Nondiffractive propagation in sonic crystals

<div class="section abstract"><div class="htmlview paragraph">This paper presents the design of an additional structure based on acoustic metamaterial (AMM) for the reduction of vibro-acoustic transfer function of a car body panel. As vehicles are lighter and those engine forces are bigger recently, it has become more difficult to reduce the vibration and noise transfer through body panels by using just conventional NVH countermeasures. In this research, a new approach based on AMM is tried to reduce the vibration and noise transfer of a firewall panel. First, a unit cell structure based on the locally resonant metamaterial is devised and the unit cell’s design variables are studied to increase the wave attenuation in the stop band of a dispersion curve, where the Floquet-Bloch theorem is used to estimate the dispersion curve of a two-dimensional periodic structure. Also, the vibration transfer and the vibro-acoustic transfer are predicted in a FE model of meta-plate which is composed of a periodic system of the devised unit cell. Next, the driving point mobility of a meta-plate is tested and its design is updated for the better performance in a vehicle. Finally, the revised structures which are mounted on a firewall are tested to verify the vibration transfer and vibro-acoustic transfer characteristics in the firewall. As a result, it is shown that the suggested meta-plate structure has a good effect on reducing the noise transfer through car body panels.</div></div>

Acoustic metamaterials are subwavelength-engineered structures that can exhibit behaviour not seen in conventional materials. The effective material properties for acoustic metamaterials are the bulk modulus and density. Negative effective material properties can create band gaps, where wave propagation is forbidden. Hence, acoustic metamaterials can achieve high levels of noise control performance. Active control has been combined with passive acoustic metamaterials to enhance the level of attenuation or broaden the bandwidth of the band gap. However, the width of the band gaps for these materials are still limited by the use of resonators. This study will investigate whether active control can be employed to directly minimise the effective material properties, which requires an optimization procedure. To begin to understand this optimization problem, the effective material properties have been calculated as a function of the real and imaginary parts of the control source strength at various frequencies for monopole and dipole sources. The resulting error surfaces demonstrate that the two configurations could achieve negative effective material properties; however, the cost functions are not always convex without constraints. Therefore, to adaptively manipulate the effective material properties using an active control system would require the development of an advanced optimization procedure.

A multiple scattering formulation of two-dimensional (2D) acoustic metamaterials is presented. This approach is comprehensive and can lead to frequency-dependent effective parameters (scalar bulk modulus and tensorial mass density), as it is possible to have not only positive or negative ellipsoidal refractive index, but also positive or negative hyperbolic refractive index. The correction due to multiple scattering interactions is included in the theory and it is demonstrated that its contribution is important only for lattices with high filling fractions. Since the surface fields on the scatterers are mainly responsible for the anomalous behavior of the resulting effective medium, complex scatterers can be used to engineer the frequency response. Anisotropic effects are also discussed within this formulation and some numerical examples are reported. A homogenization theory is also extended to electromagnetic wave propagation in 2D lattices of dielectric structures, where Mie resonances are found to be responsible for the metamaterial behavior.

Cross-shape piezoelectric patches were originally proposed to improve the band-gap properties of acoustic metamaterials with shunting circuits. The dispersion curves are characterized through the application of finite element method. Also, the theoretical band-gap predictions are verified by simulation results obtained from COMSOL. The investigation results show that the proposed scheme distinguishes itself from the conventional square patches by broader band gaps, whose bandwidth is almost doubled. The inherent capacitance of the piezoelectric patch is strongly related to the boundary conditions, so the local resonant band gap is strongly affected by the shape of piezoelectric patches as well. As a result, the band-gap width and location of metamaterials with different shape patches are rather different, even with the same size patches. Also, negative modulus (NM) and Poisson’s ratio were observed around the resonant frequencies. The transmission properties of finite periods agree well with band-gap predictions. An obvious attenuation zone (AZ) is produced around the band-gap location, in which the wave propagation is decayed strongly. Similarly, the width of AZ of the proposed metamaterial is much larger than that of the conventional one. Hence, the proposed scheme demonstrates more advantages in the application to vibration isolation when compared with the conventional.

Acoustic metamaterials have been widely investigated over the past few decades and have realized acoustic parameters that are not achievable using conventional materials. After demonstrating that locally resonant acoustic metamaterials are capable of acting as subwavelength unit cells, researchers have evaluated the possibility of breaking the classical limitations of the material mass density and bulk modulus. Combined with theoretical analysis, additive manufacturing and engineering applications, acoustic metamaterials have demonstrated extraordinary capabilities, including negative refraction, cloaking, beam formation and super-resolution imaging. Owing to the complexity of impedance boundaries and mode transitions, there are still challenges in freely manipulating acoustic propagation in an underwater environment. This review summarizes the developments in underwater acoustic metamaterials over the past 20years, which include underwater acoustic invisibility cloaking, underwater beam formation, underwater metasurfaces and phase engineering, underwater topological acoustics and underwater acoustic metamaterial absorbers. With the evolution of underwater metamaterials and the timeline of scientific advances, underwater acoustic metamaterials have demonstrated exciting applications in underwater resource development, target recognition, imaging, noise reduction, navigation and communication.

Design of low-frequency and broadband acoustic metamaterials with I-shaped antichiral units

Effective dynamic properties of acoustic metamaterials made of multilayered flexible thin-plates with periodically attached mass-spring resonators are studied. By using the transfer matrix method, the thin-plate acoustic metamaterial under the plane wave incidence is characterized by a homogeneous effective medium with anisotropic mass density. An approximate analytic expression of effective mass density is derived for a single-layer metamaterial in the normally incident case, and it is shown that the effective mass density can follow either Lorentz or Drude medium models. For the obliquely incident case, it is found that effective mass density is dependent on the lateral wave number of incident waves. Such spatial dispersion comes from the coincidence effect between the incident acoustic wave and flexural wave in the thin plate, and it occurs at much lower frequencies than that for a uniform plate without resonators. Based on the observed spatial dispersion, an acoustic device made of thin-plate metamaterials is designed for frequency-controlled acoustic directive radiation in the low-frequency regime.

In the last few years, highly anisotropic metamaterials have been explored in various geometries, showcasing interesting routes to achieve better control of sound propagation. As an extreme example, hyperbolic metasurfaces have been shown to offer broadband enhanced sound-matter interactions and diffraction-less propagation of acoustic waves, providing opportunities for sub-diffraction imaging and enhanced sound emission. In this study, we show that structure design of a locally resonant metamaterial enables extreme anisotropic responses, ranging from elliptic to hyperbolic propagation of acoustic surface waves, offering interesting opportunities for extreme sound guiding and steering at the subwavelength scale well compatible with a wide range of additive manufacturing techniques.

The low frequency structure-borne sound problem in multi-storey timber buildings and potential of acoustic metamaterials: A review

We demonstrate a new technique for femtosecond microfabrication in transparent dielectrics, which employs non-diffracting Bessel-Gauss beams instead of commonly used Gaussian beams. The main advantage achieved this way is the ability to record linear photomodified tracks, extending along the line of non-diffracting beam propagation without sample translation, as would be required for Gaussian beams. The initial near infrared Gaussian laser beam was transformed into the non-diffracting Bessel-Gauss beam by a glass axicon (apex angle 160 deg). The beam was imaged into the bulk of the sample by a telescope consisting oftwo positive lenses, which allowed to vary the focusing cone angle from 5°to 19°, and maximum non-diffracting propagation distance up to 1 cm. We have recorded pre-programmed patterns of multi-shot damage tracks (diameter about 3 µm), extended uniformly along the z-axis by varying the damage spot coordinates in the x - y plane. The experiments were carried out in various transparent dielectrics: silica glass, sapphire, and plexyglass. Physical processes underlying the Gauss-Bessel microfabrication, and its potential applications for stereolithography, 3D microstructuring, and photonic crystal fabrication will be discussed.

Ideal Bessel beam is a non-diffracting beam and the most attractive property of such beam is non-diffracting propagation. In optics, although the comparisons of maximum propagation distance had been done between Bessel and Gaussian beams by Durnin and Sprangle, respectively, their comparison results are conflict result from their different criteria. It is necessary and significant that the comparison is carried out at microwave band. In this paper, we therefore propose a relatively objective and just comparison criterion at millimeter wavelength, and numerical simulation results and a new conclusion are presented.

We investigate dynamic effective anisotropy in photonic crystals (PCs) through a combination of an effective medium theory, which is a high-frequency homogenization (HFH) method explicitly developed to operate for short waves, as well as through numerical simulations and microwave experiments. The HFH yields accurate predictions of the effective anisotropic properties of periodic structures when the wavelength is of comparable order to the pitch of the array; specifically, we investigate a square array of pitch 2 cm consisting of dielectric rods of radius 0.5 cm and refractive index n=6√ within an air matrix. This behaves as an effective medium, with strong artificial anisotropy, at a frequency corresponding to a flat band emerging from a Dirac-like point in transverse magnetic (TM) polarization. At this frequency, highly directive emission is predicted for an electric source placed inside this PC, and this artificial anisotropy can be shown to coincide with a change of character of the underlying effective equation from isotropic to unidirective, with coefficients of markedly different magnitudes appearing in the effective equation tensor. In transverse electric (TE) polarization, we note a second radical change of character of the underlying effective equation, this time from elliptic to hyperbolic, near a frequency at which a saddle point occurs in the corresponding dispersion curves. Delicate microwave experiments are performed in both polarizations for such a PC consisting of 80 rods, and we demonstrate that a directive emission in the form of a + (respectively, an X) is indeed seen experimentally at the predicted frequency 9.5 GHz in TM polarization (respectively, 5.9 GHz in TE polarization). These are clearly dynamic effects since in the quasistatic regime the PC just behaves as an isotropic medium.

The growing demand for low-frequency, broadband vibration and noise suppression technologies in next-generation mechanical equipment has become increasingly urgent. Effective negative mass locally resonant structures represent one of the most paradigmatic classes of acoustic metamaterials. Their unique elastic wave bandgaps enable efficient suppression of low-frequency vibrations, while inherent nonlinear effects provide significant potential for the design and tunability of these bandgaps. To achieve ultra-low-frequency and ultra-broadband vibration attenuation, this study employs Duffing oscillators exhibiting negative-stiffness characteristics as structural elements, establishing a bistable nonlinear acoustic-metamaterial mechanical model. Subsequently, based on the effective negative mass local resonance theory, the perturbation solution for the dispersion curves is derived using the perturbation method. Finally, the effects of mass ratio, stiffness ratio, and nonlinear term on the starting and cutoff frequencies of the bandgap are analyzed, and key geometric parameters influencing the design of ultra-low vibration reduction bandgaps are comprehensively investigated. Subsequently, the influence of external excitation amplitude and the nonlinear term on bandgap formation is analyzed using numerical computation methods. Finally, effective positive mass, negative mass, and zero-mass phenomena within distinct frequency ranges of the bandgap and passband are examined to validate the theoretically derived results. The findings demonstrate that, compared to a positive-stiffness system, the bandgap of the bistable nonlinear acoustic metamaterial incorporating negative-stiffness Duffing oscillators shifts to higher frequencies and widens by a factor of 2. The external excitation amplitude F changes the bandgap starting frequency and cutoff frequency. As F increases, the starting frequency rises while the cutoff frequency decreases, resulting in a narrowing of the bandgap width. Within the frequency range bounded by the bandgap starting frequency and cutoff frequency, the region between the resonance frequency and cutoff frequency corresponds to an effective negative mass state, whereas the region between the bandgap starting frequency and resonance frequency exhibits an effective positive mass state. Critically, the bandgap encompasses both effective positive mass and negative mass regions, wherein vibration propagation is suppressed. Concurrently, a zero-mass state emerges within this structure, with its frequency precisely coinciding with the bandgap cutoff frequency. This study provides a theoretical foundation and practical guidelines for designing nonlinear acoustic metamaterials targeting ultra-low-frequency and ultra-broadband vibration and noise mitigation.

In this paper, we present the first realization of an elastic metamaterial allowing independent tuning of negative density and stiffness for elastic waves propagating along a designated direction. In electromagnetic (or acoustic) metamaterials, it is now possible to tune permittivity (bulk modulus) and permeability (density) independently. Apparently, the tuning methods seem to be directly applicable for elastic case, but no realization has yet been made due to the unique tensorial physics of elasticity that makes wave motions coupled in a peculiar way. To realize independent tunability, we developed a single-phased elastic metamaterial supported by theoretical analysis and numerical/experimental validations.

In this introductory chapter the reader is acquainted with the range of topics covered. The concept of “normal” electromagnetic waves is introduced in connection with basic problems of crystal optics. Methods are discussed, within the framework of macroscopic electrodynamics, for a theoretical investigation of these waves, making use of the dielectric-constant tensor as a characteristic of the medium. This chapter illustrates the frequency and spatial dispersion of the tensor; it indicates the main effects of spatial dispersion in crystals (gyrotropy, optical anisotropy of cubic crystals, and additional light waves). The concept of excitons and polaritons is introduced. It is shown that crystal optics with spatial dispersion, which includes all of ordinary crystal optics as a special case, is closely associated with the theory of excitons.KeywordsLongitudinal WaveNormal WaveSpatial DispersionMicroscopic TheoryCrystal OpticThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.