Narrow Results

Defect state of phononic crystals (PCs) has attracted fast-growing attention due to wave energy localization, which can serve as an effective means of controlling elastic waves. In this paper, we investigate the defect state of a one-dimensional (1D) broadband controllable pillared PC beam consisting of pillared permanent magnets on an aluminium beam through numerical simulations and experiments. First, the width and position of the band gap are altered by adjusting the height of the magnetic pillars’. Then, building on this foundation, we successfully observe the controllable defect states of longitudinal waves at the defects of pillared PC beams through a simple adjustment of the height of the defective magnetic pillars’. Finally, we conduct an experimental validation to confirm the feasibility of the localization behavior of elastic waves in the pillared PC system. This research offers a straightforward method to dynamically control the defect state of PCs and enhance the applications for defected PCs, spanning novel filters, defect detectors, and broadband energy harvesting.

The bending vibration band structure of phononic crystal (PC) beam is solved by a unified formulation of the modified transfer matrix (MTM) method in this paper. The improvement of MTM method is the introduction of constitutive matrix U and matrix of derivative functions V, which standardizes and simplifies the deduction by the matrix operation. The band structure of an epoxy-aluminum PC Timoshenko beam is calculated by both MTM method and plane wave expansion (PWE) method. The results show that the present MTM method has a great advantage in the precision of the result. In addition, the formulation of transfer matrix derived from Timoshenko beam condition is a general form which is also suitable for other general beam structures just by replacing corresponding matrices.

In this paper, a kind of sandwich phononic crystal (PC) plate with silicon rubber scatterers embedded in polymethyl methacrylate (PMMA) matrix is proposed to demonstrate its low-frequency Lamb wave band gap (BG) characteristics. The dispersion relationship and the displacement vector fields of the basic slab modes and the locally resonant modes are investigated to show the BG formation mechanism. The anti-symmetric Lamb wave BG is further studied due to its important function in reducing vibration. The analysis on the BG characteristics of the PC through changing their geometrical parameters is performed. By optimizing the structure, a sandwich PC plate with a thickness of only 3 mm and a lower boundary (as low as 23.9 Hz) of the first anti-symmetric BG is designed. Finally, sound insulation experiment on a sandwich PC plate with the thickness of only 2.5 mm is conducted, showing satisfactory noise reduction effect in the frequency range of the anti-symmetric Lamb BG. Therefore, this kind of sandwich PC plate has potential applications in controlling vibration and noise in low-frequency ranges.

In this paper, the defect state and band gap characteristics in a two-dimensional slit structure phononic crystal, consisting of slotted steel tubes embedded in an air matrix, are investigated theoretically and experimentally. Using the finite element method and supercell technique, the dispersion relationships and power transmission spectra of the slit structures are calculated. The vibration modes of the band gap edges are analyzed to clarify the mechanism of the generation of the band gaps. Additionally, the influence of the slit width on the band gaps in slit structure is investigated. The slit width was found to influence the band gaps; this is critical to understand for practical applications. Based on this finding, a method to form defect scatterers by changing the slit width of a single central scatterer, or one row of scatterers, in the perfect PC was developed. Defect bands can be induced by creating defects inside the original complete band gaps. The frequency can then be tuned by changing the slit width of defect scatterers. Meanwhile, the relationship between point defect and line defect is investigated. Finally, we verify the results of theoretical research by experiments. These results will help in fabricating devices such as acoustic filters and waveguides whose band frequency can be modulated.

Phoxonic crystal (PXC) is a promising artificial periodic material for optomechanical systems and acousto-optical devices. The multi-objective topology optimization of dual phononic and photonic max relative bandgaps in a kind of two-dimensional (2D) PXC is investigated to find the regular pattern of topological configurations. In order to improve the efficiency, a multi-level substructure scheme is proposed to analyze phononic and photonic band structures, which is stable, efficient and less memory-consuming. The efficient and reliable numerical algorithm provides a powerful tool to optimize and design crystal devices. The results show that with the reduction of the relative phononic bandgap (PTBG), the central dielectric scatterer becomes smaller and the dielectric veins of cross-connections between different dielectric scatterers turn into the horizontal and vertical shape gradually. These characteristics can be of great value to the design and synthesis of new materials with different topological configurations for applications of the PXC.

In this paper, a new two-dimensional (2D) phononic crystal structure composed of periodic slit metal tubes, in which the unit cell consists of straight or curved backstraps, is proposed, and the propagation characteristics of acoustic waves in this structure are theoretically investigated. Using the finite-element method, we calculate the dispersion relations and transmission coefficients of this structure. The results show that, in contrast to the only slit metal tubes, the periodic slit metal tubes with straight or curved backstraps are proved to display band gaps (BGs) at much lower frequency range. Meanwhile, the effect of the slit width of the backstraps on the BGs is investigated. The results show that the positions and widths of the BGs can be effectively modulated by the backstraps without changing the mass density or lattice constant of the material. The lowest frequency falls by about 200 Hz. Moreover, we investigated how the BGs are affected by the location parameter of the backstraps, finding that the acoustic BGs are sensitive to the location parameter of the backstraps. Numerical results show that BGs are significantly dependent upon the slit width and location parameters of the backstraps. The BGs are optimized because, the effect of the Helmholtz resonators of the slit tube is strengthened and changed when the location and slit width of the backstraps change. These results provide a good reference for optimizing BGs, generating filters and designing devices.

The effects of symmetries on the bandgap in a newly designed hybrid phononic crystal plate composed of rubber slab and epoxy resin stub are studied for better controlling of bandgaps. The point group symmetry is changed by changing the orientation of the stub. The translation group symmetry is changed by changing the side length and the height of adjacent stubs. Results show that the point group symmetry and translation group symmetry can be important factors for controlling of the bandgaps of phononic crystal. Wider bandgap is obtained by suitable orientation of the stub. Lower bandgap appears when the differences between the adjacent stubs become bigger in supercell.

A new zigzag lattice phononic crystal with holes is designed. Nondominated sorting genetic algorithm-II (NSGA-II) is used for the optimization of the newly designed phononic crystal (PC). Results indicate that geometrical parameters are key factors as well as density and elastic modulus for the determination of the bandgaps (BGs). The width of the BG of the optimized PC with holes can be increased three times higher than the initial design without holes.

The interface state in two-dimensional (2D) sonic crystals (SCs) was obtained based on trying or cutting approach, which greatly limits its practical applications. In this paper, we theoretically demonstrate that one category of interface states can deterministically exist at the boundary of two square-lattice SCs due to the geometric phase transitions of bulk bands. First, we derive a tight-binding formalism for acoustic waves and introduce it into the 2D case. Furthermore, the extended 2D Zak phase is employed to characterize the topological phase transitions of bulk bands. Moreover, the topological interface states can be deterministically found in the nontrivial bandgap. Finally, two kinds of SCs with the $C_{4v}$ symmetry closely resembling the 2D Su–Schrieffer–Heeger (SSH) model are proposed to realize the deterministic interface states. We find that tuning the strength of intermolecular coupling by contacting or expanding the scatterers can effectively induce the bulk band inversion between the trivial and nontrivial crystals. The presence of acoustic interface states for both cases is further demonstrated. These deterministic interface states in 2D acoustic systems will be a great candidate for future waveguide applications.

In this paper, a ring-slotted spiral local resonant phononic crystal structure is investigated. The energy band characteristics and transmission losses of the structure are calculated using the finite element method. The numerical results show that the structure can generate bandgap in the range of 23.54–102.87 Hz. Combined with the modal coupling theory, the vibrational modes of the ring-slotted spiral local resonant phononic crystal are analyzed to reveal the bandgap formation mechanism of the structure. The effects of the various dimensional parameters and material hardness on the bandgap of the structure are analyzed by varying them. The results show that by varying the filling radius of silicone rubber in the ring-slotted spiral local resonant phononic crystal, the structure can be made to have an onset frequency of 19.42 Hz and generate a bandgap in the range of 19.42–78.16 Hz. A new idea is provided for the application of phononic crystal in low-frequency environment for vibration and noise reduction.

A new arrayed phononic crystal (PnCs) with defects is proposed. The supercell method is used to calculate the band structures. Energy localization can be found around the defects and energy harvesting (EH) can be realized by the attachment of piezoelectric patches around the designed defects. The EH can be concentrated on the frequency of 64–64.1kHz with output voltage of 8.22V. By the change of the piezoelectric patch from circular to oval shape, the frequency of EH can be changed. By the optimization of geometric shapes of piezoelectric patches and the optimal design of unit cell, the EH output voltage can be increased to 4.21 times higher than the original state and the EH frequency band is effectively broadened. The amplification factor can be increased to 327.13.

In this paper, we make a great effort to find out the impact of parameters for elastic wave propagation in a plate with a phononic crystal layer coated on half-infinite uniform substrate by the method of plane wave expansion, and the characteristic or the position of the band structure. In calculation, a phononic crystal consisting of circular steel cylinders that form a square lattice in a silicon matrix is considered as the layer and the substrate is formed by silicon. Our results show that there exist distinct band gaps when the substrate is correspondingly soft and infinite. The stop band of the system is demonstrated. Parameters that influence the formation of band gaps are stated. We also give a qualitative explanation of the results.

A low-frequency vibration energy generator has been proposed by using a locally resonant phononic crystal plate which has spiral beams connecting the scatterers and the matrix. Finite element analysis shows that at the flat bands frequencies of the phononic crystal, locally resonant leads to the spiral beams having strong deformations which are perpendicular to the plate. A designed structure with three PC cells arranged in the same direction was adopted for the experiments. Piezoelectric patches were adhered on the end of the spiral beams and then the collected vibration energy could be converted into electric energy. The maximum single-channel output voltage which reached as much as 13 V was obtained at the first flat band frequency 29.2 Hz in the experiment. Meanwhile, in the low-frequency range of 0–500 Hz, it showed that the piezoelectric transformation could be conducted at a dozen of resonant frequencies. Furthermore, through modulating the structure parameters, this phononic crystal has the potential to realize broad-distributed vibration energy harvesting.

Longitudinal vibration of thin phononic crystal plates with a hybrid square-like array of square inserts is investigated. The plane wave expansion method is used to calculate the vibration band structure of the plate. Numerical results show that rotated square inserts can open several vibration gaps, and the band structures are twisted because of the rotation of inserts. Filling fraction and material of the insert affect the change law of the gap width versus the rotation angles of square inserts.

The propagation of the elastic wave in phononic crystal is different from the normal uniformity medium. The finite-difference time-domain (FDTD) method is irrelevant to structure model and used widely. Moreover, when the numerical stability of FDTD iterations is satisfied, the elastic waves’ transmission property through periodical and quasi-periodical phononic crystal can be achieved. In this paper, the transmission coefficients of elastic wave through two systems are numerically calculated and the results of band gaps are analyzed. The results are helpful to study phononic crystal.

The plane wave expansion (PWE) method is used to calculate the band gaps of two-dimensional (2D) phononic crystals (PCs) with a hybrid square-like (HSL) lattice. Band structures of both XY-mode and Z-mode are calculated. Numerical results show that the band gaps between any two bands could be maximized by altering the radius ratio of the inclusions at different positions. By comparing with square lattice and bathroom lattice, the HSL lattice is more efficient in creating larger gaps.

Based on the finite element method (FEM), characteristics of the local resonance band gap and the Bragg scattering band gap of two periodically-distributed vibrator structures are studied. Conditions of original anti-resonance generation are theoretically derived. The original anti-resonance effect leads to localization of vibration. Factors which influence original anti-resonance band gap are analyzed. The band gap width and the mass ratio between two vibrators are closely correlated to each other. Results show that the original anti-resonance band gap has few influencing factors. In the locally resonant structure, the Bragg scattering band gap is found. The mass density of the elastic medium and the elasticity modulus have an important impact on the Bragg band gap. The coexistence of the two mechanisms makes the band gap larger. The band gap covered 90% of the low frequencies below 2000 Hz. All in all, the research could provide references for studying the low-frequency and broad band gap of phononic crystal.

Three-component pillared phononic crystal plates (PPCPs) usually contain viscoelastic materials. The influence of viscoelasticity on the band structures cannot be ignored. Based on the finite element method (FEM) and the standard linear solid model, this paper proposes a method to obtain the band structures of three-component PPCP containing viscoelastic rubber. The influence of the rubber storage modulus shifting along with frequency on the vibration band gaps is investigated, and the band structures of loss factor under different relaxation time are obtained.

We investigate through numerical simulation the anomalous reflection (AR) of acoustic waves with perfect phononic crystals (PCs). Broadband AR is observed in a wide angle for the oblique incidence. The AR is due to the unsymmetrical specific acoustic impedance (SAI) profile along the surface, which is caused by the high frequency incidence. The findings in this paper complement the theories for the AR of acoustic waves with PCs, and may find applications in acoustic engineerings.

Viscoelastic materials can dissipate energy and hinder propagation for plane waves, which can adjust the band structures of phononic crystals (PCs). In this study, the wave propagation in a two-dimensional PC with a viscoelastic matrix is investigated. The Maxwell model is utilized to analyze the effect of material parameters on the frequency dependence of viscoelasticity. Material parameters include the relaxation time, the initial value and the final value of the shear modulus. Band structures of viscoelastic phononic crystals (VPCs) are solved by combining the plane wave expansion method and iterative algorithm based on Bloch theory. The effects of the viscoelasticity on the band structures are studied using the single-mode and multi-mode Maxwell models. Results reveal that the viscoelasticity of the materials not only extends the band gaps but also shifts the band gaps to lower frequencies. Furthermore, the viscoelasticity simulated by the multi-mode model can precisely adjust anyone of the band gaps of VPCs separately. Results provide insights into the design and applications of VPCs.