamaterial

Topologically gapless edge states, characterized by topological invariants and Berry’s phases of bulk energy bands, provide amazing techniques to robustly control the reflectionless propagation of electrons, photons and phonons. Recently, a new family of topological phases, dictated by the bulk polarization, has been observed, leading to the discovery of the higher-order topological insulators. The higher-order topological states located on the “boundaries of boundaries” can be used to limit and control the transmission of optical waves, acoustic waves and elastic waves. So far, the higher-order topological states have been demonstrated in two-dimensional mechanical, electromagnetic, optical, acoustic and elastic systems. However, the study of higher-order topological states in three-dimensional acoustic systems, which can increase the possibility of topological metamaterial design, is rarely reported. In this letter, we propose a three-dimensional acoustic metamaterial supporting topologically protected second-order hinge states along with topologically protected first-order surface states within the same bandgap. Only the nearest neighbor couplings are considered in this metamaterial, and the coupling strengths can be adjusted by changing the diameters of the connection pipes. The intra-cell coupling strength t 1 is proportional to the diameters of the intra-cell connection pipes d 1, and the inter-cell coupling strength t 2 is proportional to the diameters of the inter-cell connecting pipes d 2. The band structure of the unit cell of three-dimensional acoustic metamaterial with the same intra-cell and inter-cell coupling strengths can form a two-fold nodal line along the K-H direction of its Brillouin zone. When intra-cell and inter-cell coupling strengths are different, the two-fold nodal line is lifted to form a complete bandgap, yielding two different kinds of acoustic metamaterials, that are, trivial and topological non-trivial metamaterials. The numerical results of band structures and eigenfrequencies indicate that: When the intra-cell coupling strength t 1 is less than the inter-cell coupling strength t 2, the acoustic metamaterial has 3 second-order hinge bands, 12 first-order surface bands and 18 second-order hinge eigenfrequencies, 72 first-order surface eigenfrequencies in the complete bandgap range respectively; when the inter-cell coupling strength t 2 is less than the intra-cell coupling strength t 1, there is neither any energy bands nor any eigenfrequencies in the complete bandgap range. The second-order hinge states and first-order surface states have great immunity against defects, favorably evidencing the strong robustness of the topological states. The numerical results of the transmission spectra furtherly verify the above phenomena. When t 1 2, the transmission spectrum of the second-order hinge reaches its peak at 4670 Hz. For the first-order surface transmission spectrum, a high peak, located in the bandgap, is observed around 4555 Hz. When t 1 >t 2, the surface and hinge transmission spectra are very low within the complete bandgap, the acoustic energy is concentrated only at the excitation cylinder, showing that the acoustic wave will not propagate in any part of the acoustic metamaterial in the complete bandgap range and the acoustic metamaterial is trivial. The realization of the higher-order topological states in three-dimensional acoustic metamaterial breaks through the limitation of that in two-dimensional system, realizes the topologically transform of acoustic energy among bulk, surface and hinge states and has the potential application prospect in acoustic energy recovery and high-precision acoustic sensor.

Three-Dimensional Acoustic Metamaterial with Localized Resonances

A three-dimensional acoustic negative refractive index metamaterial based on the idea of localized resonant structures is designed in the long-wavelength limit. Such behavior results from the double negativity of the effective constitutive parameters, bulk modulus and mass density, in a limited frequency range. This acoustic metamaterial is composed of balloon-contained water spheres (BLWSs) and hard rubber-coated lead spheres (HRLSs) embedded in epoxy matrix. Dispersion relation calculations by using the effective parameters, shows a negative dispersion band related to the negative refractive index for longitudinal waves. The physical realization of such metamaterial for acoustic waves could lead to many unusual applications as in the case of electromagnetism, including the manufacturing of an acoustic cloaking device.

Homogenization of acoustic metamaterials of Helmholtz resonators in fluid

By using a two-step homogenization approach, we derive analytical formulas of effective mass density ${\ensuremath{\rho}}_{e}$ and effective bulk modulus ${B}_{e}$ for two- and three-dimensional acoustic metamaterials of Helmholtz resonators (HRs) in fluid. A negative ${B}_{e}$ is found at certain frequencies due to the monopolar resonance, leading to a low-frequency acoustic band gap. A unified picture is presented for metamaterials of HRs and three-component metamaterials of negative ${\ensuremath{\rho}}_{e}$. Our work supports recent observations in a one-dimensional array of HRs [N. Fang et al., Nat. Mater. 5, 452 (2006)] and presents important high-dimensional extensions for exploring more fascinating phenomena.