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This work presents a high-sensitivity solution sensor based on a phoxonic crystal nanobeam with lateral fins. The fins improve the stability of the suspended nanobeam and its detection performance is unaffected. Acoustic–optic dual-mode cross-detection improves the detection accuracy over the single-mode method. The acoustic and optical energies are concentrated in the defect and slot regions due to the combination of the gradient cavity and slot, which enhances the acoustic–optic interaction with the object to be measured, improving the detection sensitivity. Using the mode bandgaps of photonic and phononic crystals, the sensing characteristics are investigated using the finite element method. The impact of various concentrations on the transmission spectra of optical electromagnetic waves and acoustic elastic waves is investigated. The maximum sensitivity is 2149.5 kHz/ms−1, with Q of over 105 in the acoustic mode and 457.1 nm/RIU in the optical mode. The proposed nanobeam cavity with lateral fins can be used to realize miniaturized multi-mode acoustic–optic sensors. It also provides mechanical support, thermal transport, and channels for lateral carrier injection for the suspended nanobeam. [ABSTRACT FROM AUTHOR]

Based on the quantum valley Hall effect analogy, this work proposes a phononic crystal plate with ligament-type beams to obtain the topological valley transmission of elastic waves. A pure Bragg degenerate state appears in the high-frequency region with a resonator introduced. By rotating the central scatterer and the beams, the mirror symmetry is broken to form a topological bandgap. Subsequently, this work finds that two selective edge states also appear beside the commonly non-trivial crossing edge states in the topological bandgap by calculating the projected band and eigenvalue spectrum of the supercell with different valley Hall phases phononic crystals. Their appearance is due to band separation of the topological edge states caused by an increase in the rotation angle. Both selective edge states can transmit topologically in specific paths. They will help further to broaden the width of the frequency band of topological transmission. Besides, an elastic wave splitter is designed and demonstrated numerically, which can form two channels and three channels in different frequency bands. With the topological selective edge state disappearing, a topological corner state exists in the edge bandgap. This work provides a theoretical reference for practical applications of broadband elastic wave topological transmission and elastic energy trapping. [ABSTRACT FROM AUTHOR]

Recently, the mode conversion of elastic waves has attracted much attention, due to its scientific significance and potential applications. The applications based on the high mode conversion efficiency were also explored in many fields. However, because of the complexity of elastic waves, the existing structures for the high efficient conversion of elastic waves are relatively complicated, and there are also some limitations in the practical design. Here, we report the extraordinary mode conversion of elastic waves through asymmetric brass plates partitioned by subwavelength cuts. It is demonstrated that high efficiencies (90%) and one-way conversions between transversal waves and longitudinal waves are achieved by the structured solid plate at the resonant frequency, which leads to the striking unidirectional transmission of elastic waves. Analyzing the resonant fields demonstrates that the intrinsic modes within the individual pieces derived by the cuts are responsible for this abnormal wave conversion. The simple scheme for wave conversion presented here may have potential applications, such as non-invasive flow sensing. [ABSTRACT FROM AUTHOR]

This study illustrates the successful achievement of tunable defect bands in one-dimensional defective phononic crystals (PnCs) through the incorporation of piezoelectric defects with synthetic negative capacitances (SNCs) for the first time. The efficacy of SNCs in creating tunable bandpass filters across a broad frequency range is thoroughly examined using the proposed analytical and numerical models. A newly developed electroelastically coupled transfer matrix that incorporates SNCs is presented, considering either series or parallel connection between bimorph piezoelectric elements. Defect band and transmittance analyses are conducted using the transfer matrix and S-parameter methods. Two key findings emerge from this investigation. First, when the total equivalent capacitance of the bimorph piezoelectric elements and SNC becomes zero, the defect band representing the point-symmetric defect-mode shape can be customized throughout the entire phononic bandgap. Second, the constant transmittance value, resembling short-circuit conditions, highlights the remarkable ability of SNCs to tune defect bands without energy dissipation, paving the way for fully tunable bandpass filters. To propel this research forward, future investigations could explore expanding the design space with double defects, adopting enhanced modeling techniques to account for lateral and shear effects, developing a control algorithm for the automatic optimization of SNC values in actively tunable bandpass filters, and incorporating artificial intelligence into design methods for piezoelectric defects with electrical connections. [ABSTRACT FROM AUTHOR]

This paper presents the design of a single-phase solid phononic crystal (PnC) structure featuring a regular hexagonal perforation pattern. The structure manifests three negative refraction bands, encompassing one for transverse waves and two for longitudinal waves, thereby enabling simultaneous control of shear and longitudinal waves. Due to the high symmetry of the triangular lattice, the equal frequency curves corresponding to the negative refraction band approach circular shapes, suggesting a nearly isotropic negative refraction effect. This negative refraction effect is achieved through specific mass resonance modes closely related to the porous structure designed in this paper. Initially, we analyze the band structure of the PnC, followed by designing the PnC plate structure to achieve negative refraction control for transverse waves at a frequency of 32.4 kHz, with a negative refraction index of −1. Additionally, negative refraction control for longitudinal waves is attained at frequencies of 44 and 64.54 kHz. Subsequently, we scrutinize the influence of various conditions on negative refraction, including different structural parameters, incident angles, and operating frequencies, while verifying the robustness of the designed phonon crystal structure. Leveraging the negative refraction characteristics of the structure, we construct an elastic wave lens to achieve perfect imaging of shear and longitudinal waves. Finally, employing finite element simulation and analyzing focusing imaging characteristics with different source positions, we validate that the results closely align with theoretical expectations. The solid PnC structure designed in this study holds significant potential for applications in the fields of elastic wave imaging. [ABSTRACT FROM AUTHOR]

Most previously reported Dirac valley degeneracies in continuous phononic crystal plates originate from Bragg scattering of the structures and generally have only single-band elastic-wave topological edge states. In the present work, a pair of triangular prisms is used in the construction of hexagonal-lattice phononic crystal plates to mimic the dual-band elastic valley Hall effect. Based on the spatial inversion symmetry conditions, which are related to the intrinsic frequencies of the resonators, the valley degeneracies, topological nontrivial bandgaps, and energy band inversion characteristics of multiple resonance modes are investigated by using the finite element method. Edge passbands combining distinct topology phases exist in each of the two nontrivial bandgaps of the ribbon configuration. The full-field simulations for flexural waves in the waveguide structure are demonstrated to support topologically valley-protected edge transmission in both bands, which immunizes the transport against backscattering from large corners and defects in the route. This work provides a reference for valley edge protection in subwavelength continuous elastic plate media and for the manipulation of the elastic waves at multiple frequencies. [ABSTRACT FROM AUTHOR]

• A multifunctional mechanical model with both amplified illusion and cloaking properties is proposed. • The amplified function can make a small object to produce the same displacement distribution as a large object. • Intelligent control system with the detective and control functions is introduced. • Effectively broaden the effective frequency range of structure in 3300Hz×4400 Hz and 1200Hz×3100 Hz. • The cloaking characteristics of the structure are verified through theoretical, numerical and experimental analysis. Illusion device can make an object to produce a field distribution different from its own, offering potential applications in diverse fields. In this work, we propose a multifunctional metamaterial with intelligent control systems, which exhibits amplified illusion and cloaking characteristics for detecting or hiding objects over different frequency ranges. The amplification function allows a small object to generate the same displacement distribution as a larger object, while the cloaking function renders an object invisible and undetectable. Simulation and experimental results demonstrate the exceptional amplification and cloaking properties of the multifunctional configuration. In contrast to single-function structures like cloaking and focusing, which can only fulfill a specific function, designing a multifunctional structure capable of achieving two or more properties within a single configuration presents a significant challenge. [ABSTRACT FROM AUTHOR]

The elastic wave bandgap (BG) properties of locally resonant phononic crystal (LRPC) make it has great potential in the research and development of damping composite material and the application of vibration control engineering. However, the number of BG of the traditional LRPC is only one, the BG frequency range is too concentrated, and the multi-frequency BGs is not opened, so the application in practical engineering is limited. In response to the above issues, this paper designs a concentric ring cement-based locally resonant phononic crystal (CRCBLRPC) composite material, and studies and analyzes its BG characteristics. Firstly, the improved plane wave expansion method (IPWEM) and finite element method (FEM) are used to calculate the band structure of the CRCBLRPC. Secondly, the transfer function and BG mechanism of CRCBLRPC are calculated using FEM. Then, the factors affecting the BG of CRCBLRPC are analyzed. Finally, an equivalent model of spring-mass system is proposed to theoretically estimate the BG range of CRCBLRPC. The results show that the CRCBLRPC opens multi-frequency and low frequency BGs within the 200 Hz frequency band, and the number of BGs is more than that of the traditional LRPC. Within the BG frequency range, the CRCBLRPC has a good inhibition effect on vibration. Among them, the density of the scatterer and the elastic modulus of the coating layer are the main factors affecting the BG of the CRCBLRPC. The established spring-mass system equivalent model can accurately calculate the BG range of the CRCBLRPC. The research content and related conclusions of this paper provide new perspectives and insights for the study and design of LRPC composite materials with multi-frequency and low frequency BGs, and can also provide new ideas and methods for solving low frequency vibration in practical engineering. [ABSTRACT FROM AUTHOR]

Rainbow trapping, observed in elastic waves, has attracted considerable scientific interest owing to its potential applications in energy harvesting, buffering, and wavelength-division multiplexing devices. However, previous approaches have often necessitated complex geometric modifications to the scatterer, such as altering dimensions or shifting along diagonals to corners, limiting practical utility. Here, we realize the coupled topological edge states (CTESs) of elastic waves in a two-dimensional (2D) solid phononic crystal (PC) with inversion center changes. Changing the inversion center along the x or y directions by a specific distance can induce the topological phase transition. The topological edge states (TESs) arise at the interface by combining PCs with different topologies positioned adjacent to each other. Furthermore, it is demonstrated that TES exhibits topological robustness against defects. By introducing a gradient into the PC structure by altering the geometrical parameters of scatterers along the interface, the topological rainbow trapping of elastic waves is achieved. Finally, the CTES are generated by the interaction between TESs of different interfaces, which can lead to coupled topological rainbow trapping in phononic heterostructures with different displacement parameters along the multiple interface gradient. Our results pave the way for manipulating the symmetric and antisymmetric topological modes of elastic waves in topologically coupled waveguides, which offers potential applications in selective filtering and multiband waveguiding. [ABSTRACT FROM AUTHOR]

Metamaterials (MMs), which include phononic crystals (PCs) as a particular type, exhibit anomalous wave propagation properties through artificial design of topologies or lattice forms of unit‐cells. Recent advancements in MMs signify an ascendant research trend, providing promising design ideas and means for unprecedented wave propagation properties. The imperative for on‐demand, real‐time active control of wave propagation underscores the significance of tunable manipulation of acoustic/elastic waves, promoting the design and development of tunable MMs. Furthermore, the versatility of intelligent materials and their ongoing development and innovation contribute significantly to the emergence of diverse intelligent MMs. This comprehensive survey provides an overview of recent advancements and current research trends in the interdisciplinary field of intelligent MMs with electro‐/magneto‐mechanical couplings. The primary objective of the review is to emphasize significant progress in agile manipulation of acoustic/elastic waves in electro‐/magneto‐mechanical coupled MMs, followed by an in‐depth exploration of intelligent metasurfaces, topological MMs, non‐Hermitian parity‐time symmetric wave systems, odd elastic MMs, and spatiotemporally modulated MMs. Special emphasis is given to multi‐field coupling effects. The review concludes with a summary and outlines potential prospects, offering a timely and informative guide for future studies on actively tunable PCs and MMs in practical engineering applications. [ABSTRACT FROM AUTHOR]

This paper introduces a structural design which has superior energy harvesting ability. The proposed structure is based on the ability of most periodic structures to prohibit elastic waves from propagating in a specific frequency range of the phonon band gap. By leading into acoustic black hole (ABH) units and utilizing the energy concentration characteristics of the ABH structure, the filtering effect can be made more significant. These two characteristics can produce significant strain and energy localization, which is conducive to energy harvesting. In this paper, we obtained ABH unit capable of producing broadband gaps by adjusting the geometric parameters of the ABH structure, and chose a cantilever as the research object for energy harvesting, by applying a piezoelectric patch on the unit located near the fixed end to gain a broader application in the actual situation. The results show that the beam combining the energy concentration characteristics of band gap and ABH structure has a significant improvement in energy harvesting efficiency. Optimization on the parameters of ABH unit shows that the band gap characteristic of the periodic ABH structure can further optimize the energy harvesting efficiency of practical energy harvesters, and opens up a new possibility of energy harvesting of ABH structure. [ABSTRACT FROM AUTHOR]

Incident particles in the Klein tunnel phenomenon in quantum mechanics can pass a very high potential barrier. Introducing the concept of tunneling into the analysis of phononic crystals can broaden the application prospects. In this study, the structure of the unit cell is designed, and the low frequency (< 1 kHz) valley locked waveguide is realized through the creation of a phononic crystal plate with a topological phase transition interface. The defect immunity of the topological waveguide is verified, that is, the wave can propagate along the original path in the cases of impurities and disorder. Then, the tunneling phenomenon is introduced into the topological valley-locked waveguide to analyze the wave propagation, and its potential applications (such as signal separators and logic gates) are further explored by designing phononic crystal plates. This research has broad application prospects in information processing and vibration control, and potential applications in other directions are also worth exploring. [ABSTRACT FROM AUTHOR]

Architected materials can break the limit of what is possible compared to natural materials, however, once fabricated they retain fixed properties. A growing trend in research is devoted to materials with properties that can be tuned post fabrication in a programmable manner. Such tunability can be achieved through magnetic, electric, or thermal stimuli to responsive elements within the metamaterial's architecture. In this paper, the first experimental demonstration of ferroelectric programmability of 3D printed polymeric metamaterials is presented to control elastic waves using electrical poling. Electrical poling effects are harnessed to change the mechanical properties of polyvinylidene fluoride (PVDF). The poling‐induced softening is utilized to reverse metamaterials behavior from attenuating waves to propagating them and vice versa. The utility of the proposed platform is demonstrated to program a desired set of pixels within the metamaterials to open a path for waves to propagate in a waveguide. The findings introduce a methodology for elastic wave guiding by electrical poling, which can open the door for numerous applications in various fields such as vibration isolation, wave guiding, and energy harvesting. [ABSTRACT FROM AUTHOR]

Mechanical bound states in the continuum (BICs) present an alternative avenue for developing high-frequency, high-Q mechanical resonators, distinct from the conventional band structure engineering method. While symmetry-protected mechanical BICs have been realized in phononic crystals, the observation of accidental mechanical BICs—whose existence is independent of mode symmetry and tunable by structural parameters—has remained elusive. This challenge is primarily attributed to the additional radiation channel introduced by the longitudinal component of elastic waves. Here, we employ a coupled wave theory to predict and experimentally demonstrate mechanical accidental BICs within a high-aspect-ratio gallium arsenide phononic crystal grating. We observe the merging process of accidental BICs with symmetry-protected BICs, resulting in reduced acoustic radiation losses compared to isolated BICs. This finding opens up new possibilities for phonon trapping using BIC-based systems, with potential applications in sensing, transduction, and quantum measurements. Mechanical bound states in the continuum (BICs) offer a novel approach for realizing high-frequency, high-Q mechanical resonators. Here, the authors theoretically predict and experimentally demonstrate mechanical accidental BICs in a high-aspect-ratio phononic crystal grating, and their merging with symmetry-protected BICs. [ABSTRACT FROM AUTHOR]

Phononic crystals embedded with acoustic black hole (ABH) structure have excellent performance absorbing structural waves in elastic bodies. However, it is not easy to be applied in practice because of the narrow sound absorption band. In this paper, we propose a new type of phononic crystal that embeds the acoustic black hole structure and destructive interference structure. The simulated and measured elastic wave transmission indicate that the vibration in the structure is reduced by 40 dB in the broad range of 100–50,000 Hz, which may provide a new path for wide-frequency vibration isolation and noise control. [ABSTRACT FROM AUTHOR]

In search of novel phononic crystals to effectively control the propagation of elastic waves, we propose a new single-material phononic crystal (PnC) with unit cells containing tapered resonators (TRs). The thickness of the circular taper radially decreases outward from the center. The device modulates dispersion of the wave by a local resonance mechanism and by slowly varying the group velocity of elastic waves. The TRs are layered on the top of a conventional PnC slab with a square arrangement of air holes. The band structure of the PnC is theoretically studied and a comparison is drawn between the avoided level crossings and the symmetry-protected ordinary degeneracies. In the absence of a bandgap, the zero group velocity at the band maximum restricts the waves from propagating. Moreover, the design shows anomalous dispersion phenomena such as self-collimation and bi-refringence, which are rare in conventional PnCs. We trace the origins of these phenomena by analyzing equifrequency contours associated with relevant frequencies. We show that the self-collimation effect persists even with a small variation in the angle of incidence and a perturbative hole at the center of each of the TRs. Within the classical limit, the scale invariance of the elastic wave equation makes the device useful in both the low frequency ultrasonic and the high frequency phononic regime. [ABSTRACT FROM AUTHOR]

Based on the analogy of the quantum valley Hall effect, a ligament-type phononic crystal plate with local resonators is designed in this study to facilitate the valley state transport of low-frequency elastic waves. We analyze the key factors affecting the local resonance modes and reduce the frequency of the Dirac cone by changing the connection form of the structure's beams. The spatial inversion symmetry of the structure is broken to open a new band gap by introducing a mass difference in the resonator pair. The robustness of the designed structure's topological valley waveguide under defects and bends is verified. Based on this characteristic, we introduce the gradient heights into the supercell structure where elastic waves at different frequencies split and stop significantly on the supercell structure to achieve sub-wavelength topological rainbow trapping. This design provides a theoretical reference for exploring the low-frequency elastic topological mode and the application of topological rainbow capture in sub-wavelength structures. [ABSTRACT FROM AUTHOR]

A local-resonance piezoelectric phononic crystal consisting of a quadrangular prism piezoelectric scatterer polarized along the z -axis and wrapped by a plexiglass layer is proposed in this work. The short-circuit external electrical boundary condition is selectively added to the upper and lower surfaces of the piezoelectric scatterer to tune the distribution of polarized charges generated by the localized vibration modes. The band structures of the unit cell are calculated using the finite element method, where the upper boundary of the second complete bandgap is replaced by a passband of type of quadrupole local resonance mode. This passband lies entirely in the second bandgap under the open-circuit external electrical condition. The results of the band structures are verified by the transmission loss of the semi-infinite structure in the frequency domain. Two piezoelectric waveguides with complex paths are designed, showing that elastic waves propagate completely along the given waveguide paths at a particular frequency range. The proposed phononic crystals without additional circuit elements can be assembled into waveguides with arbitrary reconfigurable paths, transmitting elastic waves. [ABSTRACT FROM AUTHOR]

A stress-based unsplit-field perfectly matched layer (PML) method with enhanced numerical stability is proposed to simulate elastic waves in heterogeneous unbounded domains. The proposed PML method attenuates the waves by forcing the satisfaction of mixed-field equations constructed using a complex coordinate stretching in the frequency domain. Unlike other unsplit-field PMLs, which introduce coordinate stretching before combining the constitutive and compatibility equations, the proposed method first combines the two equations and then stretches the resulting equation. The stretched equation is converted back to the time domain using the inverse Fourier transform to yield transient elastic wave equations in the PML-truncated domain. Semi-discrete equations of motion for displacement and stresses were obtained using standard Lagrange-family finite elements. In a series of numerical examples involving semi-infinite elastic media, the accuracy of the wave solutions calculated using the proposed PML method was evaluated using a displacement L 2 -norm, a normalized L 2 -error, and an energy norm. The examples further validated the wave absorption performance of the PML and evaluated the long-term stability of solutions utilizing the Ricker pulse excitation with various central frequencies. The numerical experiments indicate that the solutions obtained using the proposed PML are significantly more stable than those obtained using the existing strain-based unsplit-field PMLs. The proposed method is particularly useful for applications requiring explicit time integration of semi-discrete equations of motion because the mass matrix can be diagonalized. The PML method and its associated solution strategies can be applied to various engineering problems, such as soil-structure interaction analysis, monitoring of structures, and geophysical probing. • The stress-based unsplit-field perfectly matched layer has enhanced numerical stability. • Constitutive and compatibility equations are first combined and then stretched. • Solutions are more stable than those from existing strain-based unsplit-field PMLs. • The proposed perfectly matched layer has excellent wave-absorbing capability. [ABSTRACT FROM AUTHOR]

Numerical seismic wave field simulation is essential for studying the dynamic responses in semi-infinite space, and the absorbing boundary setting is critical for simulation accuracy. This study addresses spherical waves incident from the free boundary by applying dynamic equations and Rayleigh damping. A new multi-directional viscous damping absorbing boundary (MVDB) method is proposed based on regional attenuation. An approximate formula for the damping value is established, which can achieve absorbing the boundary setting by only solving the mass damping coefficients without increasing the absorbing region grid cells or depending on the spatial and temporal walking distance. The validity and stability of the proposed method are proven through numerical calculations with seismic sources incident from different angles. Meanwhile, the key parameters affecting the absorption of the MVDB are analyzed, and the best implementation scheme is provided. In order to meet the requirements of mediums with different elastic parameters for boundary absorption and ensure the high efficiency of numerical calculations, the damping amplitude control coefficients k can be set between 1.02 and 1.12, the thickness of the absorbing region L is set to 2–3 times of the wavelength of the incident transverse wave, and the thickness of the single absorbing layer is set to the size of the discrete mesh of the model Δl. [ABSTRACT FROM AUTHOR]

Rainbow trapping is a significant strategy for capturing waves of different frequencies at different spatial positions. It offers significant potential for multi-frequency on-chip nanophotonic devices in the era of big data and has attracted much interest recently, and topological rainbow trapping that is immune to disorder has been observed in optics and acoustics. Reported here is the topological rainbow trapping of elastic waves using gradient valley phononic crystal plates (PCPs) with a hexagonal lattice, based on valley edge states that are localized at the boundary between two PCPs with opposite valley topological phases. The gradient valley PCPs are achieved by gradually adjusting the height of the scatterers or the thickness of the PCPs. The topological rainbow trapping of elastic waves is shown by applying vertical vibration to the studied gradient PCPs, which are simple in structure and easily fabricated, providing a good solution for manipulating and trapping elastic waves. [ABSTRACT FROM AUTHOR]

A generalized supercell model is established to predict band structures of phononic crystals (PnCs) microplate with or without defects. Microstructure effect in elastic flexural waves is described by the modified couple stress theory. The plane-wave expansion (PWE) method and the supercell technique are applied to solve the wave equations. The generalized supercell model contains P × Q square inclusions that can be adjusted according to different situations. The current model can be used to solve various defect state problems of multiphase materials (arbitrary) composite PnCs microplates. Single-point defect and multiple defects cases are calculated. The results demonstrate that the current model can well predict defect states of the PnCs microplates whether there is coupling between defects and supercell or not. This new model can provide help for the design and application of PnCs with multiple defects at the microscale in different fields. [ABSTRACT FROM AUTHOR]

Topological phononic crystals (PnCs) with topologically protected boundary states have important applications in the fields of acoustic wave transmission and control. However, previous studies based on solid‐state PnC systems are mostly limited by fixed structures, resulting in the difficulty to deform the edge states, which partly limits its practical applications. Herein, a 2D solid topological PnC coupled with the defect is designed to achieve the adjustable valley edge state and rainbow trapping. First, by breaking the spatial inversion symmetry, the valley Hall phase transition of elastic wave is realized and valley edge states are obtained. Next, by introducing defects of different widths between the two different valleys' topological PnCs, both the defect‐adjusted valley edge state and defect state are achieved. Then, by designing different topological PnCs waveguides, the robust transport characteristics of the two above states are compared. Subsequently, a new power divider based on the defect‐adjusted valley edge state is designed, which is found to possess various manners of operation such as equal and unequal power divisions. Finally, based on defect adjustment of the edge states, a rainbow trapping is implemented. This research provides an important guidance for ultrasonic devices, such as waveguides, energy harvesters, and power dividers. [ABSTRACT FROM AUTHOR]

Using the piezoelectric (PZT) effect, energy-harvesting has become possible for phononic crystal (PnC). Low-frequency vibration energy harvesting is more of a challenge, which can be solved by local resonance phononic crystals (LRPnCs). A novel three-dimensional (3D) energy harvesting LRPnC is proposed and further analyzed using the finite element method (FEM) software COMSOL. The 3D LRPnC with spiral unit-cell structures is constructed with a low initial frequency and wide band gaps (BGs). According to the large vibration deformation of the elastic beam near the scatterer, a PZT sheet is mounted in the surface of that beam, to harvest the energy of elastic waves using the PZT effect. To further improve the energy-harvesting performance, a 5 × 5 super-cell is numerically constructed. Numerical simulations show that the present 3D super-cell PnC structure can make full use of the advantages of the large vibration deformation and the PZT effect, i.e., the BGs with a frequency range from 28.47 Hz to 194.21 Hz with a bandwidth of 142.7 Hz, and the maximum voltage output is about 29.3 V under effective sound pressure with a peak power of 11.5 µW. The present super-cell phononic crystal structure provides better support for low-frequency vibration energy harvesting, when designing PnCs, than that of the traditional Prague type. [ABSTRACT FROM AUTHOR]

• A time domain evaluation technique to validate the band structure is proposed. • The application of the localized radial basis function collocation method is extended. • The direct method is further applied to enhance the performance of the method. In this paper, the localized radial basis function collocation method is applied to investigate the in-plane elastic wave propagation of 2D phononic crystals. The direct method with local support domain in one line is used to enhance the stability of the localized radial basis function collocation method when dealing with the derivative calculations in the boundary and interface conditions. The Houbolt method is employed to discretize the time, and then the Fast Fourier Transform is adopted to obtain the band structure according to the wave vectors in the first Brillouin Zone. Different acoustic impedance ratios, filling rates, and lattice forms are studied. The numerical results can be used to validate the band structures obtained directly from the frequency domain. [ABSTRACT FROM AUTHOR]

To measure the energy of the source of acoustic pulses in the absolute scale of units (J) from the registered pulses, an analysis of the energy balance "source of pulses"–"transmitting medium"–"receiver of pulses" was carried out using a spectral analysis device. Comparison of two independent methods for determining the energy of elastic interaction (capacitive method and photoelasticity method) gave a discrepancy between the results of less than 12%. The spectral composition of the interaction energy is determined. The results make it possible to determine both the parameters of the signal source and the structure of the transmitting average signal conversion. To measure stresses in an elastic wave, a piezoelectric receiver, in which a piezofilm served as a sensitive element. This receiver differs from receivers made on the basis of piezoceramic elements, has a significantly lower non-linearity of the amplitude–frequency characteristic, since it has only two natural frequencies. [ABSTRACT FROM AUTHOR]

This paper proposes an explicit solution for the design of a target-frequency-customized, one-dimensional phononic crystal (PNC) with a defect for piezoelectric energy harvesting under longitudinal waves. Due to the innate narrow bandwidth nature of the defect modes of a PNC at the target frequency, there is a great need to generate an electromechanically coupled defect band of a piezoelectric-defect-introduced PNC. This work considers the transfer matrix method which has been widely used in analytical approaches. The need for defect bands to be included in a bandgap inspires the use of a quarter-wave stack as a unit cell to match the bandgap's central frequency with the target frequency. In band structure analysis, considering that the electromechanically coupled defect band corresponds to a set of real wavenumbers despite being within the bandgap, several possible solutions for the piezoelectric defect's length are derived in an explicit fashion. Since switching from a short- to an open-circuit condition causes defect bands to slightly increase due to piezoelectric effects, an explicit solution that reflects the piezoelectric defect's electrical characteristics is finally proposed. Finite-element-based numerical validation studies are conducted to study two aspects, specifically parametric studies (i.e., the natural numbers in the solution to the piezoelectric defect's length, the supercell sizes, and the defect locations) and supporting studies (i.e., the electrical boundary conditions and unit cell designs). At the target frequency, it is demonstrated that the proposed PNC design actualizes the formation of one defect band and the representation of the peak output voltage. [ABSTRACT FROM AUTHOR]

Topological phononic crystals and acoustic metamaterials have attracted enormous research attention in recent years due to the presence of robust and disorder-immune wave propagation. In this study, a sinusoidal lightweight elastic topological insulator with protected interface modes is investigated at a subwavelength frequency region. By a wave dispersion study, the dual Dirac cones are observed at a subwavelength frequency region due to the employment of two distinct cylinders connected with sinusoidal ligaments. Both cylindrical masses and sinusoidal ligaments are found responsible for opening low-frequency bandgaps that manipulate elastic wave wavelengths almost 30 times larger than the lattice size. Consequently, the subwavelength bandgap closing-and-reopening phenomenon with phase transitions is further captured and opposite signs of the valley Chern numbers are obtained for different structural parameters. A supercell structure is constructed based on the phase transition, and dual topologically protected interface modes (TPIMs) are captured with different quality factors. The comparison of topologically protected interface modes shows that TPIM I is in a higher and wider frequency range, while TPIM II is positioned in a comparatively narrow and extremely low-frequency range. Finally, the robust elastic wave propagation along various designated paths is demonstrated. The proposed lightweight topologically protected phononic lattice may spark future investigation of topological edge states in metadevices at a subwavelength frequency region. [ABSTRACT FROM AUTHOR]

The propagation of acoustic or elastic waves in artificial crystals, including the case of phononic and sonic crystals, is inherently anisotropic. As is known from the theory of periodic composites, anisotropy is directly dictated by the space group of the unit cell of the crystal and the rank of the elastic tensor. Here, we examine effective velocities in the long wavelength limit of periodic acoustic and elastic composites as a function of the direction of propagation. We derive explicit and efficient formulas for estimating the effective velocity surfaces based on the second-order perturbation theory, generalizing the Christoffel equation for elastic waves in solids. We identify strongly anisotropic sonic crystals for scalar acoustic waves and strongly anisotropic phononic crystals for vector elastic waves. Furthermore, we observe that under specific conditions, quasi-longitudinal waves can be made much slower than shear waves propagating in the same direction. [ABSTRACT FROM AUTHOR]

Elastic wave metamaterials, such as phononic crystals (PnCs) always composed of several materials in terms of periodical structures, possess unique acoustic characteristic which can exhibit outstanding performance in forbidding wave propagation with some specific frequencies. In this paper, due to the thermal sensitivity of the thermally induced shape memory polymers (SMP) and period thermal fields, a tunable planar acoustic metamaterial which is constituent homogeneous is proposed and designed to realize the function of waveguides. A thin plate model composed of homogenous thermally induced SMP and adhered with a series of metallic films at the top boundary which plays the role of local heating sources is established. The homogenous plate can be transferred into acoustic metamaterial once the non-uniform period thermal fields are imported. Based on the Fourier law of heat conduction and finite element method (FEM), a two-dimensional numerical model via COMSOL Multiphysics is carried out to perform the in-plane mode band structures and transmission spectra. The results show that the bandgap will be effectively opened and change obviously as the injected heat flux increases. Furthermore, band structures of 7 × 1 supercell with thermal defect are performed to reveal the design guideline of waveguides which is supposed to be the basis of line-type and L-type waveguides. The tunable characteristics of waveguides based on thermal fields with thermal defects are also discussed. These results may pave a new avenue for the design of tunable acoustic metamaterial composed of thermal sensitive material which own a prospect to be applied in area of acoustic waveguides. [ABSTRACT FROM AUTHOR]

Extensive prior research has delved into the localization of elastic wave energy through defect modes within phononic crystals (PnCs). The amalgamation of defective PnCs with piezoelectric materials has opened new avenues for conceptual innovations catering to energy harvesters, wave filters, and ultrasonic receivers. A recent departure from this conventional paradigm involves designing an ultrasonic actuator that excites elastic waves. However, previous efforts have mostly focused on single-defect scenarios for bending-wave excitation. To push the boundaries, this research takes a step forward by extending PnC design to include double piezoelectric defects. This advancement allows ultrasonic actuators to effectively operate across multiple frequencies. An analytical model originally developed for a single-defect situation via Euler–Bernoulli beam theory is adapted to fit within the framework of a double-defect set-up, predicting wave-excitation performance. Furthermore, a comprehensive study is executed to analyze how changes in input voltage configurations impact the output responses. The ultimate goal is to create ultrasonic transducers that could have practical applications in nondestructive testing for monitoring structural health and in ultrasonic imaging for medical purposes. [ABSTRACT FROM AUTHOR]

This paper deals with the time reversal approach along with signal classification using ϕ -divergences in biomedical applications for localization and statistical classification of ultrasonic nonlinearities. The time reversal (TR) approach in combination with nonlinear elastic wave spectroscopy (NEWS) is used to obtain the nonlinear signature of air bubbles with different sizes and ultrasound contrast agents in a liquid. An optimized chirp-coded signal in the range of 0.6–3 MHz is used as a compression coding. The signal classification is performed using the fuzzy classification method and the divergence decision tree algorithm using specific ϕ -divergence spectral measures extracted from the received ultrasonic response containing acoustic nonlinearities. The classification results prove that different types of nonlinearities extracted with classical "pulse inversion" based coding methods can be identified. Simultaneously, the different positions of scattered sources are distinguished by ϕ -divergence methods. The potential of time reversal nonlinear elastic wave spectroscopy methods for understanding of ultrasonic wave propagation in complex media is clearly exhibited. [ABSTRACT FROM AUTHOR]

• A method for complex band structure computation of phononic crystals is proposed. • Local optimization semi-Cartesian grid is proposed to improve the grid quality near the interface. • Floquet transform is applied to transform the elastic wave equation into quadratic eigenvalue equation. • Complex band structures of phononic crystals with sharp-edged scatterer shapes are computed and analyzed. In this paper, we propose a finite element method based on the Floquet transform and local optimization semi-Cartesian grid to compute the complex band structure of phononic crystals. Floquet transform is applied to transform the elastic wave equation into a quadratic eigenvalue equation. Value-periodic test function independent of the interface is defined to derive the weak formulation. The local optimization semi-Cartesian grid is proposed to improve the quality of triangular elements near the interface. Our results are in good agreement with ones obtained by other mature methods, and the purely propagative mode coincides with the traditional band diagram. In addition to simple scatterer shapes such as circle or square, the proposed method is able to calculate the complex band structures of phononic crystals with complicated scatterer shapes. Numerical experiments demonstrated the effectiveness of this method in the computation of anisotropic inhomogeneous medium. The complex band structures under different lattice types, scatterer shapes, material properties, rotation angle and modes are obtained, and their effects on the width and number of band gaps are analyzed. [ABSTRACT FROM AUTHOR]

Piezoelectric metamaterials with inductance shunt circuits connected to the transducers have attractive potential for guiding and attenuating elastic waves. However, it is challenging to evaluate their wave attenuation capability experimentally because the signals of transmitted waves within the bandgap have extremely small amplitudes and are submerged in noise. The present paper reports a method for revealing the wave attenuation features of a piezoelectric metamaterial beam by taking advantage of the physical correlation between the excitation and the transmitted and incident waves. Correlations between the excitation and the measured waves are calculated in real time to eliminate noise. It is demonstrated that wave attenuation features within the bandgap can be recovered from noise with an amplitude that is 69.1 dB larger than that of the transmitted wave. The transmission diagram is presented, and wave attenuation of up to −50.7 dB can be observed. Also, the correlation-based signal processing procedure is effective for illustrating the resistance-load-based wave attenuation behavior of the piezoelectric metamaterial beam. This method can be extended to the experimental analysis of many other types of metamaterials and phononic crystals. [ABSTRACT FROM AUTHOR]

The topological interface state for an elastic wave in a one-dimensional system, as reported in the literature, mainly occurs through Bragg scattering, making it difficult to achieve subwavelength wave control and flexible tunability. Here, inspired by the band-folding mechanism, this paper confirms that an interface state can likewise be excited by local resonance. The topological phase transition is accomplished by purposely arranging the locations of local resonators. The system is composed of a uniform thin beam with periodically attached local resonators made from an electrorheological elastomer subjected to adjustable electric fields. By simply doubling the primitive unit cell, the passing bands in the dispersion relation are folded and a folding point falls below the locally resonant bandgap, which can be lifted up by simply tuning the distance between two local resonators to realize a topological phase transition. Furthermore, we demonstrate the dynamic tunability of the working frequency of the topological interface state by using an external electric field to adjust the starting frequency of the local resonance. Since the excited frequency of the interface mode is lower than the resonance frequency, this work overcomes the ineffectiveness of the Bragg topological phononic crystal at low frequencies. Moreover, the use of an electroactive resonator whose parameters are readily tuned also enables the flexible design of a frequency-variable topological system without requiring a geometrical modification of the base structure. This technique may have potential applications, such as vibration isolation or in fabricating a robust waveguide. [ABSTRACT FROM AUTHOR]

We demonstrate that higher-order topological insulators with C4 symmetry can be realized in two-dimensional elastic phononic crystals. Both one-dimensional topological edge states and zero-dimensional topological corner states are visualized and can transform each other by tuning the crystalline symmetry in a hierarchical structure. The systematic band structure calculations indicate that elastic wave energy in the hierarchical structures can be localized with remarkable robustness, which is very promising for new generations of integrated solid-state phononic circuits with a great versatility. In addition, the corner states residing in a much wider bandgap greatly increase the signal-to-noise ratio of topological devices. [ABSTRACT FROM AUTHOR]

This paper systematically studies wave attenuation and band structure in functionally graded corrugated phononic crystal beams. The unit cell of the corrugated beam consists of the functionally graded parts and the homogeneous part. Considering the Timoshenko beam theory, the periodic boundary condition, and the particular coordinate transformation relation, the elastodynamic equation of functionally graded composite corrugated phononic crystal beams is established and discretized with the higher-order spectral elements. Based on Hamilton's principle and Fourier transformation, a semi-analytical approach for the corrugated beam is proposed in the framework of the Bloch theorem, which can provide the exact explicit complex solutions. Besides, the accuracy and convergence of the proposed method are discussed by comparison with the classical methods. The underlying mechanism that induces bandgaps and wave attenuation are demonstrated by analyzing the complex band structure of the corrugated phononic crystal beam. The results indicate that the appearance of bandgaps is the manifestation of exponentially decreasing transmission of evanescent waves in the corrugated beam. By tuning the superlattice configuration of the beam, customized bandgaps and broadband wave attenuation with lower frequency domain can be realized flexibly. Additionally, it can be observed that all elastic waves become evanescent modes by introducing the structural loss factor into the phononic crystal beam. This work gives several exciting and interesting results. A new thought has been developed for designing advanced acoustic materials and manipulating wave motion, which has much potential in functional acoustic devices with unique properties. [ABSTRACT FROM AUTHOR]

Low noise and vibrations are requirements for engineering structures to realize comfort and ensure systems are environmental friendly. Periodic structures such as phononic crystals have been investigated to suppress noise and vibrations because they inhibit elastic wave propagation in the frequency ranges referred to as the band gap. This study led to the proposal of a metaplate (MP) with periodic hollow structures to form band gaps by changing the surface shapes of the thin plates. MPs such as this can be beneficial from the viewpoints of manufacturing cost and structural reliability when applied to engineering structures. To evaluate the potential ability of the proposed MP to suppress vibrations, we obtained the band gap frequency of out-of-plane deformation waves using the wave finite element method. To efficiently evaluate the band gaps, the internal degrees of freedom in a unit cell are reduced based on the modal analysis technique. Furthermore, the out-of-plane and in-plane deformation waves are separated using kinematic energy to extract the band gap related to the out-of-plane deformation waves. Based on this numerical framework, we demonstrate that periodic hollow shapes can form a band gap in the frequency range of interest in engineering problems. Moreover, the potential of the MP was investigated using hollow shape design and material selection, and the results indicate that the proposed MP is beneficial for tuning the band gap frequency in a unit cell of which the size is acceptable for engineering structures. Finally, vibration suppression caused by band gap is experimentally demonstrated via impact testing of an MP fabricated using additive manufacturing. [ABSTRACT FROM AUTHOR]

This paper is concerned with the inverse scattering of acoustic waves by an unbounded periodic elastic medium in the three-dimensional case. A novel uniqueness theorem is proved for the inverse problem of recovering a bi-periodic interface between acoustic and elastic waves using the near-field data measured only from the acoustic side of the interface, corresponding to a countably infinite number of quasi-periodic incident acoustic waves. The proposed method depends only on a fundamental a priori estimate established for the acoustic and elastic wave fields and a new mixed-reciprocity relation established in this paper for the solutions of the fluid-solid interaction scattering problem. [ABSTRACT FROM AUTHOR]

The control and manipulation of acoustic and elastic waves is an important research topic in engineering sciences. In acoustics, an adequate combination of different materials can contribute to an efficient and broadband sound isolation. The realization of a vibration‐free environment for high‐precision mechanical systems in laboratories and measuring environments is also desirable in many practical cases. Therefore, advanced materials and structures with outstanding acoustic and elastodynamic properties are of great importance in engineering applications. In this paper, a numerical tool based on the finite element method (FEM) is developed for computing the dispersion relations or band structures of two‐dimensional (2D) phononic crystals (PCs) composed of an elastic matrix and periodically distributed cylindrical inclusions. [ABSTRACT FROM AUTHOR]

Locally resonant phononic crystals are a kind of artificial periodic composite material/structure with an elastic wave band gap that show attractive application potential in low-frequency vibration control. For low-frequency vibration control problems of ship power systems, this paper proposes a phononic crystal board structure, and based on the Bloch theorem of periodic structure, it uses a finite element method to calculate the band structure and the displacement fields corresponding to the characteristic mode and vibration transmission curve of the corresponding finite periodic sandwich plate structure, and the band gap characteristics are studied. The mechanism of band gap formation is mainly attributed to the mode coupling of the phononic crystal plate structure. Numerical results show that the sandwich plate structure has a double periodicity, so it has a multi-stage elastic wave band gap, which can fully inhibit the transmission of flexural waves and isolate the low-frequency flexural vibration. The experimental measurements of flexural vibration transmission spectra were conducted to validate the accuracy and reliability of the numerical calculation method. On this basis, the potential application of the proposed vibration isolation method in a marine power system is discussed. A vibration isolation platform mounted on a steel plate is studied by numerical simulation, which can isolate low-frequency vibration to protect electronic equipment and precision instruments. [ABSTRACT FROM AUTHOR]

We study the one-way transmission and mode conversion of elastic waves by a hybrid phononic-crystal structure that consists of two mutually perpendicular phononic-crystal waveguides connected by a resonant cavity. Based on the mode matching mechanism between the cavity and waveguides, the symmetrical waves incident on the waveguide entrance are converted into antisymmetric modes and exit the waveguide. However, for the same waves incident on the structure from the waveguide exit, no output waves are transmitted toward the waveguide entrance because the modes in the waveguides and the cavity are mismatched. On the basis of this unique property, we designed a polarization-sensitive composite structure to measure the angle between two components of incident mixed elastic waves. [ABSTRACT FROM AUTHOR]

Significant prior research has explored elastic wave-energy localization via defect modes of phononic crystals (PnCs). The integration of defect-introduced PnCs and piezoelectric materials has paved the way for the development of new conceptual products for applications in energy harvesters, wave filters, and ultrasonic sensors. Recently, an attempt has been made to deviate from this paradigm and design an ultrasonic transducer that generates elastic waves. Unfortunately, previous work has been limited to a single-defect situation. Therefore, as an advanced approach, the present work aims to expand the PnC design space into double defects, which will make ultrasonic transducers useful at several frequencies. As a first step, this study targets longitudinal wave generation. To predict the wave-generation performance, a previous analytical model that was built for energy-harvesting purposes under a single-defect situation is modified to be suitable for the present wave-generation purpose under a double-defect situation. Moreover, two parametric studies are executed to analyze how the output responses change based on changes to the input voltage setting and the spacing between the double defects. We hope that these ultrasonic transducers could be potentially applicable for nondestructive testing in structural health monitoring and ultrasonic imaging in medical science. [ABSTRACT FROM AUTHOR]

In this paper, a novel H-shaped radial phononic crystal (H-RPC) structure is proposed to suppress the anchor loss of a Lamb wave resonator (LWR), which has an ultra-high frequency (UHF) and ultra-wideband gap characteristics. Compared to previous studies on phononic crystal (PC) structures aimed at suppressing anchor loss, the radial phononic crystal (RPC) structure is more suitable for suppressing the anchor loss of the LWR. By using the finite element method, through the research and analysis of the complex energy band and frequency response, it is found that the elastic wave can generate an ultra-wideband gap with a relative bandwidth of up to 80.2% in the UHF range when propagating in the H-RPC structure. Furthermore, the influence of geometric parameters on the ultra-wideband gap is analyzed. Then, the H-RPC structure is introduced into the LWR. Through the analysis of the resonant frequency, it is found that the LWR formed by the H-RPC structure can effectively reduce the vibration energy radiated by the anchor point. The anchor quality factor was increased by 505,560.4% compared with the conventional LWR. In addition, the analysis of the LWR under load shows that the LWR with the H-RPC structure can increase the load quality factor by 249.9% and reduce the insertion loss by 93.1%, while the electromechanical coupling coefficient is less affected. [ABSTRACT FROM AUTHOR]

Phononic crystals of the smaller scale show a promising future in the field of vibration and sound reduction owing to their capability of accurate manipulation of elastic waves arising from size-dependent band gaps. However, manipulating band gaps is still a major challenge for existing design approaches. In order to obtain the microcomposites with desired band gaps, a data drive approach is proposed in this study. A tandem neural network is trained to establish the mapping relation between the flexural wave band gaps and the microphononic beams. The dynamic characteristics of wave motion are described using the modified coupled stress theory, and the transfer matrix method is employed to obtain the band gaps within the size effects. The results show that the proposed network enables feasible generated micro phononic beams and works better than the neural network that outputs design parameters without the help of the forward path. Moreover, even size effects are diminished with increasing unit cell length, the trained model can still generate phononic beams with anticipated band gaps. The present work can definitely pave the way to pursue new breakthroughs in micro phononic crystals and metamaterials research. [ABSTRACT FROM AUTHOR]

Inspired by the morphology and material composition of spider capture silk, we report a one-dimensional (1D) bead-chain phononic lattice (BCPL) that is lightweight and possesses tunable bandgaps. Among the mechanical parameters of the stress-free structure, we demonstrate that the width and midfrequency of the bandgaps depend mainly on the shear modulus and the mass density of the beads, while the axial pre-stretching exhibits a flexible and appreciable bandgap tunability. Based on this, mimicking the local morphology of the orb-web, we subsequently propose a two-dimensional (2D) BCPL with the 1D BCPL as components. Numerical simulations verify its wave filtering and directional transmission capabilities, which are regulated by tensile deformation. This work is expected to shed some light on the design and development of lightweight tunable elastic wave modulation devices. [ABSTRACT FROM AUTHOR]

Locally resonant acoustic metamaterials (LRAMs) effectively reduce low-frequency noise, since their locally resonant systems act as spatial frequency filters. However, they have narrow bandgaps (BGs), impose additional weight on the primary system, and work only at the adjusted frequency range. For widening BGs, the unit cells must be large in size or contain dense materials. As a solution to the disadvantages mentioned above of LRAMs, this paper proposes a novel three-dimensional lightweight re-entrant meta-structure composed of a cross-shaped beam scatterer embedded in a host plate with holes based on the square lattice metamaterial. By combining the re-entry networks mechanism and the Floquet–Bloch theory, on the basis of cross-shaped beam theory and perforation mechanism, we demonstrate that such a lightweight LRAM structure can filter elastic waves across a broad frequency range (not just a specific narrow region) while simultaneously reducing structure weight to a significant degree. The band structures, transmission loss spectrum (TL), and displacement vector fields are calculated utilizing the finite-element method (FEM) for a finite period structure comprising 5 unit cells. Meanwhile, vibration modes at the edges of BGs are studied carefully to elucidate the formation mechanism, dynamic response, and dispersion features of BGs. In addition, the influences of material and geometrical properties on the dispersion characteristics are examined by the sensitivity analysis, and the results are discussed with the equivalent spring–mass models. Numerical results demonstrate that the structure is capable of generating multiple ultra-wide BGs with over 680% resonant bandgap coverage factor with a high vibration insulation peak, where the sound reduction of the super-cell exceeds 120 dB within (0–12 kHz), based on the local resonance mechanism. This research provides a new physical insight into wide spatial frequency range filtering and light-weighting structures. [ABSTRACT FROM AUTHOR]

In solid state physics, a bandgap (BG) refers to a range of energies where no electronic states can exist. This concept was extended to classical waves, spawning the entire fields of photonic and phononic crystals where BGs are frequency (or wavelength) intervals where wave propagation is prohibited. For elastic waves, BGs are found in periodically alternating mechanical properties (i.e., stiffness and density). This gives birth to phononic crystals and later elastic metamaterials that have enabled unprecedented functionalities for a wide range of applications. Planar metamaterials are built for vibration shielding, while a myriad of works focus on integrating phononic crystals in microsystems for filtering, waveguiding, and dynamical strain energy confinement in optomechanical systems. Furthermore, the past decade has witnessed the rise of topological insulators, which leads to the creation of elastodynamic analogs of topological insulators for robust manipulation of mechanical waves. Meanwhile, additive manufacturing has enabled the realization of 3D architected elastic metamaterials, which extends their functionalities. This review aims to comprehensively delineate the rich physical background and the state‐of‐the art in elastic metamaterials and phononic crystals that possess engineered BGs for different functionalities and applications, and to provide a roadmap for future directions of these manmade materials. [ABSTRACT FROM AUTHOR]

A design method of a phononic crystal structure with a local effect is introduced, and the mechanism and influencing factors (elastic modulus, density, local layer thickness) of the bandgap are analyzed. The finite element method is used to calculate the eigenfrequency. The first bandgap width accounts for more than 98% of the frequency below 20 000 Hz. Two kinds of materials with different wave velocities are arranged periodically to form a two-dimensional local effect structure. Due to the influence of the local effect, when the elastic wave propagates in the local layer, the wave propagation will be restrained, and the eigenfrequency spectrum presents a series of discrete energy levels. The material parameters and structural parameters of the transmission layer have a great influence on the bandgap. The first bandgap is an ultra-wide low frequency bandgap, and the bandgap frequency ranges from 238 to 18857 Hz. This periodic structure with the local effect has great potential application value in noise and vibration suppression. [ABSTRACT FROM AUTHOR]

Dissipation alone can produce counterintuitive topological wave transport that is otherwise absent in a non-dissipative system. This work demonstrates the influence of dissipation on degeneracies that arise in the context of elastic wave transport. The conditions on the parameters necessary to observe non-Hermitian degeneracies in the Bloch spectrum are precisely derived. It will be shown—contrary to the expectation from singularity theory of a linear eigenvalue problem—that a proportionally damped system with commutative damping does not exhibit non-Hermitian degeneracies. The necessity of a non-commutative and non-proportional dissipation model to observe non-Hermitian degeneracies (or exceptional points) is emphasized. Non-proportional dissipation is used to induce a non-Hermitian degeneracy in a local resonance sub-Bragg bandgap of a linear chain, without using negative damping. While Bloch waves are chosen to illustrate the influence of dissipation, the results readily extend to waves in non-periodic media as well as other wave and vibration transport problems. [ABSTRACT FROM AUTHOR]