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The wave equation revealing the wave propagation in chiral phononic crystals, established through force equilibrium law, conceals the underlying physical information, such as the essence of the motion coupling and the inertial amplification effect. This has led to a controversy over the bandgap mechanism. In this article, we theoretically unveil the reason for this controversy, and put forward an alternative approach from wave behavior to formulate the wave equation, offering an alternative pathway to articulate the bandgap physics directly. Based on the physics revealed by our theory method, we identify the obstacles in coupled acoustic and optic branches to widen and lower the bandgap. Then we introduce an approach based on spherical hinges to decrease the barriers, for customizing the bandgap frequency and width. Finally, we validate our proposal through numerical simulation and experimental demonstration. The wave equation established for chiral phononic crystals based reveals only the coupling of acoustic and optic branches, hiding the complexity of the bandgap physics. The alternative method proposed in this paper allows direct observation of the essential physics, and enables to decouple acoustic and optic branches for the manipulation of band gaps. [ABSTRACT FROM AUTHOR]

In this paper, a new structure of two-dimensional phononic crystals consisting of one or more rows of parallel rectangular rods placed periodically in a homogenous slab, in which the rods are not connected directly but linked through neck structures with the slab, is proposed, and the Lamb wave propagation in this structure is investigated with numerical analysis. The dispersion relations and the power transmission spectra are studied using the finite-element method. In contrast to the phononic crystals where the rods and the slab are completely in contact, the proposed structure with necks are proved to display band gaps at much lower frequencies. The displacement fields of the eigenmodes of the band edges are computed and analyzed to clarify the mechanism for the generation of the low-frequency band gaps. It is found that the low-frequency band gaps are attributed to the interaction between the local resonance of the rod inclusion connected with the neck and the Lamb modes of the four plates which are formed by the introduction of the neck. Furthermore, the influences of the geometry parameters of the neck on the band gaps are discussed. Numerical results show that band gaps are significantly dependent upon the width and the position of the necks while insensitive to the neck length. These properties of Lamb waves can potentially be applied to optimize band gaps, generate filters, and design acoustic devices. [ABSTRACT FROM AUTHOR]

In this paper, a novel metal-matrix phononic crystal with a low-frequency, broad and complete, locally-resonant band gap, which includes the in-plane and out-of-plane band gaps, is investigated numerically. The proposed structure consists of double-sided single “hard” cylinder stubs, which are deposited on a two-dimensional locally-resonant phononic-crystal plate that consists of an array of rubber fillers embedded in a steel plate. Our results indicate that both the out-of-plane band gap and the in-plane band gap increase after introducing single “hard” cylinder stubs. More specifically, the out-of-plane band gap is increased by the out-of-plane analogous-rigid mode, while the in-plane band gap is increased by the in-plane analogous-rigid mode. The out-of-plane and the in-plane analogous-rigid mode are formed after introduction of the single “hard” cylinder stub. As a result, a broad, complete locally-resonant band gap in the low frequency is obtained due to the broad in-plane and out-of-plane band gaps overlapping. Compared to the classical double-sided stubbed metal-matrix phononic-crystal plate, the absolute bandwidth of the complete band gap is increased by a factor of 4.76 in the proposed structure. Furthermore, the effect of simple “hard” stubs on complete band gaps is investigated. The results show that the location of the complete band gaps can be modulated using a low frequency, and the bandwidth can be extended to a larger frequency range using different “hard” stubs. The new structure provides an effective way for metal-matrix phononic crystals to obtain broad and complete locally-resonant band gaps in the low-frequency range, which has many applications for low-frequency vibration reduction. [ABSTRACT FROM AUTHOR]

We studied the expansion of locally resonant complete band gaps in two-dimensional phononic crystals (PCs) using a double-sided stubbed composite PC plate with composite stubs. Results show that the introduction of the proposed structure gives rise to a significant expansion of the relative bandwidth by a factor of 1.5 and decreases the opening location of the first complete band gap by a factor of 3 compared to the classic double-sided stubbed PC plate with composite stubs. Furthermore, more band gaps appear in the lower-frequency range (0.006). These phenomena can be attributed to the strong coupling between the “analogous rigid mode” of the stub and the anti-symmetric Lamb modes of the plate. The “analogous rigid mode” of the stub is produced by strengthening the localized resonance effect of the composite plates through the double-sided stubs, and is further strengthened through the introduction of composite stubs. The “analogous rigid mode” of the stubs expands the out-of-plane band gap, which overlaps with in-plane band gap in the lower-frequency range. As a result, the complete band gap is expanded and more complete band gaps appear. [ABSTRACT FROM AUTHOR]

In this paper, we theoretically investigate the propagation characteristics of Lamb wave in a two-dimensional (2D) asymmetric phononic crystal (PC) plate composed of cylinder stubs of different radius deposited on both sides of a thin homogeneous plate. The dispersion relations, transmission spectra and displacement fields of the eigenmodes are calculated by using the finite element method (FEM). Two complete bandgaps (BGs) can be found in low-frequency range and the transmission spectra coincide with the band structures. We investigate the evolution of dispersion relations with the decrease of the upper stub radius. The physical mechanism of the upper stub radius effect is also studied with the displacement fields of the unit cell. Numerical results show that the symmetry of the stub radius can remarkably influence the band structures and the asymmetric double-sided plate exhibits a new bandgap (BG) in lower frequency range due to the coupling between the lower stub's resonant mode and the plate's Lamb mode becomes weak and the adjacent bands separate. Moreover, we further investigate the effect of the stub height on the dispersion relations and find that the BGs shift to lower frequency regions with the increase of the stub height. In addition, the BGs' sensitivity to the upper stub radius and the stub height is discussed. The low-frequency BGs in the proposed PC plate can potentially be used to control and insulate vibration in low frequency range. [ABSTRACT FROM AUTHOR]

In this paper, we present the theoretical investigation of Lamb wave propagation in one-dimensional radial phononic crystal (RPC) plates with periodic double-sided corrugations. The dispersion relations, the power transmission spectra, and the displacement fields of the eigenmodes are studied by using the finite element method based on two-dimensional axial symmetry models in cylindrical coordinates. Numerical results show that the proposed RPC plates with periodic double-sided corrugations can yield several band gaps with a variable bandwidth for Lamb waves. The formation mechanism of band gaps in the double-sided RPC plates is attributed to the coupling between the Lamb modes and the in-phase and out-phases resonant eigenmodes of the double-sided corrugations. We investigate the evolution of band gaps in the double-sided RPC plates with the corrugation heights on both sides arranged from an asymmetrical distribution to a symmetrical distribution gradually. Significantly, with the introduction of symmetric double-sided corrugations, the antisymmetric Lamb mode is suppressed by the in-phase resonant eigenmodes of the double-sided corrugations, resulting in the disappearance of the lowest band gap. Furthermore, the effects of the geometrical parameters on the band gaps are further explored numerically. [ABSTRACT FROM AUTHOR]

We numerically investigate the propagation characteristics of Lamb waves in composite plate-type acoustic metamaterial constituted of one-side cylindrical stubs deposited on a two-dimensional binary locally resonant phononic plate. Numerical results show that, with the introduction of composite plate-type acoustic metamaterial, locally resonant band gap shifts to lower frequency, and a significant enlargement of the relative bandwidth by a factor of 3 can be obtained, compared to one-side locally resonant stubbed plates. We show that the band gap enlargement is attributed to the coupling between the local resonant Lamb modes of two-dimensional phononic plate and the resonant modes of the stubs. [ABSTRACT FROM AUTHOR]

In this paper, we theoretically investigate the band structures of Lamb wave in one-dimensional radial phononic crystal (PC) slabs composed of a series of alternating strips of epoxy and aluminum. The dispersion relations, the power transmission spectra and the displacement fields of the eigenmodes are calculated by using the finite element method based on two-dimensional axial symmetry models in cylindrical coordinates. The axial symmetry model is validated by three-dimensional finite element model in Cartesian coordinates. Numerical results show that the proposed radial PC slabs can yield several complete band gaps with a variable bandwidth exist for elastic waves. Furthermore, the effects of the filling fraction and the slab thickness on the band gaps are further explored numerically. It is worth observing that, with the increase of the filling fraction, both the lower and upper edges of the band gaps are simultaneously shifted to higher frequency, which results from the enhancement interaction between the rigid resonance of the scatterer and the matrix. The slab thickness is the key parameter for the existence and the width of complete band gaps in the radial PC slabs. These properties of Lamb waves in the radial PC plates can potentially be applied to optimize band gaps, generate filters and design acoustic devices in the rotary machines and structures. [ABSTRACT FROM AUTHOR]

In this paper, a novel two-dimensional phononic crystal composed of periodic Jerusalem cross slot in air matrix with a square lattice is presented. The dispersion relations and the transmission coefficient spectra are calculated by using the finite element method based on the Bloch theorem. The formation mechanisms of the band gaps are analyzed based on the acoustic mode analysis. Numerical results show that the proposed phononic crystal structure can yield large band gaps in the low-frequency range. The formation mechanism of opening the acoustic band gaps is mainly attributed to the resonance modes of the cavities inside the Jerusalem cross slot structure. Furthermore, the effects of the geometrical parameters on the band gaps are further explored numerically. Results show that the band gaps can be modulated in an extremely large frequency range by the geometry parameters such as the slot length and width. These properties of acoustic waves in the proposed phononic crystals can potentially be applied to optimize band gaps and generate low-frequency filters and waveguides. [ABSTRACT FROM AUTHOR]

In this paper, a discretized multi-freedom-degree (DMFD) model is presented to predict the lowest locally resonant (LR) band gap in phononic structures. The DMFD model is adopted to improve the accuracy and the application of previous conventional prediction models. Firstly, the model is applied to the one-dimensional ternary LR structure to show the improvement in precision that is independent of the decrease of the density of the scatterer. Then, the model is extended to the evaluation of the resonance frequencies in a two-dimensional binary LR structure, and the estimates from the present model, which are in good agreement with the previous results, verify our model. Each parameter in the DMFD model allows a clear physical insight into the band-gap mechanism. This model could provide a pre-estimation of the lowest gap of binary and ternary LR structures. [ABSTRACT FROM AUTHOR]

Abstract: The propagation of Lamb waves in a new phononic crystal slab composed of rectangular cylinder inclusions embedded periodically in a host material is investigated. The band structure of the phononic crystal is calculated and the influences of the geometry parameters of inclusions on the band structure are discussed. Results show that large band gap occurs in the phononic crystal slab and the band gap is significantly dependent on the width, height and rotation of the inclusions. Moreover, the eigenmodes of the Lamb waves are given to explain the relationship between the band gap and the geometry parameters of the inclusions. [Copyright &y& Elsevier]

Abstract: In this paper, the numerical investigation of elastic wave propagation in two-dimensional phononic crystals composed of an array of steel stepped resonators on a thin rubber slab is presented. For the first time the rubber material is used as the matrix of the PCs. With the finite-element method, the dispersion relations of this novel PCs structure and some factors of the band structure are studied. Results show that, with the rubber material as matrix, the PC structures exhibit extremely low-frequency band gaps, in the frequency range of hundreds of Hz or even tens of Hz; the geometrical parameters and the material parameters can modulate the band gaps to different extents. Furthermore, to understand the low-frequency band gaps caused by this new structure, some resonance eigenmodes of the structure are calculated. Results show that the vibration of the unit cell of the structure can be seen as several mass–spring systems, in which the vibration of the steel stepped resonator decides the lower boundary of the first band gap and the vibration of the rubber that is not in contact with the resonator decides the upper boundary. [Copyright &y& Elsevier]

In this paper, we study the band gap properties of a two-dimensional phononic crystal composed of periodic cylinders embedded in a homogenous matrix. The cylinders are not connected with the matrix directly but linked with it through the neck structures constituted by part of a circle. The dispersion relations, transmission spectra, and displacement fields of the eigenmodes of this phononic crystal are studied using the finite-element method. In contrast to the typical phononic crystals where the cylinders and matrix are in contact completely, the proposed structures with necks display larger band gaps at lower frequencies. The reason for the occurrence of the low-frequency band gaps as well as the effects of the geometrical parameters of the neck structures on the gaps are further explored numerically. Results show that the openings of the band gaps are attributed to the resonance of the cylinders and the interaction between the cylinders and the matrix, resulting from the introduction of the necks. The band gaps are significantly dependent upon the geometrical parameters such as the rotation angle of the necks which is defined as the angle between the centerline of the neck and the x-axis, the arc length of the necks, and also the filling ratio of the inclusions. The study in this paper is relevant to the design of tuning band gaps and isolators in the low-frequency range. [ABSTRACT FROM AUTHOR]

The artificially periodic structures with the bandgap (BG) features provide a fantastic way for elastic wave manipulation. However, omnidirectional control of elastic waves at low-frequency remains a challenge, especially in the engineering application, due to the great different material parameters of the structure's components. In this work, we present the design of a three-dimensional syndiotactic metastructure (STM) and isotactic metastructure (ITM) composed of a single material with the same density and stiffness. A low-frequency broad bandgap occurs in the global band structure of STM. Meanwhile, it also retains the same high-frequency ultra-wide BG as that of ITM. The formation of the low-frequency BG of STM is attributed to the simultaneous activation of rotation and translation modes. The static deformation analysis indicates that STM has a unique translational and rotational coupling mechanism. The frequency response results reveal that the coupling mechanism can also enhance the attenuation of high-frequency BG. • Three-dimensional syndiotactic elastic metastructure with single-phase material. • Realization of ultra-low frequency band gap with the same stiffness and density. • High-frequency broad bandgap is realized by modal separation. • The attenuation of high-frequency bandgap in syndiotactic metastructure is enhanced. [ABSTRACT FROM AUTHOR]