Split Hollow Sphere Research Articles

Subwavelength thermally controlled acoustic topological interface states in split hollow spheres

This article puts forward theory and design approaches for three thermally controlled subwavelength acoustic topological insulators. They are presented by immersing arrays of split hollow spheres (SHSs) or cubes in an air background and performing a study on the band structures and topological interface states. The periodically immersed rhombic shape unit cell comprising of two SHSs is analyzed firstly. A subwavelength local resonance bandgap and a Dirac point at the corner of the irreducible Brillouin zone are observed. After inducing a gap for the Dirac cone with unequal inner radius of spheres, we observe topological phase transition by mode shape and valley Chern-number analysis. Generally, local resonance systems are always limited to narrow and fixed bandgaps, therefore active and passive control of the structure are demonstrated. A strip supercell is constructed to induce topologically protected interface mode and to capture highly localized acoustic energies at the interface. Similar analyses are performed on the enlarged hexagonal model with six SHSs and the rhombic model with two split hollow cubes. This study provides a new degree of freedom for active control of acoustic topological modes and sound wave propagation.

Tri-Band Negative Modulus Acoustic Metamaterial With Nested Split Hollow Spheres

We presented tri-band negative modulus acoustic metamaterials (AM), whose operation characteristics could be flexibly designed by changing the three hole sizes (i.e., a1, a2, and a3) of the tri-layer nested split hollow spheres (NSHSs). We demonstrate numerically that tri-band negative modulus can be obtained and each resonant frequency corresponds to the hole size of each split hollow sphere. However, for the case when a1> a2> a3, the negative modulus band in the high frequency region vanishes. An effective sound-force analogue model with coupling interaction is further developed for the accurate prediction of the three resonant frequencies based on equating the tri-layer NSHSs to three spring oscillators in series. As a result of the analytical formulas, three resonant frequencies could be precisely controlled, and a nested AM with a tri-band negative modulus can be flexibly constructed. The proposed AM could be easily extended to multiple operation bands and can be further coupled with negative mass density structures for constructing multi-band double-negative AMs.

Structural optimization scheme for acoustic cloaking structures considering general surfaces

ABSTRACT The present study presents the application of a structural optimization scheme for a Double Split Hollow Sphere (DSHS) based acoustic cloaking structure for irregular surfaces. For acoustic wave cloaking, many scientific devices utilizing phase differences have been developed. Considering the irregular surfaces of objects to be concealed, acoustic wave reflections become complex with random phase differences and determinations of the involved geometric parameters of cloaking structures become impractical. To determine the geometric parameters of acoustic cloaking devices with DSHS systematically, the present study applies a structural optimization scheme. The present scheme computes and minimizes the differences between the acoustic pressures reflected from irregular surfaces and the reference acoustic pressures without irregular surfaces by optimizing the location and geometric parameters of the DSHS. To show the validity of the present scheme, structural optimization problems are solved for several three-dimensional problems with complex and irregular surfaces.

Simulated and Experimental Research of Multi-Band Acoustic Metamaterial with a Single Resonant Structure.

We present a multi-band acoustic metamaterial (AMM) with a single structural unit of a nested split hollow sphere (NSHS). The transmissions of the NSHS-AMM from the simulation and experiment revealed two dips which were attributed to local coupling resonance. Using the retrieval method from the experimental data, we calculated the effective modulus of the NSHS-AMM and found it to be negative near the bands of the two dips. The AMM with a negative modulus can be easily tuned due to the coupling effect in the NSHS. The two dips can be simultaneously tuned by changing the diameter and the direction angle of the split holes of the interior and exterior split hollow sphere (SHS) in the NSHS. We designed a three-nested SHS-AMM with a negative modulus in three bands. Given the obvious local coupling resonance in the NSHS, such NSHS-AMMs may provide a viable path for the design of broadband AMMs or acoustic metasurfaces.

Tunable Two-Layer Dual-Band Metamaterial with Negative Modulus.

A tunable dual-band acoustic metamaterial (AM) with nested two-layer split hollow spheres (TLSHSs) is presented here, which was achieved by adjusting the hole diameter and the ratio of the two layers’ volumes. This work comprises theoretical and numerical studies. Based on sound-force analogy (SFA), TLSHSs can be considered equivalent to a model of two spring oscillators in series. The equations of two resonant frequencies were derived, which precisely provided the relation between two resonant frequencies and the hole diameter as well as the ratio of the two layers’ volumes. The analytical formulas and simulation results by the finite element method (FEM) showed that there were two resonant frequencies for the TLSHSs, and their dynamic modulus became negative near the resonant frequencies. As the the diameter of two holes increased, both of the resonant frequencies underwent a blue shift. As the relative volume ratio increased, both of the resonant frequencies underwent a red shift. The calculation and simulation results were in good agreement. This kind of precisely controllable dual-band AM with negative modulus can easily be coupled to other structures with negative mass density, thereby achieving a double-negative AM in an expected frequency range.

An Acoustic Hyperlens with Negative Direction Based on Double Split Hollow Sphere

This study develops a new acoustic negative-refraction metamaterial that utilizes a synthesized double split hollow sphere (DSHS) for its unit cell. Recent relevant research has affirmed the concept that acoustic metamaterials can show unusual behavior that has not been observed in nature previously. However, as some hypothetical metamaterial designs have material properties not found in nature, the realization of practical metamaterials requires practical and complicated models. As a contribution to the development of acoustic metamaterials, the present study proposes a new anisotropic unit structure that encompasses Helmholtz resonators. This structure is referred to as the DSHS, is easy to manufacture, and has the advantage in that it uses the natural medium in its original form. By drawing the equifrequency or isofrequency contours of the designed two-dimensional (2D) anisotropic unit structure using the Floquet–Bloch’s principle, the properties of the present metamaterial can be understood. Numerical simulations are also conducted to identify and present the characteristics of the presented acoustic metamaterial. Through these, a new refraction phenomenon is identified that deviates from Snell’s law, and an acoustic hyperlens is numerically implemented that overcomes the diffraction limit.

Mutual Inductance and Coupling Effects in Acoustic Resonant Unit Cells.

We present an acoustic metamaterial (AMM) consisting of a dumbbell-shaped split hollow sphere (DSSHS). Transmission results of experiments and simulations both presented a transmitted dip at the resonant frequency of AMM, which demonstrated its negative modulus property. As the two split holes in the DSSHS had strong coupling effects for the acoustic medium in the local region, the dip could be simply manipulated by tuning the distance between the split holes. When the distance was large enough, the mutual inductance tended to disappear, and a weak interaction existed in the structure. According to the property of weak interaction, a multiband AMM and a broadband AMM with a negative modulus could be achieved by arraying DSSHS clusters with different distances. Furthermore, mutual inductance and coupling in DSSHS reinforced the local resonance, and this kind of cell could be used to design the acoustic metasurface to abnormally control the refractive waves.

Multibands acoustic metamaterial with multilayer structure

A multiband acoustic metamaterial (AM) with negative modulus is presented. To realize the multibands, we conduct the unit structure of a resonator with multilayers in which we adjust the number of layers of local resonance cells, namely, multilayer split hollow spheres or cubes (SHSs or SHCs). The results obtained by the finite element method show that a single-layer SHS has one transmission dip and the resonance generates a negative modulus; two-layer SHSs exhibit two transmission dips, while three-layer SHSs and three-layer SHCs have three transmission dips and their dynamic modulus become negative near the resonant frequency. Thus, the number of multiband resonant frequencies is regulated by adjusting the number of layers. This regulation is independent of the sphere and cube of the resonance cell, and this structure is simple. The developed multiband AM can easily be coupled to other structures with negative mass density, thereby obtaining a double-negative AM. It is also applicable in fields such as cloak or sub-wavelength imaging.

Research advances in acoustic metamaterials and metasurface

Acoustic metamateiral (AM) is an artificially structured material with the unique properties that cannot be found in nature materials, such as negative refraction, slab focusing, super-resolution imaging, cloaking, inverse Doppler effect, etc. In this paper we first review the research advances in AM in recent 20 years and then mainly discuss the properties of the meta-atom AM (MAAM), meta-molecule AM (MMAM), meta-atom cluster AM, and meta-molecule cluster AM. The MAAM consists of local resonant meta-atoms, whose resonant frequency is related to the geometry size of the structure. The MAAM presents the transmission dip and inversed phase near the resonant frequency. The meta-atoms discussed in the paper contain the split hollow sphere and hollow tube (HT), which can be used to realize the AM with single negative modulus and AM with single negative mass density near the frequency, respectively. The effective parameter of the MAAM is calculated from the transmission and reflection data in experiment according to the homogeneous-medium theory. By combining the two kinds of meta-atoms together, the assembled two-layered composite AM presents a transmission peak similar to the electromagnetic metamaterial in the overlapping resonant frequency region. The effective parameters calculated by experimental data demonstrate that the composite AM could realize simultaneously negative modulus and negative mass density near the peak frequency. In the double-negative band, this kind of double-negative AM can faithfully distinguish the acoustic sub-wavelength details (/7). Furthermore, by coupling the two kinds of meta-atoms in a structure, we design a flute-like meta-molecule structure of perforated hollow tube, which can be used to fabricate double-negative AM in high or low frequency band. The experimental results also show that the double-negative AM has the properties of flat focusing and negative refraction effect. Based on the weak interaction of the meta-atoms, the meta-atom cluster AM can be fabricated by arraying different sized meta-atoms. The meta-atom cluster AM composed of different sized meta-atoms of SHSs can realize multi-band or broadband negative modulus, and the different sized meta-atoms of HTs can realize broadband negative mass density. Similarly, the meta-molecule cluster AMs are constructed with seven kinds of flute-like perforated hollow tubes, which can overcome the limitations of arbitrary broadband negative bulk modulus and mass density to provide a region of inverse Doppler effects. It is also shown that the inverse frequency shift values will be enhanced with the increase of frequency. As the resonant unit can realize the effect of discontinuous phase, it can be used to design acoustic metasurface (AMS) to control the acoustic wavefronts at will and realize the anomalous manipulation of acoustic waves. Finally, we introduce the research status and tendency of AMS in coming years.

The Effect of Geometrical Parameters on Resonance Characteristics of Acoustic Metamaterials with Negative Effective Modulus

There has been an explosion of interest in acoustic metamaterial in the last ten years. The tunable negative acoustic metamaterial is an important issue for designing metamaterials. The acoustic metamaterial is restricted by the narrow bandgap of sound waves for the local resonance of metamaterial unit cells. By shifting the sizes of the unit cell, the acoustic metamaterial could potentially overcome the limit of the narrow resonance frequency. In this research, we focus on the resonant behavior of split hollow sphere (SHS) in the waveguide. Firstly, we analyze the resonance characteristics of SHS and get an analytical formula for the effect of geometrical parameters on the resonance frequency. Furthermore, the resonance frequency of SHS is verified with finite-element method analysis based on COMSOL Multiphysics simulation. The results are in good agreement with theory model. It is observed that there is a blue shift of the resonance frequency with the gradual increase of the neck radius of SHS, a V-type response curve with the increase of inner radius of SHS, and a red shift with the increase of outer radius of SHS. Using the method of estimate of resonance, we could get a precisely controllable unit structure with negative effective modulus and offer a way to optimize the realization of double negative acoustic metamaterial.

Ultrasound acoustic metamaterials with double-negative parameters

We experimentally demonstrate a double-negative acoustic metamaterial (AM) that combines a hollow tube and a split hollow sphere into a structurally simple perforated hollow tube with the ability to generate simultaneous resonances in water. The effective acoustic parameters extracted from the transmission and reflection coefficients confirmed that negative effective mass density and modulus were achieved from 36.68 kHz to 36.96 kHz, and the effective index was also negative in the same frequency range. In addition, further experimental measurements confirmed that the well-designed AM could realize slab focusing phenomenon. With the unique properties, the proposed AM presents potential applications in sub-wavelength imaging and medical ultrasound treatment.

The anomalous manipulation of acoustic waves based on planar metasurface with split hollow sphere

This paper presents an acoustic metasurface (AMS) model consisting of split hollow sphere (SHS) resonator arrays with the property of negative modulus. It shows that the AMS can imprint phase discontinuities on an acoustic reflected wave as it traverses the interface between two media. By designing suitable phase gradients, the AMS enables the perpendicularly incident acoustic wave to be converted to a surface wave or reflected in any angle. Four kinds of AMSs, which can anomalously manipulate the reflected wave’s direction, are simulated to fulfill the generalized Snell’s law. The results provide an available and simple path to experimentally achieving the AMS.

An active viscoelastic metamaterial for isolation applications

Metamaterials are of interest due to their ability to produce novel acoustic behaviour beyond that seen in naturally occurring media. Of particular interest is the appearance of band gaps which lead to very high levels of attenuation within narrow frequency ranges. Resonant elements within metamaterials allow band gaps to form within the long wavelength limit at low frequencies where traditional passive isolation solutions suffer poor performance. Hence metamaterials may provide a path to high performance, low frequency isolation. Two metamaterials are presented here. An acoustic material consisting of an array of split hollow spheres is developed, and its performance is validated experimentally. The application of an acoustic/mechanical analogy allows the development of an elastodynamic metamaterial that could be employed as a high performance vibration isolator at low frequencies. A prototype isolator is manufactured, and its performance is measured. The passively occurring band gap is enhanced using an active control architecture. The use of the active control system in conjunction with the natural passive behaviour of the metamaterial enables high levels of isolation across a broad frequency range. An eventual goal of the work is to produce such materials on a small scale, and as such the metamaterials developed are designed for, and produced using, additive layer manufacturing techniques.

Design of a Passive Controllable Negative Modulus Metamaterial With a Split Hollow Sphere of Multiple Holes

We present a passive controllable negative modulus metamaterial based on a split hollow sphere (SHS) with multiple holes. The metamaterial is obtained by changing the number of split holes. The experimental results show that the position of one split hole does not affect the transmission dip, whereas the resonance frequency depends on the relative position of two holes. Furthermore, when the number of split holes is increased, the resonance frequency undergoes a blueshift. Simulation results via the finite element method (FEM) are in accord with experimental data. The design of a negative modulus metamaterial at an expected frequency is simple, and the proposed method is expected to provide a basis for the simultaneous control of acoustic metamaterials (AMs) through a variety of methods.

Acoustic metamaterial based on multi-split hollow spheres

We firstly present a kind of acoustic metamaterial (AM) with resonant microstructure of double split hollow sphere (DSHS). Simulation and experimental results show that the DSHS AM has a transmission dip and accompanied phase advance near the resonant frequency. Effective properties extracted by homogenized-media theory show that the negative modulus of the DSHS AM occurs near the dip frequency. With the increase of the diameter of the double holes in the DSHS, the resonant intensity will be stronger which leads to a greater negative modulus. By adjusting the double holes of DSHS structure with different diameter or angle, the negative-modulus band of the AMs with the modified unit cells will become tunable. Furthermore, we extend the DSHS AMs to the AMs with multi-split hollow sphere (MSHS), which still possess the property of negative modulus. This concept may pave a theoretical way to study the micro-sized and nano-sized MSHS AMs fabricated by chemical manufacturing techniques, which have potential application in the future.

Experimental validation of the band-gap and dispersive bulk modulus behavior of locally resonant acoustic metamaterials

Over the last decade there has been significant interest in the design and production of acoustic metamaterials with physical qualities not seen in naturally occurring media. Progress in this area has been stimulated by the desire to create materials that exhibit novel behavior such as negative refraction due to negative material parameters, and band gaps in the frequency response of the material. An acoustic metamaterial is presented that consists of an acoustically transparent mesh with an array of split hollow spheres. Split hollow spheres are analogous to the split ring resonators found in many electromagnetic metamaterials and act as Helmholtz resonators providing a resonant band gap at low frequencies where achieving a Bragg gap would be impractical, and providing a dispersive effective bulk modulus that can become negative. Since an eventual goal of the work is to produce such materials on a micro-scale, the metamaterial is designed for, and produced using, 3D printing techniques (additive layer manufacturing). Results are presented for material comparing theory and experiment, and methods for increasing the bandwidth of the behavior in question are proposed, including a mixed resonator solution and the integration of active components into the material.

Double-negative acoustic metamaterial based on hollow steel tube meta-atom

We presented an acoustic “meta-atom” model of hollow steel tube (HST). The simulated and experimental results demonstrated that the resonant frequency is closely related to the length of the HST. Based on the HST model, we fabricated a two-dimensional (2D) acoustic metamaterial (AM) with negative effective mass density, which put up the transmission dip and accompanied inverse phase in experiment. By coupling the HST with split hollow sphere (SHS), another kind of “meta-atom” with negative effective modulus in the layered sponge matrix, a three-dimensional (3D) AM was fabricated with simultaneously negative modulus and negative mass density. From the experiment, it is shown that the transmission peak similar to the electromagnetic metamaterials exhibited in the double-negative region of the AM. We also demonstrated that this kind of double-negative AM can faithfully distinguish the acoustic sub-wavelength details (λ/7) at the resonance frequency of 1630 Hz.

Tunable acoustic metamaterial with negative modulus

A tunable negative modulus metamaterial is presented, and it is achieved by adjusting the medium density and an effective volume of a split hollow sphere (SHS). This work comprises experimental and numerical studies. The effects of water/air component and the steel ball on the transmission properties were investigated in the impedance tube system. The experimental results show that the transmission dip has a significant blue-shift with increasing water content, whereas the steel ball has a relatively small influence on the resonant frequency. The simulated results by the finite-element method (FEM) are in agreement with the experimental results. Based on medium parameters among the SHS, acoustic metamaterial (AM) with negative modulus can easily be designed in the expected frequency domain, and it provides a convenient route to tune AMs.

Multi-band and broadband acoustic metamaterial with resonant structures

We design an acoustic metamaterial (AM) with multi-band of negative modulus composed of different sized split hollow spheres (SHSs). From acoustic transmitted experiment, the AM exhibits simultaneously negative modulus at frequencies 914, 1298 and 1514 Hz. Based on the multi-band designed concept, broadband AM is fabricated by arraying gradually sized SHS. The transmission results indicate that this medium can achieve negative modulus at the frequency range from 900 to 1500 Hz. This kind of broadband AM is very convenient to couple with other structures to gain the double-negative AM.

Acoustic metamaterial with split hollow spheres

We propose an acoustic metamaterial (AM) composed of local resonant split hollow sphere (SHS). The results of numerical simulation and acoustic experiment show that the effective modulus of the AM with SHS is negative. To further investigate the intrinsic resonant mechanism of the SHS, we study the transmission of the AM by adjusting the geometry sizes of the SHS, such as the diameter of split hole and the diameter of hollow sphere. It is found that the geometry sizes of SHS will greatly affect the frequency of transmission dip, say, the resonant frequency. Moreover, we investigate the effects of the arrangement in AM on transmission feature. When the lattice constant and the number of SHSs change, the frequency range of resonance in the single-layer AM keeps unchanged. However, the resonant intensity of AM becomes stronger with the increase of the number of SHSs in single layer and the number of SHS layers.