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Reciprocity is a generic feature in various physical systems because it is directly associated to the symmetry of physical laws under time reversal. The breaking of the reciprocity is vitally important in numerous fields, such as the control of energy flux, imaging technologies and topological insulators. For instance, electrical diodes, as a typical nonreciprocal representative in electronic systems, have already contributed to substantial scientific revolutions in many aspects, including integrated circuits, lighting and signal indication. Motivated by the electrical diodes, thermal diodes exhibiting the rectifying effect on thermal energy are achieved in nonlinear lattices. Similarly, the nonreciprocity in photonic systems can be realized by many mechanisms, such as the nonlinearity of optical medium and the mode conversion. Synchronously, the concept of the nonreciprocity further extends to phononic systems. The main means to achieve acoustic nonreciprocity are based on the nonlinearity of acoustic material, dynamic element, and magnetoelastic interaction. However, the nonlinear approach introduces the inherently low conversion efficiency, the dynamic scheme has difficulty in application at high-speed modulation or on nanoscale, and the method based on magnetoelastic interaction has small bandwidth and high frequency, which have severe limitations for practical application of the nonreciprocity. From the perspectives of principles, history, and problems, this paper reviews in detail the progress of the nonreciprocity based on nonlinearity, dynamic components, and magnetoelastic interactions. Some existing problems with these methods were pointed out. For example, the nonreciprocal solution based on nonlinear media has low energy conversion efficiency, it is difficult to miniaturize the nonreciprocal device based on dynamic components because of itself complexity, and the bandwidth of nonreciprocity based on magnetoelastic interaction is narrow. Correspondingly, improvement of the energy conversion efficiency based on the nonlinear medium, more reasonable design of a dynamic modulation system, and widening broadband of nonreciprocity in the magnetoelastic system, can be researched in the future. For example, in order to reduce the nonreciprocal frequency of magnetoelastic system, it is worth studying the unidirectional transmission of sound waves in the magnetoelastic system under a dynamic magnetic field. For the sake of realizing a nonreciprocal system with no external power source and high conversion efficiency, the nonreciprocity of acoustic waves in a magnetoelastic system under a zero magnetic field may become a focus of future research. In addition, since each scheme has its advantages, the combined effects of multiple schemes may overcome the shortcomings of a single scheme and achieve more significant nonreciprocal effects. So far, the combined effects between nonlinearity and dynamic components have not received much attention. We expect that research of nonreciprocity will be extended to both nonlinear and spatiotemporally modulated systems in the future. The combined effects between nonreciprocity and magnetoelastic interaction may become an important content of future research. Finally, considering practical engineering application, there are still many aspects worthy of further study, such as the miniaturization of nonreciprocal devices, optimal design of nonreciprocity based on optimization theory, and adjustable nonreciprocity based on smart materials or structures. In short, the nonreciprocity of acoustic metamaterials is an important field of scientific research, which has potential applications, such as rectification, vibration and noise reduction, sensing, and bioimaging.

Topological elastic metamaterials have emerged as a new frontier in the quest of topological phases in condensed matter physics. Their exotic topological properties open a wealth of promising engineering-oriented applications that are difficult to realize with traditional elastic metamaterials, such as robust and defect insensitive waveguiding, signal sensing, and splitting. In this review, we retrospectively examine the underlying physical concept of topologically ordered states of elastic waves, starting from the one-dimensional (1D) example based on the Su–Schrieffer–Heeger (SSH) model. We then move on to two-dimensional (2D) topological metamaterials, discussing elastic analogues of quantum Hall, pseudospin-Hall, valley-Hall phases. Finally, we survey the latest developments in the field including three-dimensional (3D) elastic topological phases and higher-order topological insulators (TIs). Altogether, this paper provides a comprehensive overview of the flourishing research frontier on topological elastic metamaterials, and highlights prominent future directions in this field.

The topological transport of Lamb wave in phononic crystal slabs provides a great potential in reinforcing nondestructive testing, high sensitivity sensing, and information processing. In this paper, the authors investigate the pseudospins edge states of fundamental antisymmetric Lamb waves in a snowflakelike phononic slab. Significantly, the fourfold Dirac degeneracy for antisymmetric Lamb mode is accidentally formed at the Γ point with the critical angle of the snowflakelike holes, which does not require the folding of the lattices. Meanwhile, based on the rotating-scatterer mechanism, the mirror symmetry is broken and the topological multipole phase transitions are well induced during the gradual change of the scattering strength among the scatterers with the rotation angle. The topologically protected edge states and its unidirectional robust propagation are further demonstrated. The proposed topological phononic slabs will be a more hopeful option to apply in engineering practices.

The remarkable properties of topological insulators have inspired numerous studies on topological transport for bulk waves, but the demonstrations of topological edge states with tunable frequency are few attempts. Here, we report on the active frequency tunability of topologically protected edge states for in-plane bulk waves by applying a thermal field. We find that the center frequency of topological band gap is shifted down and the band width is enlarged as the temperature increases. Meanwhile, the frequency range of topologically protected edge states is also shifted to low frequency region with the higher temperature. Furthermore, the robust propagation of in-plane bulk waves along a desired path is demonstrated within different frequency bands. The tunable frequency for both topological band gaps and topologically protected edge states achieves the active control of the transport for in-plane bulk waves, which may dramatically facilitate practical applications of novel phononic devices.

Reciprocity is a fundamental property of wave propagation in linear time-invariant media. However, it is substantially harder to break reciprocity for elastic waves in a linear elastic system with the help of a magnetostatic field, since elastic waves are spinless in nature. Here, we realize nonreciprocal elastic waves in one-dimensional linear magnetoelastic phononic crystal slabs by an external magnetostatic field. The asymmetric dispersion of spin waves, which is induced by the simultaneous breaking of the time-reversal and spatial-inversion symmetries, results in an efficient elastic wave diode effect in a periodic system due to magnetoelastic interactions. Remarkably, a bidirectional nonreciprocity of elastic waves is achieved based on the folding-back effect of the periodic structure. Our proposed scheme opens up avenues for the design of nonreciprocal devices, such as on-chip tunable diodes, rectifiers, and topological insulators.

Zero-angle refraction of elastic waves in metamaterials has attracted attention for its extraordinary wave collimation properties. However, earlier implementations relied on the specific flat equifrequency curve of the phononic crystals suffer from a narrow range of incident angles or operating bandwidths, which severely hinders the exploration and design of functional devices. Here, we propose an elastic near-zero refractive index metamaterial of a triangular lattice to realize topological zero refraction with arbitrary angles of incidence and wide working frequency range. Topological robustness of the zero-angle refraction of pseudospin-Hall edge state against defects is experimentally demonstrated. Furthermore, tunable wave mode conversion associated with the zero-angle refraction is revealed and discussed. These results provide a paradigm for the simultaneous control of the refraction properties of longitudinal and transverse waves that can be employed for designing the topological elastic antennas and elastic wave collimator. Topological acoustic systems exhibit exotic properties including zero refraction, but typically only in a small region of frequency space. In this work, a zero-index acoustic metamaterial is proposed and fabricated functioning over a wide frequency regime in the presence of lattice defects.

We propose two-dimensional reconfigurable phononic crystal slabs that support topologically protected edge states for Lamb waves. It consists of a triangular lattice of triangular-like air holes perforated in a slab and two sandwich cylinders are placed in the matrix of each unit cell. The pseudospin–orbit coupling is achieved by shifting the sandwich cylinders up or down. The robust transport of Lamb waves along reconfigurable interfaces is further demonstrated. The dynamically reconfigurable design provides an excellent platform for tuning the frequency range of topological edge states and steering efficient transport of Lamb waves along arbitrary pathways, which can be employed for elastic-wave communications, signal processing, and sensing.

Topological insulator (TI) that possesses topologically protected characteristic of guiding the wave against disorders and structural perturbations without backscattering has attracted significant research interest in various fields including electromagnetic, acoustic and elastic system. However, for the mechanical system, realizing an elastic analogue of three-dimensional (3D) TI supporting the topologically protected wave propagation in two-dimensional (2D) plane is still a challenge due to the complicated mode polarization of elastic wave in 3D. This paper theoretically and experimentally investigates the robust and layer-selective transports of elastic wave in 3D monolayer- and bilayer-stacked plate-like metamaterial structures. Firstly, considering 3D monolayer-stacked structure, the 2D valley surface states are achieved numerically along the 2D projected plane based on the mechanism of quantum valley Hall effect. The simulation and experimental measurement are performed to confirm the robust transport of 3D elastic wave and backscattering immunity against the straight channel and sharp bends. Then, by stacking the monolayer into bilayer with a twisted angle of 60°, non-zero interlayer coupling of elastic valley layer is introduced and the layer-related topological phase is revealed in the 3D bilayer-stacked structure, giving rise to the 2D topological layer-dependent surface states. Finally, the 3D robust layer-selective transports of elastic wave are tested by experiment. This research provides exciting application perspectives for ultrasonic devices with robustness, lower-power consumption and high-dimensional manipulation.

The introduction of the concept of valley pseudospin to phononic crystals has made a remarkable topologically protected interface transport of sound, which opens a novel research area referred to as valley Hall topological insulators. Here, we demonstrate the simultaneous multi-band edge states of shear vertical waves in two-dimensional phononic crystals with veins. The multi-band edge states are topologically valley-protected and are obtained by simultaneously gapping multiple Dirac points at K (or K′) under the inversion symmetry breaking. As the relative radius of the two adjacent steel columns varies, the band diagram undergoes a topological transition which can be characterized by topological charge distributions and opposite valley Chern numbers. Subsequently, the vortex chirality of the bulk valley modes is unveiled. With numerical simulations, simultaneous multi-band valley dependent edge states and the associated valley-protected backscattering suppression around the curved waveguide are further demonstrated. Our work could become a promising platform for applications of multi-functional topological acoustic devices.

The asymmetric propagation of the first order antisymmetric (A1) Lamb wave in a tapered plate respectively carved with sharp bottom corner and round bottom corner is theoretically investigated. Through numerical simulation of A1 Lamb wave in time domain, we find that when the thickness of the waveguide abruptly decreases to below the cut-off thickness, about half of the A1 mode is converted into the fundamental symmetrical S0 and antisymmetrical A0 modes to pass through the defected region. Furthermore, the transmitted modes A0 and S0 are completely apart from each other and can be quantitatively evaluated. Conversely, when the thickness change is very smooth, most of the energy of A1 Lamb wave is reflected back. It is the unique mode conversion behavior that leads to great transmission difference value of A1 Lamb wave along the opposite directions. Finally, the influence of geometrical parameters on the transmission coefficient is also studied. The higher efficiency and proper working frequency range can be realized by adjusting the slope angle θ, height h 1 and h 2. The simple asymmetric systems will be potentially significant in applications of ultrasound diagnosis and therapy.

The extensive research on photonic topological insulators has opened up an intriguing way to control electromagnetic (EM) waves. In this work, we numerically demonstrate reconfigurable microwave photon analogues of topological insulator (TIs) in a triangular lattice of elliptical cylinders, according to the theory of topological defects. Multiple topological transitions between the trivial and nontrivial photonic phases can be realized by inhomogeneously changing the ellipse orientation, without altering the lattice structure. Topological protection of the edge states and reconfigurable topological one-way propagation at microwave frequencies, are further verified. Our approach provides a new route towards freely steering light propagations in dielectric photonic crystals (PCs), which has potential applications in the areas of topological signal processing and sensing.

Negative refraction of elastic waves has attracted significant research interest due to its potential prospects in acoustic imaging, communication, and structural health monitoring. However, previous implementations based on Bragg interference suffer from lattice-scale size restrictions or defect-sensitive characteristics, hindering their application in compact subwavelength systems. Here, we propose a new design of ternary valley-Hall phononic crystals (PCs) with subwavelength topological negative refraction. By introducing the subwavelength resonators into a complex lattice similar to graphene allotrope, the valley polarized edge modes induced by locally resonant state are obtained, and the defect-immune topological negative refraction of the edge states outcoupling into free space is established. Furthermore, the total mode conversion from longitudinal to transverse waves is demonstrated by the wave mode separation and the equifrequency curves (EFCs) analysis on the negative refraction. Finally, utilizing the valley-selective excitation, a topological elastic valley filter is designed by coupling the valley-projected edge states with bulk valley polarizations. The research provides new possibilities for robust control of isolated transverse elastic waves in the deep subwavelength regime that can be employed for designing compact communication devices.

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 [Formula: see text] 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.

Topological defects with symmetry-breaking phase transitions have captured much attention. A vortex generated by topological defects exhibits exotic properties, and its flow direction can be switched by altering the spin configurations. Contrary to electromagnetic and acoustic domains, the topological transport of in-plane bulk waves in periodic structures with topological defects is not well explored due to the mode conversion between longitudinal and transverse modes. Here, we propose an elastic topological insulator with spontaneously broken symmetry based on the topological theory of defects and homotopy theory. Multiple topological transitions for in-plane bulk waves are achieved by topologically modifying the ellipse orientation in a triangular lattice of elliptical cylinders. The solid system, independent of the number of molecules in order-parameter space, breaks through the limit of point-group symmetry to emulate elastic pseudospin-orbit coupling. The transport robustness of the edge states is experimentally demonstrated. Our approach provides new possibilities for controlling and transporting in-plane bulk waves.

In this paper, through numerical simulation of the first order shear horizontal guided waves propagation in a homogeneous tapered plate, we have realized sound unidirectional transmission based on the mode conversion mechanism. We also find that the contrast transmission ratio of unidirectional transmission is highly influenced by the slope angle of tapered edge. And the working frequency range of the asymmetric transmission can be easily controlled by the height of tapered surface or the thickness of slab. This asymmetric system shows potentially significant applications in various sound devices.

Asymmetric acoustic wave propagation is important for control and manipulation of the acoustic wave signals in various devices. However, previous approach to find optimal asymmetric acoustic transmission (AAT) is through repeatedly adjusting the geometrical parameters, thus causing time-consuming. Here we propose a study on the multi-objective optimization of the AAT, aiming to achieve the widest working frequency range (fr) and the highest transmittance peak (η) with regard to the design variables. For this purpose, the Radial Basis Function (RBF) neural work and finite element (FE) method are applied to obtain the valuable data in the procedure. Furthermore, local sensitivity analysis of design parameters on the fr and η are analyzed. Ultimately, the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) is adapted for getting the Pareto-optimal solutions. The optimization results show great improvement for the overall performance of the AAT, which could be potentially significant in designing various sound devices.

We realize an elastic second-order topological insulator hosting both one-dimensional gapped edge states and zero-dimensional in-gap corner modes in the double-sided pillared phononic crystal plates with square lattice. Changing the width of two neighbor pillars breaks the inversion symmetry and induces the band inversion to emulate the quantum spin Hall effect where the gapless edge states are obtained. Further breaking the space-symmetry at interface, the gapless edge states are gapped and inducing the edge topological transitions and then giving rise to the zero-dimensional in-gap corner modes. Our work offers a novel way for elastic wave trapping and robustly guiding.

The phenomenon of the broadband transmission enhancement of acoustic waves is important for its prospective applications in various devices. To achieve broadband transmission enhancement of acoustic waves, we investigate the acoustic transmission in a metallic grating device with linearly tapered slits through eigen-mode matching theory (EMMT) and finite element (FE) simulation. The tapering provides a gradual filling fraction variation from the entrance to the exit of the slits, destroying the Fabry–Perot resonance and thus leading to broadband and wide-angle enhanced transmission in the audible regime. In addition, acoustic waves are strongly localized and enhanced at the slit exits, in contrast with straight slits.

This paper theoretically investigates unidirectional and tunable acoustic transmission in a structure of double layer metallic grating immersed in water. Though numerical simulations, we find that the asymmetric acoustic transmission can be achieved by changing the width and the thickness of the double layer metallic gratings. We also find that the contrast transmission ratio of unidirectional transmission is highly influenced by the ratio of the thickness h1/h2. And further study indicates that the working frequency range of the asymmetric transmission can be easily controlled by adjusting the location of the double layer metallic gratings. This constructed acoustic system shows many potential applications of medical ultrasound diagnosis and related fields.

This paper theoretically investigates the band gaps of Lamb mode waves in two-dimensional magnetoelastic phononic crystal slabs by an applied external magnetostatic field. With the assumption of uniformly oriented magnetization, an equivalent piezomagnetic material model is used. The effects of magnetostatic field on phononic crystals are considered carefully in this model. The numerical results indicate that the width of the first band gap is significantly changed by applying the external magnetic field with different amplitude, and the ratio between the maximum and minimum gap widths reaches 228%. Further calculations demonstrate that the orientation of the magnetic field obviously affects the width and location of the first band gap. The contactless tunability of the proposed phononic crystal slabs shows many potential applications of vibration isolation in engineering.

ThxynA, an extracellular xylanase of T. halotolerans YIM 90462 T , was purified to homogeneity from a fermentation broth by ultra-filtration, ammonium sulphate precipitation, hydrophobic chromatography and ion exchange chromatography. The purified xylanase has a molecular mass of 24 kDa and is optimally active at 80 °C and pH 6.0. The enzyme is stable over a broad pH range (pH 6.0–10.0) and shows good thermal stability when incubated at 70 °C for 1 h. The K m and V max values of the enzyme are 11.6 mg/mL and 434 μmol mg −1 min −1 , respectively, using oat spelt xylan as a substrate. Moreover, the enzyme seemingly has both xylanase activity and cellulase activity. These unique properties suggest that it may be useful for industrial applications.

A xylanase gene (thxyn11A) from the Thermobifida halotolerans strain YIM 90462T was cloned and expressed in Escherichia coli. The open reading frame (ORF) of thxyn11A has 1,008 bp encoding a mature xylanase with a high degree of similarity (80 %) to the xylanase from Nocardiopsis dassonvillei subsp. dassonvillei DSM 43111. This enzyme (Thxyn11A) also possesses a glycosyl hydrolases family 11 (GH11) domain and a high isoelectric point (pI = 9.1). However, Thxyn11A varies from most GH11 xylanases, due to its large molecular mass (34 kDa). Recombinant Thxyn11A demonstrated a strong pH and temperature tolerance with a maximum activity at pH 9.0 and 70 °C. Xylotriose, the end-product of xylan hydrolysis by Thxyn11A, serves as a catalyst for hemicellulose pretreatment in industrial applications and can also function as a food source or supplement for enterobacteria. Due to its attractive biochemical properties, Thxyn11A may have potential value in many commercial applications.

We investigated theoretically the band structures of Lamb waves in a one-dimensional (1D) phononic crystal (PC) plates coated symmetrically or asymmetrically with finite Tungsten or Silicon loading layers on both sides. Numerical results show that when a thin PC plates is bordered with Silicon loading layers, the midgap frequency of the first band gap of the S 0 mode increases approximately linearly with the increase of the thickness of solid loading layers; this is contrary to the trend of a thin plates bordered with Tungsten loading layers. These properties can be applied to design acoustic sensors for multilayer materials detection and aircraft icing forecast.

Topological phononic insulators (TPnIs) show promise for application in the manipulation of acoustic waves for the design of low-loss transmission and perfectly integrated communication devices. Since solid phononic crystals exist as a transverse polarization mode and a mixed longitudinal-transverse polarization mode, the realization of topological edge states for both out-of-plane and in-plane bulk elastic waves is desirable to enhance the controllability of the edge waves in solid systems. In this paper, a two-dimensional (2D) solid/solid hexagonal-latticed phononic system that simultaneously supports the topologically protected edge states for out-of-plane and in-plane bulk elastic waves is investigated. Firstly, two pairs of two-fold Dirac cones, respectively corresponding to the out-of-plane and in-plane waves, are obtained at the same frequency by tuning the crystal parameters. Then, a strategy of zone folding is invoked to form double Dirac cones. By shrinking and expanding the steel scatterer, the lattice symmetry is broken, and band inversions induced, giving rise to an intriguing topological phase transition. Finally, the topologically protected edge states for both out-of-plane and in-plane bulk elastic waves, which can be simultaneously located at the frequency range from 1.223 to 1.251 MHz, are numerically observed. Robust pseudospin-dependent elastic edge wave propagation along arbitrary paths is further demonstrated. Our results will significantly broaden its practical application in the engineering field.

Using the finite element method, we have calculated the transmission spectra of Lamb wave modes which propagate in one-dimensional three-component Fibonacci quasiperiodic composite plates made of three different materials, and analyzed the influence of filling fraction, the ratio of the thickness of the plates to the lattice period and especially the number of generations on the band gaps of Lamb wave modes. The band gap splitting depends on the number of generations which is different from those of one-dimensional two-component Fibonacci composite plates. Engineering band gaps can be obtained by turning different parameters and the number of generations.

Using the plane-wave expansion method, we study the propagation of Lamb wave mode in three-component phononic crystals plates. The influence of filling fraction, material parameters and especially the ratio of the thickness of the plates to the lattice period on the band gaps of Lamb wave mode are analyzed by numerical simulations. The optimum gap is obtained by tuning the thickness of the plates and the filling fraction.

The study for exotic topological effects of sound has attracted uprising interests in fundamental physics and practical applications. Based on the concept of valley pseudospin, we demonstrate the topological valley transport of plate-mode waves in a homogenous thin plate with periodic stubbed surface, where a deterministic two-fold Dirac degeneracy is form by two plate modes. We show that the topological property can be controlled by the height of stubs deposited on the plate. By adjusting the relative heights of adjacent stubs, the valley vortex chirality and band inversion are induced, giving rise to a phononic analog of valley Hall phase transition. We further numerically demonstrate the valley states of plate-mode waves with robust topological protection. Our results provide a new route to design unconventional elastic topological insulators and will significantly broaden its practical application in the engineering field.

In this paper, we realize the topological edge modes of a shear horizontal (SH) guided wave in the one-dimensional (1D) composite structure that exist at the phononic band gaps opened at the center of the Brillouin zone (BZ), or at the zone boundary, or both. Furthermore, we investigate the topological edge modes in periodic acoustic systems result from both Bragg scattering and local resonances. In particular, we find and demonstrate that, in our system where topological and trivial defect states coexist, these results provide a new paradigm for manipulating the existence of the interface states in a set of prescribed band gaps that can have potential applications in the design of novel acoustic devices.

We report the simultaneous existence of acoustic and optical asymmetric transmission by combining a periodic array of silicon rods in air with a periodic grating (grating-phoxonic crystals). Theoretically and numerically, we demonstrate that the grating-phoxonic crystals with a square lattice of silicon rods can exhibit simultaneous asymmetric propagation in the same reduced frequency range both for sound and light. The sound and light can transmit through the composite structure when incident from the grating interface but are completely reflected for the reverse direction incidence. Furthermore, when the silicon rods are tuned into a triangular lattice, reversed asymmetric transmissions are also achieved. Sound and light are blocked when incident from the grating interface while being fully able to pass through the composite structure for the reverse direction incidence. These two tunable dual acoustic and optical asymmetric transmissions show great potential for acoustic-optic devices by simultaneously manipulating sound and light.

The cut-off frequency of higher modes of shear horizontal (SH) guided wave propagating in a plate depends on the thickness due to dispersive characteristic. Through numerical simulation of the first higher (SH 1 ) mode of SH guided wave propagation in an asymmetric structure, we have realized sound unidirectional transmission based on breaking spatial inversion symmetry. It demonstrated that when the SH 1 mode are launched into the system from the left side, it mostly converts to the fundamental mode in the defected region and attain a high transmission; on the contrary, when the waves are incident from the right side, the conversion is weak, most SH 1 mode is reflected and the transmission is low. This asymmetric system should be potentially significant in putting to good use in a variety of applications.

We suggest that Lamb wave band gaps in one-dimensional phononic crystals can be substantially enlarged by using multiple heterostructures which consist of several pieces of phononic crystal with different ratios of the thickness to the lattice period. This is possible because each substructure shows a different band gap and the band structure of a Lamb wave is strongly affected by the ratio of the plate thickness to the lattice period. This effect has been demonstrated by using finite element simulations on two different one-dimensional systems.

The unidirectional transmission of Lamb wave in low-frequency domains is realized by graded grating phononic crystal slabs This exotic phenomenon stems from the threshold frequency of the fundamental antisymmetric Lamb mode conversion to the fundamental symmetric Lamb mode is different at the different locations of the acoustic diode. This should be potentially significant in helping design chip-scale directional phononic devices.

A theoretical study is presented on the propagation properties of Lamb wave modes in phononic crystal slabs consisting of a row or more of parallel square cylinders placed periodically in the host material. The surfaces of the slabs are parallel to the axis of periodicity. The dispersion curves of Lamb wave modes are calculated based on the supercell method. The finite element method is employed to calculate the band structures and the transmission power spectra, which are in good agreement with the results by the supercell method. We also have found that the dispersion curves of Lamb waves are strongly dependent on the crystal termination, which is the position of the cut plane through the square cylinders. There exist complete or incomplete (truncated) layers of square cylinders with the change of the crystal termination. The influence of the crystal termination on the band gaps of Lamb wave modes is analyzed by numerical simulations. The variation of the crystal termination leads to obvious changes in the dispersion curves of the Lamb waves and the widths of the band gaps.

We study the propagation of Lamb waves in a one-dimensional phononic crystal slabs bordered with asymmetric uniform layers based on the supercell plane wave expansion method (SC-PWE). The phononic crystal slabs are made of silicon and tungsten. The uniform substrate and superstrate layers can be tungsten layer, rubber layer or one is a tungsten layer and another is a rubber layer. The thickness or material of the substrate is different from that of the superstrate. The validity is proved by using the finite-element (FE) method with the Comsol Multiphysics 3.5a. The results show that the band structure can be tuned by changing the thickness of the substrate or the superstrate. These structures may be used as filters, sensors or wave guides.

A thermophilic bacterium, designated strain RHA1T, was isolated from a sediment sample collected from a hot spring in Tengchong county, Yunnan province, south-west China, and was characterized by using a polyphasic approach. Based on its phenotypic and phylogenetic characteristics, strain RHA1T was affiliated to the genus Laceyella. The strain formed white aerial and yellow–white substrate mycelia, bearing single endospores on short sporophores. The cell-wall peptidoglycan contained meso-diaminopimelic acid. Whole-cell hydrolysates contained ribose and glucose. The major fatty acids were iso-C15 : 0 (62.39 %) and anteiso-C15 : 0 (17.55 %). The predominant menaquinone was MK-9. The G+C content of the genomic DNA of strain RHA1T was 47.9 mol%. Based on DNA–DNA hybridization data, chemotaxonomic characteristics and differential physiological properties, strain RHA1T is considered to represent a novel species of the genus Laceyella, for which the name Laceyella sediminis sp. nov. is proposed; the type strain is RHA1T ( = DSM 45263T = CCTCC AA 208058T).

A theoretical study is presented on the propagation properties of Lamb wave modes in thin plates consisting of a row of parallel square cylinders placed periodically in the host material. The surfaces of the plates are parallel to the axis of periodicity. The dispersion curves of the Lamb wave modes are calculated based on the supercell method. Finite element method is employed to calculate the transmitted power spectrum, which is in good agreement with the results obtained by the supercell method. The influence of the filling fraction on the band gaps of the Lamb wave modes is analyzed by numerical simulations.

We have computed the dispersion curves of plate-mode waves propagating in periodic composite structures composed of isotropic aluminum cylinders embedded in an isotropic nickel background. The phononic crystal has a square symmetry and the calculation is based on the plane-wave expansion method. Along GammaX or GammaM directions, shear-horizontal modes do not couple to the Lamb wave modes which are polarized in the sagittal plane. Whatever the direction of propagation in between GammaX and GammaM, shear-horizontal modes convert to Lamb waves and couple with the flexural and dilatational modes. This phenomenon is demonstrated both through the mode splitting in the lower-order symmetric band structure and through the calculation of all three components of the particle displacements. The phononic case is different from the pure isotropic plate case where shear-horizontal waves decouple from Lamb waves whatever the direction of propagation.

We study theoretically the propagation of lower-order Lamb waves in one-dimensional composite thin plates. The dispersion curves of Lamb modes propagating parallel to the surfaces of the thin plates in the periodic direction are calculated based on the plane wave expansion method. The existence of band gaps for low-order Lamb wave modes is demonstrated in the systems made of alternating strips of tungsten materials and silicon resin. The finite element method is employed to calculate the transmitted power spectra, which is in good agreement with the results by plane wave exposition. A crucial parameter, i.e., the ratio of the plate thickness $(L)$ to the lattice spacing $(D)$, is discussed in detail for the influence of formation of band gaps.

The shear horizontal (SH) guided wave band structures and transmission coefficients in a homogenous plate with periodic tapered surface, whose width is gradually decreases from the lower base to the upper base, are calculated based on the eigen-mode matching theory (EMMT) method. The finite element method (FEM) is also employed to calculate the band structures, which is in good agreement with the results by EMMT method. Numerical results show that the SH guided wave band structures in reduced frequency keep unchanged even if the whole homogenous plate with periodic tapered surface is filled with different materials. We also present the numerical investigations of the geometrical factors' effect on the band structures, including the upper base width, the lower base width, the tapered surface thickness and the plate thickness. These properties of SH guided wave can potentially be utilized to design acoustic sensors, tune band gaps and generate filters.

The Lamb wave band structure of a one-dimensional thin plate with periodic Gaussian surfaces is calculated based on the eigen-mode matching theory (EMMT) method. The finite element method is also employed to calculate the transmission power spectra and the band structure, which are both in good agreement with the results of the EMMT method. In contrast with the straight stubs, the low-frequency band gap of the system with the Gaussian surfaces is wider, when the Gaussian domain's height and area are equal to those of the stub, and the two systems' main plate size and materials are the same. This can be confirmed by the ‘spring–mass' model, which can be used to estimate the resonant frequency. We also investigate the effects of the geometrical parameters on band structure, including the height of the Gaussian domain, the plate thickness and the filling fraction. The results suggest that the band gaps have a close relevance to them.

Asymmetric Lamb wave propagation is important for control and manipulation of the Lamb wave signals in various devices. Through numerical simulation of the Lamb wave propagation in phononic crystal slabs with graded grating, we proposed and studied a linear phononic device that shows asymmetric Lamb wave transmission in low-frequency domains. This exotic phenomenon stems from the threshold frequency of the fundamental antisymmetric Lamb mode conversion to the fundamental symmetric Lamb mode is different at the different locations of the acoustic diode. Remarkably, a bi-directional asymmetric Lamb wave propagation is achieved by tuning the grade of the grating depths. The back propagating acoustic waves of the second band of hybridized Lamb modes plays the essential role in the phenomena for relatively high-frequency regions. This should be potentially significant in helping design chip-scale integrated phononic devices.

We investigate the band structures in a homogeneous plate with periodic truncated cones for the square lattice based on finite element method (FEM). The radius of the truncated cone is gradually reduced from the lower base to the upper base. Compared to the classical stubbed phononic plates, a considerable enlargement of the bandwidth by a factor of 2.04 is obtained by varying the semiangle of the truncated cone, while the truncated cone's weight is only 65.19% of that of the cylinder of the stubbed case. Moreover the relative bandwidth is also enlarged by a factor of 1.68. We show that this band gap enlargement is due to the acoustic waves of different wavelengths is localized at the different parts of the truncated cone. These characteristics of elastic or acoustic waves suggest potential applications in aerospace.

In this paper, we present the numerical investigation of Lamb wave propagation in a homogenous plate with periodic tapered surface, which gradually increases the width from the lower base to the upper base. The dispersion relations, the power transmission spectra, and the displacement fields of the eigenmodes are studied by using the finite-element method. We investigate the effects of the geometrical parameters (including the ratio of the lower base width to the upper base width, and the ratio of the upper base width, the thickness of the tapered surface, and the thickness of the homogenous plate, respectively, to the lower base width) on the band gaps. Numerical results show that the band gaps can be effectively shifted by changing the geometrical parameters. Especially, the width of the first band gap changes approximately linearly by changing the ratio of the upper base width to the lower base width and in return. The transmission bands of the structure with the tapered surface are more flat than those of the structure with the stubbed surface. Moreover, the proposed homogenous plate with periodic tapered surface exhibits lower and smaller band gap than that of the homogenous plate with periodic stubbed surface due to weak localized resonance of the tapered surface with the upper base wider than the lower base. These properties of elastic or acoustic waves can potentially be utilized to tune band gaps, slow the group velocity, generate filters, and design acoustic sensors.