Acoustic Band Structure Research Articles

Impact induced compression and decompression waves in porous meta-materials modeled using a continuum theory of phase transitions

Porous meta-materials with both regular and random microstructure are of intense research interest today due to their interesting dynamical properties, including but not limited to, their acoustic band structure, shock absorption properties, and fracture toughness. Some of these materials can exist in a rarefied or densified state depending on the state of stress, and recover their original configuration after a cycle of loading and unloading. Often, they exhibit a hysteretic stress–strain response under quasistatic uniaxial compression. As such, many aspects of their mechanical behavior can be captured using a continuum theory of phase transitions. In this work, the dynamical behavior of such materials is explored. It is shown that the impact problem for these materials can result in propagating shocks, phase boundaries, and fans. The impact problems admit multiple solutions for the same set of initial and boundary conditions leading to non-uniqueness. This non-uniqueness can be remedied using a nucleation criterion and kinetic laws, as is known from the continuum theory of phase transitions. The fan solutions which arise in decompressive impact problems have not received much attention in the literature and may be regarded as a novel contribution of this work. The analysis presented here may have applications in the dynamic behavior of a broad class of porous materials including architected truss-like metastructures and random fiber networks.

Imaging an Acoustic Topological Edge Mode on a Patterned Substrate with Microwave Impedance Microscopy

The topological properties of an acoustic metamaterial's phononic band structure would be useful for developing functional acoustic and thermal devices. While previous demonstrations of topological properties have been limited to low-frequency airborne sound, high-frequency acoustic waveguides utilizing the topological edge state are increasingly in demand for quantum technologies, sensing, and microwave communication. In this work, the authors use innovative microscopy to visualize topological acoustic edge states at frequencies as high as 2.4 GHz on a patterned substrate, which bodes well for the feasibility of topological surface-acoustic-wave devices.

Acoustic performance of architected hybrid metamaterials for sound attenuation applications

Acoustic insulators in sound attenuation applications usually have a structure with a characteristic dimensions equivalent to the operating wavelength, posing significant challenges in low-frequency sound attenuation applications. Recent advancements in material science, advanced materials called acoustic metamaterials (AMMs) have paved the way for designing efficient noise insulation passive and active devices. This paper proposes heterogeneous integrated passive metamaterials for enhanced sound insulation in broad frequency bands. Six acoustic meta-unit cells (UCs) with deep subwavelength thickness were proposed and analyzed numerically for the acoustic band structure and transmission characteristics. Out of these six UCs, three high-performing UCs were chosen for further analysis. Finite element (FE) analysis results showed that the maximum transmission loss conforms with the computed band structures. Next, we proposed several heterogeneous meta-structures consisting of different combinations of chosen meta-unit cells. The FE analysis results showed that a broader band of sound absorptions can be achieved through the hybrid design of AMMs. Our research revealed that the suggested structures may be utilized to create metamaterials with a wider absorption band, making them suitable for a variety of applications.

Acoustic modes of locally resonant phononic crystals: Comparison with frequency-dependent mass models

Locally resonant acoustic materials were proposed to control sound using structures with feature size orders of magnitude smaller than the acoustic wavelength in air. We analytically derive the effective, frequency-dependent mass densities of resonant oscillators consisting of a heavy mass within a light shell, embedded in foam, in two dimensions, using a rigid core-shell approximation. The effective mass is expressible in closed form by elementary functions, enabling a mapping of the low-frequency physics to a simple one-dimensional model involving a point mass harmonically coupled within a box. The acoustic band structure of a two-dimensional square lattice of these oscillators is evaluated in the effective, frequency-dependent mass density model and compared with the exact solution. For the out-of-plane oscillation within this two-dimensional phononic crystal, the nonlinear eigenvalue equation resulting from the frequency-dependent density is solved with the Cutting Surface Method to yield the acoustic band structure. This agrees with the exact band structure obtained by finite element method calculations within $2%$ numerical error. For the in-plane oscillations involving internal translations or rotations within the core-shell resonators, the one-dimensional mass-in-a-box model recaptures the exact acoustic modes at only certain high-symmetry points of the two-dimensional Brillouin zone. The description of more complex resonances within acoustic metamaterials requires a fundamental generalization of current effective mass models.

Complete phononic band gaps in the 3D Yablonovite structure with spheres

In this work we present the theoretical and experimental verification of complete phononic band gaps in the Yablonovite structure with additional spheres in a face-centered cubic arrangement. The Finite Difference Time Domain method was used in the calculations of band structure and transmission spectrum. Different spatial directions and different polarizations of the incident acoustic field were investigated numerically and experimentally. Phononic band gaps in the acoustic band structure and in the transmission spectrum were calculated for all the examined cases of spatial directions and polarizations. The complete band gaps of the theoretical findings were confirmed by experimental measurements of 3D-printed prototype samples. All results are in very good agreement and validate complete phononic band gaps in these structures.

Wave propagation on a ferroelectric liquid crystal based acoustic metamaterial

In the present work, the acoustic band structure of a 2D phononic crystal (PnC) containing an organic ferroelectric (low molecular weight liquid crystal polimer in C-smectic phase - LMWLCS) and topological insulator (GeTe) were investigated by the finite element method and experimentally. 2D PnC with square lattices composed of GeTe cylindrical rods embedded in the LMWLCS matrix are studied to find the allowed and stop bands for the waves of certain energy. Phononic band diagram ω = ω(k) for a 2D PnC along the Г-X-M-Г path in the square Brillouin zone shows few stop bands in the frequency range between 10–110 kHz.

Realization of an Acoustic Third-Order Topological Insulator.

The recent discovery of higher-order topological insulators (TIs) has opened new possibilities in the search for novel topological materials and metamaterials. Second-order TIs have been implemented in two-dimensional (2D) systems exhibiting topological "corner states," as well as three-dimensional (3D) systems having one-dimensional (1D) topological "hinge states." Third-order TIs, which have topological states three dimensions lower than the bulk (which must thus be 3D or higher), have not yet been reported. Here, we describe the realization of a third-order TI in an anisotropic diamond-lattice acoustic metamaterial. The bulk acoustic band structure has nontrivial topology characterized by quantized Wannier centers. By direct acoustic measurement, we observe corner states at two corners of a rhombohedronlike structure, as predicted by the quantized Wannier centers. This work extends topological corner states from 2D to 3D, and may find applications in novel acoustic devices.

Twist-projected two-dimensional acoustic topological insulators

Acoustic analogs of electronic or photonic topological insulators provide unique approaches to manipulate sound wave propagation. Inspired by twist-induced topological photonic insulators, here we propose a type of two-dimensional acoustic topological insulator (TI) via projecting a section of a three-dimensional twisting structure to a plane, assembling the projected meta-atoms into metamolecules, and arranging the metamolecules into unit cells to form a honeycomb lattice. It follows that in this acoustic TI, topological phases mimic pseudospin-up and pseudospin-down states, and the pseudospin-orbital couplings are tuned via changing the rotation angles of the meta-atoms, which eventually leads to band inversion. By calculating acoustic band structures, pressure field distributions, and spin Chern numbers of bands, we verify that the topological phase transition occurs around the double Dirac cone and present the topological phase diagram as a function of the rotation angle of the meta-atoms. Once the coupling between adjacent metamolecules is sufficiently strong, mode inversion of topological states emerges. Furthermore, we numerically demonstrate the existence of topologically protected edge states. It is shown that robust pseudospin-dependent one-way transmission is immune to defects at the edge of topological distinct regions, which can be applied to acoustic wave transmissions and communications. Our approach in acoustic systems provides a strategy to explore abundant topological states in two-dimensional systems.

Multiferroic based 2D phononic crystals: Band structure and wave propagations

In the present work the acoustic band structure of a two-dimensional phononic crystal containing an organic ferroelectric (PVDF- polyvinylidene fluoride) and muliferroic material (LiVCuO4) were investigated by the plane-wave-expansion method. A two-dimensional PC with square lattices composed of LiVCuO4 cylindrical rods embedded in the PVDF matrix are studied to find the existence of stop bands for the waves of certain energy. This phononic bandgap – forbidden frequency range – allows sound to be controlled in many useful ways in structures that can act as sonic filters, waveguides or resonant cavities. Phononic band diagram ω = ω(k) for a 2D PC, in which non-dimensional frequencies ωa/2πc (c-velocity of wave) were plotted versus the wavevector k along the Γ-X-M-Γ path in the square Brillouin zone show four stop bands in the frequency range 0.01–8.0 kHz. The ferroelectric properties of PVDF and unusual properties of multiferroic LiVCuO4 give us the ability to control the wave propagation through the PC in over a wide frequency range.

Phononic band gap and wave propagation on multiferroic-based acoustic metamaterials

In the present work, the acoustic band structure of a two-dimensional (2D) phononic crystal containing a multiferroic and liquid were investigated by the plane-wave-expansion method. 2D PnC with triangular and honeycomb lattices composed of LiCu2O4 cylindrical rods embedded in the seawater matrix are studied to find the existence of stop bands for the waves of certain energy. Phononic band diagram ω=ω(k) for a 2D PC, in which nondimensional frequencies ωa/2πc (c-velocity of wave) were plotted versus the wavevector k along the г-X-M-г path in the Brillouin zone show few stop bands in the frequency range between 10 and 110 kHz.

Tuning frequency band gaps of tensegrity mass-spring chains with local and global prestress

This work studies the acoustic band structure of tensegrity mass-spring chains, and the possibility to tune the dispersion relation of such systems by suitably varying local and global prestress variables. Building on established results of the Bloch–Floquet theory, the paper first investigates the linearized response of chains composed of tensegrity units and lumped masses, which undergo small oscillations around an initial equilibrium state. The stiffness of the units in such a state varies with an internal self-stress induced by prestretching the cables forming the tensegrity units, and the global prestress induced by the application of compression forces to the terminal bases. The given results show that frequency band gaps of monoatomic and biatomic chains can be effectively altered by the fine tuning of local and global prestress parameters, while keeping material properties unchanged. Numerical results on the wave dynamics of chains under moderately large displacements confirm the presence of frequency band gaps of the examined systems in the elastically hardening regime. Novel engineering uses of the examined systems are discussed.

Wave Propagations in Metamaterial Based 2D Phononic Crystal: Finite Element Analysis

In the present work, the acoustic band structure of a two-dimensional (2D) phononic crystal (PnC) containing composite material were investigated by the finite element method. Two-dimensional PC with triangular and honeycomb lattices composed of composite cylindrical rods are in the air and liquid matrix. The existence of stop bands are investigated for the waves of certain frequency ranges. This phononic band gap - forbidden frequency range - allows sound to be controlled in many useful ways in structures. These structures can be used as sonic filters, waveguides or resonant cavities. Phononic band diagrams ω=ω(k) for a 2D PnC were plotted versus the wavevector k along the Γ-X-M- Γ path in the first Brillouin zone. The calculated phonon dispersion results indicate the existence of full acoustic modes in the proposed structure along the high symmetry points.

Acoustic band gaps and elastic stiffness of PMMA cellular solids based on triply periodic minimal surfaces

In this paper, the acoustic band structure, sound attenuation, and uniaxial elastic modulus of three cellular solids are studied computationally. The cellular solids are generated based on mathematical surfaces, called triply periodic minimal surfaces (TPMS), which include Schwarz Primitive, Schoen IWP, and Neovius surfaces. Finite element method is used to find the acoustic band gaps and sound attenuation of the TPMS structures. The numerical investigation revealed the existence of acoustic bandgaps at low frequencies and low relative densities compared to other cellular structures reported in the literature. The band gap analysis is numerically validated using structures with finite dimensions subjected to varying pressure with multiple frequencies. The influence of the porosity of TPMS on the width of the band gaps is also reported. In the considered porosity range, it is found that lower porosities result in wider acoustic band gaps. Furthermore, the uniaxial moduli of these TPMS are numerically determined using periodic boundary conditions. When the uniaxial modulus of the TPMS-structures is studied against their porosities, it is found that the response of the TPMS-structures lies between stretching- and bending-dominating.

Multi-channel unidirectional transmission of phononic crystal heterojunctions

Two square steel columns are arranged in air to form two-dimensional square lattice phononic crystals (PNCs). Two PNCs can be combined into a non-orthogonal 45[Formula: see text] heterojunction when the difference in the directional band gaps of the two PNC types is utilized. The finite element method is used to calculate the acoustic band structure, the heterogeneous junction transmission characteristics, acoustic field distribution, and many others. Results show that a non-orthogonal PNC heterojunction can produce a multi-channel unidirectional transmission of acoustic waves. With the square scatterer rotated, the heterojunction can select a frequency band for unidirectional transmission performance. This capability is particularly useful for constructing acoustic diodes with wide-bands and high-efficiency unidirectional transmission characteristics.

Ultrasonic bandgaps in 3D-printed periodic ceramic microlattices

The transmission of longitudinal ultrasonic waves through periodic ceramic microlattices fabricated by Robocasting was measured in the 2–12MHz frequency range. It was observed that these structures (scaffolds of tetragonal and hexagonal spatial arrangements with periodicity at length-scales of ∼100μm) exhibit well-detectable acoustic band structures with bandgaps. The locations of these gaps at relatively high frequencies were shown to be in close agreement with the predictions of numerical models, especially for tetragonal scaffolds. For hexagonal scaffolds, a mixing between longitudinal and shear polarizations of the propagation modes was observed in the model, which blurred the matching of the calculated band structures with the experimentally measured bandgaps.

Tunable Acoustic Wave Propagation Through Planar Auxetic Metamaterial

AbstractThis paper presents a tunable planar auxetic metamaterial (PAM) for controlling and filtering acoustic waves and provides guidelines for bandgap design of the proposed PAMs. Numerical results for deformed and undeformed PAMs were obtained from several finite element analyses based on Bloch–Floquet theory. The acoustic band structures of the PAMs were calculated with periodic boundaries. Tunable bandgaps in certain frequency ranges were generated by various deformations applied to the PAMs. Wave attenuation in experimental transmission loss at specific frequencies was demonstrated, showing favorable agreement with the bandgaps obtained from numerical calculations. Both the numerical and experimental results indicate that the proposed structure demonstrates great tunability and offers significant advantages over the regular materials for controlling sound wave propagation and filtering sound waves within specific frequency ranges.

AVBVICVII ferroelectrics as novel materials for phononic crystals

ABSTRACTIn the present work the acoustic band structure of a two-dimensional (2D) phononic crystal (PC) containing a semiconducting ferroelectric - AVBVICVII (A = Sb, Bi; B = S, Se, Te; C = I, Br, and Cl) was investigated theoretically and numerically by the plane-wave-expansion (PWE) method. Two-dimensional PC with square lattices composed of semiconducting ferroelectric cylindrical rods embedded in the organic/inorganic matrix is studied to find the existence of stop bands for the waves of certain energy. This phononic bandgap - forbidden frequency range - allows sound to be controlled in many useful ways in structures that can act as sonic filters, waveguides or resonant cavities. Phononic band diagram ω = ω(k) for a 2D PC was plotted versus the wavevector k along the Г-X-M-Г path in the square Brillouin zone (BZ). The band diagram shows four stop bands in the wide frequency range. The unusual properties of matrix and ferroelectric properties of AVBVICVII give us ability to control the wave propagation through the PC in over a wide frequency range. We study the 2D composites by solving the basic acoustic wave equation and use Bloch wave analysis to identify the band gaps.

Thermal tuning of the interfacial adhesive layer on the band gaps in a one-dimensional phononic crystal

Phononic crystals possess unique acoustic properties due to their artificial periodic structure. They have been used in a wide range of applications such as wave guides, filters, noise suppression, vibration control, etc. In this paper, an analytic model based on the transfer matrix method is established to study the band gaps of P- and SH-waves in a one-dimensional phononic crystal consisting of alternating strips of two different materials bonded by an interfacial adhesive layer. The analysis accounting for the temperature dependent elastic property of the interfacial adhesive layer indicates a different but an effective approach for thermal tuning of the acoustic band structures. It is shown that the first band gap width may decrease over 50% as the temperature increases from 20°C to 80°C. These results provide design guidelines for thermal tuning of wave propagation in phononic crystals.

Wave propagation and acoustic band gaps of two-dimensional liquid crystal/solid phononic crystals

The vast majority of acoustic wave propagation in phononic band studies has been usually carried out by scattering inclusions embedded in a viscoelastic medium, such as air or water. In this study, we present calculated band structure results for the two-dimensional square array geometry of a solid cylindrical scatterer surrounded by a liquid crystal (LC) matrix. Liquid crystals provide a unique combination of liquid-like and crystal-like properties as well as anisotropic properties. The purpose of using LC material is to take advantage of longitudinal acoustic waves propagating parallel (||) and perpendicular (⊥) to the nematic liquid crystal (NLC) director n. The compound used in this study was a room temperature NLC, called 5CB (4-pentyl-4′-cyanobiphenyl). The acoustic band structure of a two-dimensional phononic crystal containing a 5CB NLC and lithium tantalate was investigated by the plane wave expansion method. The theoretical results show that the solid/LC system can be tuned in a favorable configuration for adjusting or shifting acoustic band gaps.

Topological insulator based locally resonant phononic crystals: Wave propagation and acoustic band gaps

ABSTRACTIn the present work the acoustic band structure of a two-dimensional phononic crystal (PC) containing an organic ferroelectric (PVDF- polyvinylidene fluoride) and topological insulator (Bi2Te3) were investigated by the plane-wave-expansion (PWE) method. Two-dimensional PC with square lattices composed of Bi2Te3 cylindrical rods embedded in the PVDF matrix are studied to find the existence of stop bands for the waves of certain energy. Phononic band diagram ω = ω(k) for a 2D PC along the Г-X-M-Г path in the square Brillouin zone show four stop bands in the frequency range 0.01–8.0 kHz.