Narrow Results

This study presents a tunable phononic crystal (PnC) composed of liquid–solid components, demonstrating adjustable waveguiding and directional transmission capabilities through the rotation of embedded scatterers. A two-dimensional model featuring grooved steel rods in water is analyzed using finite element simulations to evaluate band structures and transmission spectra. To achieve the widest full band gap, a genetic algorithm is integrated to optimize the structural parameters. By examining a supercell with a central defect, wave localization is achieved, facilitating tunable waveguide formation. Analysis of equifrequency contours reveals that, at a scatterer rotation angle of $0^{\circ }$, the structure enables directional transmission, with wave propagation preferentially aligned with specific crystal axes. This work pioneers a new strategy for designing tunable acoustic metamaterials with applications in advanced waveguiding and directed acoustic manipulation technologies.

A fast scheme based on the multi-level substructure technique is proposed for the band structure and transmission characteristics calculation of phononic crystals uniformly. The main idea is that finite element models of phononic crystals are divided into several domains by a special multi-level decomposition. For the band structure calculation, the upscaling calculation is employed to condense the internal stiffness matrix of the unit cell into the Bloch boundary. Due to the internal stiffness matrix does not change along with reduced wave vectors in an iteration process, the scheme can reduce the computational scale and improve the efficiency greatly, meanwhile it does not introduce approximation into the traditional finite element model. For the transmission characteristics calculation, the unit cell of the phononic crystal is periodic which is taken as a substructure with the same coefficient matrix. Moreover, the downscaling calculation of internal displacements can be selected flexibly. Some closely watched examples of the three-dimensional locally resonant, defect state of Lamb wave and Bragg waveguide are analyzed. Numerical results indicate that the proposed scheme is efficient and accurate, which may widely be applicable and suitable for complex phononic crystal problems, and provides a reliable numerical tool to optimize and design crystal devices.

In this paper, we study the band gaps (BGs) of two-dimensional (2D) phononic crystals (PCs) composed of self-similarity shape inclusions embedded in the homogenous matrix. The dispersion relations, transmission spectra, and displacement fields of eigenmodes of the proposed structures are calculated by use of finite element method. Due to the simultaneous mechanisms of the Bragg scattering, the structure can exhibit low-frequency BGs, which can be effectively shifted by changing the geometries and degree of the self-similarity structure. The BGs are significantly dependent upon the geometrical parameters and degree of the self-similarity structure. It is concluded that, the PCs with self-similarity structure, can modulate the location and width of BGs. But it must be pointed out, the shape of self-similarity inclusion exercises a great influence on the BGs. The study in this paper is relevant to the design of tuning BGs and isolators in the low-frequency range.

In this paper, the acoustic wave propagation in a two-dimensional phononic crystal composed of rotational multiple scatterers is investigated. The dispersion relationships, the transmission spectra and the acoustic modes are calculated by using finite element method. In contrast to the system composed of square tubes, there exist a low-frequency resonant bandgap and two wide Bragg bandgaps in the proposed structure, and the transmission spectra coincide with band structures. Specially, the first bandgap is based on locally resonant mechanism, and the simulation results agree well with the results of electrical circuit analogy. Additionally, increasing the rotation angle can remarkably influence the band structures due to the transfer of sound pressure between the internal and external cavities in low-order modes, and the redistribution of sound pressure in high-order modes. Wider bandgaps are obtained in arrays composed of finite unit cells with different rotation angles. The analysis results provide a good reference for tuning and obtaining wide bandgaps, and hence exploring the potential applications of the proposed phononic crystal in low-frequency noise insulation.

FEA method is applied in order to investigate the bandgaps of two-dimensional (2D) phononic crystals which are composed with self-similarity hollow inclusions. Transmission spectra together with dispersion relations and displacement fields have been studied with FEA in detail. The simultaneous mechanisms of Bragg scattering enable multiterm bandgaps to be unfolded by the structure that can be effectively shifted by changing the lattice constant, matrix density and degree of self similarity. The smallest bandgap is located in the infrasonic wave range. Our results verify these phononic crystals with self-similar hollow inclusion structure which can change the number, location and width of bandgaps.

In this paper, a novel composite acoustical hyperstructure of Bragg structure with local resonator is investigated theoretically for discussing the scattering performance of longitudinal vibration wave, its bandgaps are calculated using the established mathematical model. For confirming the veritable existence of bandgap and verifying the correctness of established mathematical model, the transmission spectrum of composite acoustical hyperstructure is also studied using finite-element method, and comparing the vibration transmission spectrum with bandgaps, the results indicate that the established theoretical model can correctly predict longitudinal wave bandgaps. Moreover, the bandgaps and modes shapes are calculated and compared with an unalloyed Bragg structure for probing the dispersion mechanics of composite acoustical hyperstructure, it turned out that local resonator can add one bandgap at the base of Bragg structure and the total bandgaps can be broadened. Further, for discussing the effect of spring of local resonator on bandgaps, bandgap of local resonator with different spring is calculated, the results showed that the total width of BG is larger when Young’s modulus is 1E and 16E, the total width are 772.48 and 774.30 Hz, respectively; as Young’s modulus is 0.5E and 2E, the width of BG are lower, 753.79 and 754.23 Hz, respectively. In view of longitudinal vibration wave inducing structural distortion and vibration energy conversion, the dynamic properties of composite acoustical hyperstructure are studied via strain energy density, the results indicate that reaction formation of local resonator can dissipate strain energy, when the local resonator is not activated (or waveless along with Bragg structure), un-dissipation strain energy.

In this paper, the multi-objective optimization problem (MOOP) of selecting suitable materials from four materials for phononic crystals layouts is investigated based on an optimization method combined nondominated sorting-based genetic algorithm II (NSGA-II) and finite element method (FEM). Driven by different optimization objectives, the changes in the optimized structure compared to the seed structure are the change of the bandgap mechanism from a local resonance mechanism to a Bragg scattering mechanism, the change of the included materials from four to three, and the significant change in the location and extent of the pores and other materials, respectively. The obtained nondominated Pareto solution of MOOP can balance the bandgap and the structural mass, which provides the decision-maker trade-off to select the appropriate optimized solution. Compared with the single-objective optimization problem (SOOP), the MOOP not only obtains a nondominated solution close to the result of SOOP, but also obtains other nondominated solutions of MOOP, which proves the effectiveness of the optimization algorithm in this paper. The design method in this paper can be easily extended to select suitable materials from a wider variety of materials for bandgap optimization design of PnCs, which has very promising applications.

In this paper, a phononic crystal with acoustic black hole (ABH) characteristics is designed based on the compression effect of ABHs on acoustic wavelengths. The simulation results show that the lower limit of the first bandgap of the phononic crystal with ABH is reduced by 127.8Hz, the upper limit is increased by 694.4Hz, and the bandgap width is increased by 822.2Hz compared with that of the phononic crystal without ABH. The mechanism of bandgap expansion is discussed based on the mechanism of bandgap formation and the acoustic modulation effect of the ABH. The influence of the geometric and material parameters of the ABH on the bandgap is analyzed. The ABHs offer a new way of optimizing phononic crystals, and this work can be used as a reference for their design.

We study theoretically the symmetric property and coupling efficiency of the defect modes in a two-dimensional phononic crystal by calculating band structures, field distributions and transmission coefficients of the defect modes. The results show that the point defect could act as a microcavity surrounded by the phononic crystal, and the confining ability of the phononic crystal to the resonant modes strongly depends on the thickness of the phononic crystal. By investigating the transmission spectra, we also find that the defect modes cannot be absolutely excited by the normally incident plane waves. The transmission coefficients are calculated by using the eigen-mode match theory method under the supercell technique, which is applied to the phononic crystals with the defects for the first time.

We have studied the compression (P) wave band structures at a low frequency in two-dimensional solid–solid phononic crystals. The plane-wave expansion method based on the decomposition of elastic waves was used. The pressure field distribution of P-wave localized modes at Γ points in the lowest bands, including multiple flat bands of systems comprising different configurations, were analyzed. The results show that a lower symmetry of the scatterer are an effective method to enhance the localization of vibration modes. The property has potential applications in the design of waveguides.

Analysis is given to acoustic directional radiation tuned by rotating square rods in two-dimensional (2D) solid–fluid phononic crystals (PC). The contour line method is introduced which predicts how the acoustic waves propagate at different frequency. As a specific example, for the systems of steel rods with square cross-section in a water host, we employ this approach to the analysis of the directivity successfully. The directional radiation frequency of two lowest bands are studied in this paper. The results show that the directional radiation frequency can be turned in a wide range by rotating the square rods. While the directivity of acoustic propagation keeps unchanged when the acoustic directional radiation frequency is located in the same band. Moreover, PCs exhibit excellent characteristic of single radiation branch as a corner cut off in a finite structure. Our approach may supply a new way to tune the directional radiation frequency.

Periodicity (in time or space) is a part and parcel of every living being: one can see, hear and feel it. Everyday examples are locomotion, respiration and heart beat. The reinforced N-dimensional periodicity over two or more crystalline solids results in the so-called phononic band gap crystals. These can have dramatic consequences on the propagation of phonons, vibrations and sound. The fundamental physics of cleverly fabricated phononic crystals can offer a systematic route to realize the Anderson localization of sound and vibrations. As to the applications, the phononic crystals are envisaged to find ways in the architecture, acoustic waveguides, designing transducers, elastic/acoustic filters, noise control, ultrasonics, medical imaging and acoustic cloaking, to mention a few. This review focuses on the brief sketch of the progress made in the field that seems to have prospered even more than was originally imagined in the early nineties.

We propose AND and OR logic gates based on a phononic crystal (PNC) ring resonator cavity. The proposed devices consist of ring resonator cavities coupled to PNC line defect waveguides. The logic gate performance has been analyzed and investigated using finite element methods. The design specifies a logical 0 as a transmission rate of 0.3 or less and a logical 1 as a transmission rate of 0.6 or more. The results show that such a design has stable transmission peaks, meeting the requirements of acoustic logic gates. The design has the potential to be a key component in future phononic integrated circuits.

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${}^{\circ }$ 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.

Bragg acoustical hyperstructure can scatter elastic wave, local resonance system can fight against vibration by the reaction force with reversed phase in low-frequency range, for improving the scattering performance of Bragg hyperstructure, a novel composite beam of Bragg beam with local resonator is investigated theoretically. Its dispersion relations and bang gaps are calculated by the established theoretical model. In order to confirm the veritable existence of band gaps, the transmission spectrum of flexural vibration waves are also studied by finite-element method, and comparing the relationship of vibration transmission spectrum and band gaps, the results indicate that the proposed theoretical model can accurately predict the band gaps of the proposed composite beam. For probing the dispersion mechanics, comparing the band gaps and modes shapes of the proposed composite beam with an unalloyed Bragg beam, the results denoted that local resonator can add two band gaps at the base of Bragg beam. Further, the changes of the band gaps that depend on the local resonator and on Bragg beam are studied. It is indicated that the total band gaps can be narrowed when the resonance frequency of the local resonators located at the band gaps of the Bragg beam and the branches will become approximately flat. The band gaps will broaden if the branch that depends on the local resonator gets closer to the branch on Bragg beam.

The reduction of the periodicity of phononic crystals (PnCs) usually leads to the decrease of band gap (BG) width. However, a systematic study of the relationship between the unit cell and the supercell in the proposed hybrid stepped PnCs shows that the BG width can be increased in special cases. How the periodicity of PnCs affects the final BG characteristics is important for the design of PnCs with high structural performance. Supercell of PnCs with imperfections from the rotation of the unit cell was used to demonstrate the relationship between the unit cell and the supercell, which was further used for the wave attenuations of the proposed hybrid stepped PnCs. The rotation angle and the number of the rotating scatterers can be controlled for better structural performance for the PnCs. The different changes of the equivalent stiffness corresponding to the starting and the end frequencies lead to the increase of the BG width when the ration angle of the unit cell is $35^{\circ }$ in the supercell composed of zigzag scatterers and cross scatterers. The rotation of the unit cell in the supercell leads to the decrease of the starting frequency.

The capacity of Phononic crystals (PCs) to form bandgaps (BGs) that limit the transmission of elastic/acoustic waves is a key property that is particularly beneficial for vibration/sound isolation and signal processing. In this work, a parametric analysis of Poisson’s ratio of rubber, and the density, geometry and size of scatterer on the BGs of porous, solid/solid, fluid/solid and solid/fluid PCs is presented. Based on the simulation results, it is found that the width of the first absolute bandgaps (FABGs) of porous PCs is not necessarily proportional to the porosity due to the pore shape; when Poisson’s ratio of compressible and incompressible rubber is increased, the FABG width of porous PC decreases dramatically. In addition, the FABGs of solid/solid PCs are strongly dependent on whether the rubber is a matrix or scatterer; the fluctuation of the FABGs is also highly related to the density of the solid. Fluid–structure PCs have smaller FABGs than porous and solid/solid PCs, and these FABGs usually occur within higher-order energy bands. Rubber compressibility significantly affects the FABGs of porous and solid/solid PCs, but almost not fluid-structural PCs. The results presented in this work offer guidance to tune the BG and design acoustic devices in various practical applications such as noise and vibration insulators.

We propose a new method for calculating dispersion spectra of shear waves in the two-dimensional free phononic plates made of solid matrix with periodically distributed inclusions and in the waveguides composed of a phononic layer between two periodic substrates. The method proceeds from the propagator M which involves exact integration in the depth coordinate. Because the components of M can be very large, the dispersion equation for a free plate is recast in terms of the resolvent of propagator R = (αI - M)^-1 (α is a constant) which is numerically stable. The resolvent is the central object of the method. Another key tool, which comes into play in the case of a waveguide, is a projector P expressed as a contour integral of the resolvent of the substrate. The projector allows to extract the "physical" modes decreasing into the depth of the substrates without solving the wave equation. The resulting dispersion equation for a waveguide defined via the projectors for the substrates and the resolvent for the enclosed layer is numerically stable. We provide several options for the calculation of the resolvent and projector. Besides, special attention is given to derivation of the dispersion equations for the uncoupled symmetric and antisymmetric dispersion branches in the case of mirror-symmetric structures.

We evaluated the performance of the classical and spectral finite element method in the simulation of elastodynamic problems. We used as a quality measure their ability to capture the actual dispersive behavior of the material. Four different materials are studied: a homogeneous non-dispersive material, a bilayer material, and composite materials consisting of an aluminum matrix and brass inclusions or voids. To obtain the dispersion properties, spatial periodicity is assumed so the analysis is conducted using Floquet–Bloch principles. The effects in the dispersion properties of the lumping process for the mass matrices resulting from the classical finite element method are also investigated, since that is a common practice when the problem is solved with explicit time marching schemes. At high frequencies the predictions with the spectral technique exactly match the analytical dispersion curves, while the classical method does not. This occurs even at the same computational demands. At low frequencies however, the results from both the classical (consistent or mass-lumped) and spectral finite element coincide with the analytically determined curves.

We have theoretically obtained the transmittance properties of one-dimensional phononic crystals incorporating a piezoelectric material as a defect layer. We have used the transfer matrix method in our analysis with/without defect materials. By increasing the thickness of the defect layer, we obtained a sharp peak created within the bandgap, that indicates to the significance of defect layer thickness on the band structure. The localized modes and a particular intensity estimated within the bandgap depend on the piezoelectric material properties. By applying different quantities of an external electric field, the position of the peak shifts to different frequencies. The electric field induces a relative change in the piezoelectric thickness. Our structure may be very useful in some applications such as sensors, acoustic switches, and energy applications.