Phononic Crystal Structure Research Articles

Widening the frequency bandgap and reducing thermal conductivity in phononic crystals by tuning structural parameters using a novel computational simulation method

AbstractThis paper introduces and models a phononic structure based on single-crystal silicon, aiming to investigate the width of its frequency bandgap and the impact of key parameters on thermal conductivity. The modeled phononic crystal structure features a periodic arrangement of cylindrical holes in a silicon matrix. This research holds the potential to enhance thermal management performance of thermal metamaterials. Utilizing a 3D finite element method (FEM) model in COMSOL, we have computed phonon dispersion to estimate thermal conductivity. The study systematically has explored the influence of phononic crystal parameters—specifically, porosity, lattice constant, and thickness—along with their interactions on both thermal conductivity and frequency bandgap width.A comprehensive investigation of these parameters has been conducted for their optimization to achieve the maximum frequency bandgap width and minimum thermal conductivity using the response surface method model. Eigenfrequencies and wave vector parameters are extracted from the finite element model using a MATLAB script. Subsequently, thermal conductivity is calculated through the Callaway–Holland model, a simplification of the Boltzmann transport equation (BTE).Our results indicate that the frequency bandgap begins to form at approximately 43% porosity for a lattice constant and thickness of 100 nm each. Furthermore, adjusting the parameters led to a significant reduction in thermal conductivity, decreasing from 43.89 W m−1 K−1 to 0.39 W m−1 K−1. The novelty of our research lies in thermal conductivity control of phononic crystal metamaterials through their parameter variations, or a predictive method of thermal conductivity and its parameter sensitivity. This study advances the state of the art in phononic crystal metamaterial research, contributing to improved thermal management performance by enlarging frequency bandgaps.Overall, our findings deepen the understanding of how porosity, lattice constant, and thickness influence thermal conductivity and frequency bandgap width. They offer valuable insights into optimizing phononic crystal parameters, enhancing thermal management performance, and designing more efficient and effective phononic crystal structures.

Honeycomb-Shaped Phononic Crystals on 42°Y-X LiTaO3/SiO2/Poly-Si/Si Substrate for Improved Performance and Miniaturization

A SAW device with a multi-layered piezoelectric substrate has excellent performance due to its high Q value. A multi-layer piezoelectric substrate combined with phononic crystal structures capable of acoustic wave reflection with a very small array can achieve miniaturization and high performance. In this paper, a honeycomb-shaped phononic crystal structure based on 42°Y-X LT/SiO2/poly-Si/Si-layered substrate is proposed. The analysis of the bandgap distribution under various filling fractions was carried out using dispersion and transmission characteristics. In order to study the application of PnCs in SAW devices, one-port resonators with different reflectors were compared and analyzed. Based on the frequency response curves and Bode-Q value curves, it was found that when the HC-PnC structure is used as a reflector, it can not only improve the transmission loss of the resonator but also reduce the size of the device.

Isogeometric topology optimization for maximizing band gap of two-dimensional phononic crystal structures

A smooth and efficient isogeometric topology optimization (ITO) method for maximizing band gaps in two-dimensional phononic crystals is developed in the paper. The band gaps of phononic crystals are computed by the NURBS-based isogeometric analysis, and the material distributions of two-dimensional phononic crystals are represented by the smooth, high-order continuity of the NURBS surface. The densities defined at each control point of the NURBS surface are employed as optimized design variables. The isogeometric analysis optimization using the same spline technique for both geometry and numerical analysis can benefit the optimization procedure and obtain smooth optimized structures, which can be easily used in 3D printing. The maximizing band gaps of phononic crystals for both out-of-plane and in-plane wave modes are obtained here using the present ITO approach. Numerical examples validated the effectiveness and reliability of the ITO method in broadening the band gaps and finding the optimal phononic crystals. And the numerical results show that the smooth optimized structures are obtained with fewer iterations.

A magnetically switchable demultiplexer via Terfenol-D in phononic crystal

This study introduces a novel approach for developing a controllable demultiplexer by applying a magnetic field to Terfenol-D cylinders within a solid–solid phononic crystal structure. Dynamic controllable demultiplexers are essential devices in acoustic and optical communication networks, yet adjustable elastic demultiplexers are notably lacking in current sound systems and acoustic communication technologies. The proposed phononic crystal-based demultiplexer features a square lattice (12 × 19) composed of tungsten cylinders embedded in a poly methyl methacrylate (PMMA) substrate. The switchable design consists of two identical, symmetrical parts separated by an input waveguide. In addition, each unit includes an output channel, a common input channel, and a square ring resonator, with the output channel side-coupled to the input bus waveguide. Moreover, Terfenol-D, a magnetostrictive material, is utilized in the hollow cylinders of the output channels. Switchability of the elastic demultiplexer outputs is achieved by dynamically altering the Young’s modulus of the Terfenol-D cylinders through the application of a magnetic field. This magnetic influence modifies the Young’s modulus of the Terfenol-D material in the output waveguides, enabling controllability. By varying the magnetic field applied to the demultiplexer, we find two distinct values of Young’s modulus within the structure. These two values facilitate the high transmission of two desirable peaks with narrow bandwidth through the output channels, allowing for switchable functionality based on the magnetic field’s position. The proposed demultiplexer demonstrates an average crosstalk value of −25.34 dB, indicating strong performance, along with a high average quality factor (Q) of 1773.5 and low average insertion losses of 0.85 dB in the MHz frequency range. The solid–solid elastic controllable demultiplexer is simulated using the finite element method, showcasing its potential for practical applications.

Ultrasonic scalpel based on fusiform phononic crystal structure

Abstract In response to the ultrasonic scalpels with the vibrational modal coupling which leads to a decrease in efficiency, an ultrasonic scalpel based on fusiform phononic crystals (PnCs) is proposed. An accurate theoretical model is constructed, which is mainly composed of electromechanical equivalent circuit models to analyze the frequency response function and the frequency response curves of the admittance. Bragg band gaps exist in the fusiform PnCs owing to the periodic constraint, which can suppress the corresponding vibrational modes. The vibration characteristics (vibration mode, frequency, and displacement distribution) of the ultrasonic scalpel are analyzed, and the validity of the electromechanical equivalent circuit method is verified. The results indicate that other vibration modes near the working frequency can be isolated. In addition, blades based on fusiform PnCs have a function akin to that of the horn, which enables displacement amplification.

A kind of single-phase full bandgaps phononic crystals and experimental evidence

The exceptional performance of locally resonant phononic crystals (PCs) in vibration attenuation and noise reduction within nuclear power plants has garnered widespread attention in scholarly circles. To address the need for improved predictive accuracy in substrate structures characterized by significant flexibility, a one-dimensional mechanical model rooted in the mass-spring chain paradigm has been established. This model offers a straightforward and accurate means of predicting the lower and upper frequencies of the initial bandgap within locally resonant phononic crystals. Moreover, the dynamic model elucidates modal characteristics and vibrational responses inherent to locally resonant phononic crystals. Utilizing the proposed model, a singular-phase phononic crystal structure boasting full bandgaps has been devised. This structure facilitates the omnidirectional acquisition of locally resonant bandgaps across an exceedingly low-frequency spectrum through the incorporation of cantilever beam elements. Such a design holds immense promise within the realm of large-scale mechanical vibration isolation. As a means of validation, steel samples embodying this phononic crystal model were fabricated. Experimental results demonstrated an insertion loss of approximately 18.67 dB, affirming the vibration isolation efficacy of the singular-phase phononic crystal configuration.

Coupled topological rainbow trapping of elastic waves in two-dimensional phononic crystals

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.

Acoustic analog-to-digital converter using coupled waveguides in phononic crystals

In this research, a novel application as an acoustic analog-to-digital converter (ADC) is introduced, utilizing all-solid phononic crystals. The structure consists of a two-channel directional coupler designed to achieve 2-bit quantization. As the input signal amplitude increases, additional stress is applied to the background, inducing a slight change in the mass density of the phononic crystal structure. This structure is composed of an array of iron scatterers embedded in a polymerization of methyl methacrylate (PMMA) medium, with a selected working frequency of 67.5 kHz. To guide the applied acoustic wave, a directional coupler is employed. In the proposed model, transmission values below 0.3 are interpreted as "0," while values exceeding 0.3 are considered "1." It is crucial that a transmission range of 0.4–0.6 signifies a logical "1" for both active outputs. The fabrication tolerance of the directional coupler rods has been calculated, and the maximum transmission change is equal to 0.03 in a 2 µm changing range around the central radius

Negative elastic wave refraction and focusing regulation of single-phase solid phononic crystals

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.

A novel vibration barrier for low-frequency surface waves in the ground

As for certain engineering scenarios, such as open-air quarries and underground pipeline areas, vibration barriers are in urgent need. However, their design and construction face various challenges, especially for attenuating surface waves with low frequencies. Inspired by the topography of hills and periodic phononic crystal structures, a novel vibration barrier consisting of periodic soil strips is proposed. Firstly, utilizing the finite element method and the theory of periodic structures, the dispersion band diagram is calculated for the periodic soil strips. The corresponding band gap mechanisms are discussed by the displacement field of modes in the lower boundary of band gaps. Besides, a simplified model and a theoretical expression are proposed to analyze the minimum frequency of the band gaps. Through frequency domain analysis, the influence of the damping of soil strips on isolation effects is examined, and the dissipated energy is also quantified using a spatial Fast Fourier Transform. Finally, a comparison of the isolation effect between soil strip barriers and typical trench barriers is conducted. The results show that periodic soil strips can exhibit several band gaps, within which surface waves (SWs) can be effectively isolated. Soil strip barriers exhibit similar or even better vibration isolation effects compared to trench barriers, especially for isolating low-frequency vibrations. This study enhances our understanding of surface wave mitigation using periodic barriers and provides fresh insights for designing seismic metamaterials.

Low-Frequency Bandgap Characterization of a Locally Resonant Pentagonal Phononic Crystal Beam Structure.

This paper proposes a local resonance-type pentagonal phononic crystal beam structure for practical engineering applications to achieve better vibration and noise reduction. The energy band, transmission curve, and displacement field corresponding to the vibration modes of the structure are calculated based on the finite element method and Bloch-Floquet theorem. Furthermore, an analysis is conducted to understand the mechanism behind the generation of bandgaps. The numerical analysis indicates that the pentagonal unit oscillator creates a low-frequency bandgap between 60-70 Hz and 107-130 Hz. Additionally, the pentagonal phononic crystal double-layer beam structure exhibits excellent vibration damping, whereas the single-layer beam has poor vibration damping. The article comparatively analyzes the effects of different parameters on the bandgap range and transmission loss of a pentagonal phononic crystal beam. For instance, increasing the thickness of the lead layer leads to an increase in the width of the bandgap. Similarly, increasing the thickness of the rubber layer, intermediate plate, and total thickness of the phononic crystals results in a bandgap at lower frequencies. By adjusting the parameters, the beam can be optimized for practical engineering purposes.

Buckling-driven piezoelectric defect-induced energy localization and harvesting using a Rubik’s cube-inspired phononic crystal structure

Wireless sensor networks that enable advanced internet of things (IoT) applications have experienced significant development. However, low-power electronics are limited by battery lifetime. Energy harvesting presents a solution for self-powered technologies. Vibration-based energy harvesting technology is one of the effective approaches to convert ambient mechanical energy into electrical energy. Various dynamic oscillating systems have been proposed to investigate the effectiveness of energizing low-power electronic sensor devices for supporting various IoT applications across engineering disciplines. Phononic crystal structures have been implemented in vibrational energy harvesters due to their unique bandgap and wave propagation properties. This work proposes a Rubik’s cube-inspired defective-state locally resonant three-dimensional (3D) phononic crystal with a 5 × 5 × 5 perfect supercell that contains 3D piezoelectric energy harvesting units. The advantage of defect-induced energy localization is utilized to harness vibrational energy. The 3D piezoelectric energy harvesting units are constructed by the buckling-driven assembling principle. Adapting to the low-frequency and broadband characteristics of ambient vibration sources, soft silicone gel is used to encapsulate the buckled 3D piezoelectric units, which are embedded in the 3D cubic phononic crystal to assemble an entire system. The energy harvesting performance of various defective layouts and their defect modes is discussed. The results demonstrate that the harvester functions well under multidirectional, multimodal, and low-frequency conditions. The proposed methodology also offers a new perspective on vibrational energy harvesters for defective phononic crystals with superior working performance.

Experimental design and adaptive modulation of piezoelectric cantilever phononic crystals for vibration attenuation in vehicle subframes

To attenuate the vibrations in the vehicle subframe with changing target frequency, a piezoelectric cantilever phononic crystal (PC) and its adaptive modulation strategy are investigated in this paper. First, based on the cantilever-based PC structure, the bandgap characteristics are obtained by vibration transfer calculation and piezoelectric constitutive modeling. The experimental design of the piezoelectric cantilever PC is further conducted based on the parametric analysis results of structural dimensions and the targeted vibration frequency intervals required by the vehicle subframe. The modal experiments indicate that two local resonant bandgaps and one electromagnetic oscillation bandgap appear in the solved frequency interval, and both of them exhibit excellent consistency with the theoretical calculations. Finally, an adaptive bandgap modulation strategy is proposed by controlling the shunting circuit parameters, and the execution results demonstrate that the PCs employed in the vehicle subframe can effectively achieve vibration attenuation from the powertrain systems. Starting from the experimental design and adaptive modulation of cantilever PCs with piezoelectric materials, this research presents a novel framework for the application of acoustic metamaterials in the vibration mitigation of automotive structures.

An Investigation of the Energy Harvesting Capabilities of a Novel Three-Dimensional Super-Cell Phononic Crystal with a Local Resonance Structure.

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.

Elastic foundation-introduced defective phononic crystals for tunable energy harvesting

Defective phononic crystals offer the advantage of concentrating elastic waves, thereby enhancing the potential for piezoelectric energy harvesting (PEH). However, a key limitation is their reliance on a fixed operating frequency, rendering them susceptible to the prevailing vibration environment. To surmount this constraint, this study introduces a novel approach involving a tunable elastic foundation system for defective phononic crystal structures. The newly developed phononic crystal is fashioned by integrating a periodically elastic foundation beneath a uniform beam. A defect is induced by selectively removing specific elastic foundations and integrating piezoelectric components. Explicit analytical solutions are established through the transfer matrix method and the spectral element method, which are subsequently corroborated via comparison with finite element results. The findings underscore that the periodic elastic foundations impart bandgaps in the elastic wave band structure. The absence of specific elastic foundations results in the emergence of distinct defect modes. Additionally, frequency response analysis exposes the potential for energy enhancement, albeit with inherent variations. Noteworthy is the revelation that manipulating the stiffness of the elastic foundation triggers shifts in the resonant frequency of the output voltage. Therefore, the proposed tunable elastic foundation system exhibits promising potential to engender versatile and adaptive phononic crystal configurations, thereby advancing the domain of PEH.

Research on Fabrication of Phononic Crystal Soft-Supported Graphene Resonator.

In aviation, aerospace, and other fields, nanomechanical resonators could offer excellent sensing performance. Among these, graphene resonators, as a new sensitive unit, are expected to offer very high mass and force sensitivity due to their extremely thin thickness. However, at present, the quality factor of graphene resonators at room temperature is generally low, which limits the performance improvement and further application of graphene resonators. Enhancing the quality factor of graphene resonators has emerged as a pressing research concern. In a previous study, we have proposed a new mechanism to reduce the energy dissipation of graphene resonators by utilizing phononic crystal soft-supported structures. We verified its feasibility through theoretical analysis and simulations. This article focuses on the fabrication of a phononic crystal soft-supported graphene resonator. In order to address the issues of easy fracture, deformation, and low success rate in the fabrication of phononic crystal soft-supported graphene resonators, we have studied key processes for graphene suspension release and focused ion beam etching. Through parameter optimization, finally, we have obtained phononic crystal soft-supported graphene resonators with varying cycles and pore sizes. Finally, we designed an optical excitation and detection platform based on Fabry-Pérot interference principle and explored the impact of laser power and spot size on phononic crystal soft-supported graphene resonators.

Intelligent optimization design of large-scale three-dimensional ultrasonic vibration system

Large-scale three-dimensional ultrasonic vibration systems are susceptible to the influence of coupled vibration, resulting in a series of problems such as increased energy loss, small longitudinal displacement amplitude of the radiation surface, and uneven distribution of longitudinal displacement amplitude, which can seriously affect the working efficiency of ultrasonic processing system. How to effectively control the coupled vibration of large-scale three-dimensional ultrasonic transducer systems and optimize their performance has become an urgent problem in the field of power ultrasound. The research has found that some phononic crystal slots and point defect structures can suppress the lateral vibration of large-scale transducer systems, improve the uniformity of system amplitude distribution, and artificially regulate the performance of large-scale three-dimensional ultrasonic vibration systems by changing the configuration parameters of phononic crystal structures. However, excessive design parameters will inevitably increase the complexity of system design, and, currently, the optimization design of large-scale three-dimensional ultrasonic transducer systems relies on empirical trial and error methods which has low design efficiency and low success rate, and cannot guarantee the system performance. Therefore, in the study, homogeneous dislocations and point defect structures are introduced to optimize the design of large-scale three-dimensional ultrasonic vibration systems. Data analysis techniques are used to evaluate the influences of the configuration of homogeneous dislocations and point defect structures on the longitudinal displacement amplitude, amplitude distribution uniformity, radiated sound power, working bandwidth of the system’s radiation surface. And a predictive model for the performance of large-scale ultrasonic transducer system with homogeneous dislocation structure and near periodic defect structure is established, which can achieve intelligent design of large-scale power ultrasonic transducer system, improve design efficiency and success rate, and reduce the design cost.

Optimization Design of Phononic Crystals Based on BPNN‐MPA in Applied Mathematical Analysis

Traditional finite element analysis methods have the problem of expensive and unstable band structure diagram calculation when generating phononic crystals. Therefore, this study combines back propagation neural networks with ocean predator algorithms to optimize the geometric structure of phononic crystals. The results show that the coefficient of determination for the predicted bandgap width and lower bound of Model 3 is 1.00, which is better than the comparison model. However, Models 2 and 5 have poor predictive performance for bandgap width due to overfitting during actual training. Therefore, after using the ocean predator algorithm for hyperparameter adjustment, it is found that the maximum number of failures in the validation set of Model 5 is 30, the number of hidden layer nodes is 30, and after 500 experiments, the average error of the bandgap width is 5.26%, and the average error of the lower bound of the bandgap is 1.33%. The average error of the bandgap width after hyperparameter adjustment is 4.89%, and the average error of the lower bound of the bandgap is 1.21%, both of which are effectively reduced and better than the comparison model. Overall, the combination model has high computational efficiency and stability in phononic crystal optimization and can be practically applied in the design and optimization of phononic crystal geometric structures.

Mechanical vibration absorber for flexural wave attenuation in multi-materials metastructure

Vibration isolation is a promise to suppress mechanical vibration from a host structure, similarly, a mechanical vibration absorber, a simple but effective device to attenuate flexural wave propagation, which has been implemented in civil and mechanical engineering. This paper presents a type of composite sandwich phononic crystal to attenuate the flexural wave propagation in a beam structure, which can effectively suppress mechanical vibration in a broad band gap by repetitively arranging phononic crystal. First, the elastic wave dispersion characteristic in a composite sandwich beam structure is derived, and a triangular shape phononic crystal for flexural wave attenuation by taking advantage of destructive interference is presented. Then two dimensional phononic crystals are designed by assembling four different unit-cells of metabeam. Finally, numerical experiments are conducted to verify the effectiveness of the proposed mechanical metamaterial absorbers to attenuate flexural wave propagation, the numerical results indicate that the proposed metamaterial is of good performance in mechanical vibration suppression, which can effectively mitigate structure vibration in low-frequency domain than the structure without phononic crystal and single layer metamaterial beam structure. It is the first attempt to design a mechanical metamaterial absorber with the mechanism of destructive interference with composite sandwich phononic crystal.

Multi-Material Radial Phononic Crystals to Improve the Quality Factor of Piezoelectric MEMS Resonators.

In this paper, a multi-material radial phononic crystal (M-RPC) structure is proposed to reduce the anchor-point loss of piezoelectric micro-electro-mechanical system (MEMS) resonators and improve their quality factor. Compared with single-material phononic crystal structures, an M-RPC structure can reduce the strength damage at the anchor point of a resonator due to the etching of the substrate. The dispersion curve and frequency transmission response of the M-RPC structure were calculated by applying the finite element method, and it was shown that the M-RPC structure was more likely to produce a band-gap range with strong attenuation compared with a single-material radial phononic crystal (S-RPC) structure. Then, the effects of different metal-silicon combinations on the band gap of the M-RPC structures were studied, and we found that the largest band-gap range was produced by a Pt and Si combination, and the range was 84.1-118.3 MHz. Finally, the M-RPC structure was applied to a piezoelectric MEMS resonator. The results showed that the anchor quality factor of the M-RPC resonator was increased by 33.5 times compared with a conventional resonator, and the insertion loss was reduced by 53.6%. In addition, the loaded and unloaded quality factors of the M-RPC resonator were improved by 75.7% and 235.0%, respectively, and at the same time, there was no effect on the electromechanical coupling coefficient.