Strong long-wavelength laser pulses enable direct manipulation of atomic lattices for engineering novel quantum states in complex materials.Nonlinear coupling between two infrared-active phonon modes(TO_(1) and TO_(2)...Strong long-wavelength laser pulses enable direct manipulation of atomic lattices for engineering novel quantum states in complex materials.Nonlinear coupling between two infrared-active phonon modes(TO_(1) and TO_(2)),induced by intense terahertz light fields,significantly enhances the amplitude of the TO_(1) mode and facilitates ultrafast control of transient structural distortions.This light-induced distortion reduces the lattice thermal conductivity from 8.1 W·m^(-1)·K^(-1)to 3.0 W·m^(-1)·K^(-1).The reduction originates from the nonlinear coupling,which enhances anharmonic interactions in the lattice potential energy and substantially shortens the phonon lifetime(τ).This work demonstrates a strategy applicable to other perovskite materials and provides a framework for investigating light-induced electrical,optical,and thermodynamic phase transitions.展开更多
Defective phononic crystals(PnCs)have enabled spatial localization and quantitative amplification of elastic wave energy.Most previous research has focused on applications such as narrow-bandpass filters,ultrasonic se...Defective phononic crystals(PnCs)have enabled spatial localization and quantitative amplification of elastic wave energy.Most previous research has focused on applications such as narrow-bandpass filters,ultrasonic sensors,and piezoelectric energy harvesters,typically operating under the assumption of an external elastic wave incidence.Recently,a novel approach that uses defective PnCs as ultrasonic actuators to generate amplified waves has emerged.However,the existing studies are limited to the generation of either longitudinal or bending waves,with no research addressing the concurrent generation of both.Hence,this paper proposes a straightforward methodology for the concurrent generation and amplification of both wave types utilizing defect modes at independent defect-band frequencies.Bimorph piezoelectric elements are attached to the defect,with each element connected to independent external voltage sources.By precisely adjusting the magnitude and temporal phase differences between the voltage sources,concurrently amplified wave generation is achieved.The paper highlights the advantages of the proposed analytical model.This model is both computationally time-efficient and accurate,in comparison with the COMSOL simulation results.For instance,in case studies,the analytical model reduces the computational time from one hour to mere seconds,while maintaining acceptable error rates of 1%in peak frequencies.This concurrent wave-generation methodology opens new avenues for applications in rotating machinery fault diagnosis,structural health monitoring,and medical imaging.展开更多
This paper presents a locally resonant phononic crystal with excellent noise reduction in the low-frequency range as a soundproofing plate in mufflers.A locally resonant phononic crystal is established,and the bandgap...This paper presents a locally resonant phononic crystal with excellent noise reduction in the low-frequency range as a soundproofing plate in mufflers.A locally resonant phononic crystal is established,and the bandgap range of the phononic crystal is analyzed by using COMSOL software.Taking the partition plate in the muffler as the object,the acoustic-solid coupling is studied to analyze the sound insulation characteristics of the locally resonant phononic crystal.A phononic crystal plate-like structure is established to analyze its noise reduction performance in the muffler.The results indicate that the locally resonant phononic crystal exhibits favorable low-frequency sound insulation performance within a bandgap range below 200 Hz.At 160 Hz,the noise reduction is 15 dB higher than that of ordinary partition plates.As the number of layers of the phononic crystal plate increases,its noise reduction effect gradually enhances,while the magnitude of the noise reduction increment tends to diminish.At 160 Hz,the single-,double-and triple-layer plates achieve peak reductions of 47,53 and 57 dB,respectively.Compared with the double-layer phononic crystal plate,the composite of the locally resonant phononic crystal plate and the steel plate has an average noise reduction of 5 dB higher.Through research and analysis of the composite locally resonant phononic crystal plates,more feasible combined structures can be provided for future muffler structural design.展开更多
To analyze the band gap characteristics of phononic crystals,a two-dimensional phononic crystal plate model with an elastic foundation was first established.The plane wave expansion method was used to compute the disp...To analyze the band gap characteristics of phononic crystals,a two-dimensional phononic crystal plate model with an elastic foundation was first established.The plane wave expansion method was used to compute the dispersion curves of this phononic crystal model,and the results were compared with those from the finite element method to verify their accuracy.Subsequently,a parameter study explored the effects of the elastic foundation coeffi-cient and coverage ratio on the band gap.The results indicate that as the coverage ratio of the elastic foundation increases,the band gap significantly expands,reaching its maximum value at 100%coverage.Additionally,as the elastic foundation stiffness increases,the band gap gradually widens and converges toward fixed boundary conditions.The study also investigated the band gap of phononic crystal plates with defects,finding that the vibrational energy concentrates at the defect unit cell.Furthermore,the defect band frequency can be effectively modulated by adjusting the coefficient of the elastic foundation,providing a theoretical basis for achieving efficient energy conversion.展开更多
In this paper,the dispersion,attenuation,and bandgap characteristics of in-plane coupled Bloch waves in one-dimensional piezoelectric semiconductor(PSC)phononic crystals are investigated,emphasizing the influence of p...In this paper,the dispersion,attenuation,and bandgap characteristics of in-plane coupled Bloch waves in one-dimensional piezoelectric semiconductor(PSC)phononic crystals are investigated,emphasizing the influence of positive-negative(PN)junctions.Unlike piezoelectric phononic crystals,the coupled Bloch waves in PSC phononic crystals are attenuated due to their semiconductor properties,and thus the solution of Bloch waves becomes more complicated.The transfer matrix of the phononic crystal unit cell is obtained using the state transfer equation.By applying the Bloch theorem for periodic structures,the dispersion relation of the coupled Bloch waves is derived,and the dispersion,attenuation,and bandgap are obtained in the complex wave number domain.It is found that the influence of the PN junction cannot be neglected.Moreover,the effects of the PN junction under different apparent wave numbers and steady-state carrier concentrations are provided.This indicates the feasibility of adjusting the propagation characteristics of Bloch waves through the regulation of the PN heterojunction.展开更多
Two-dimensional phononic crystal(PnC)slabs have shown advantages in enhancing the quality factors Q of piezoelectric laterally vibrating resonators(LVRs)through topology optimization.However,the narrow geometries of m...Two-dimensional phononic crystal(PnC)slabs have shown advantages in enhancing the quality factors Q of piezoelectric laterally vibrating resonators(LVRs)through topology optimization.However,the narrow geometries of most topology-optimized silicon–air 2D PnC slabs face significant fabrication challenges owing to restricted etching precision,and the anisotropic nature of silicon is frequently overlooked.To address these issues,this study employs the finite element method with appropriate discretization numbers and the genetic algorithm to optimize the structures and geometries of 2D silicon–air PnC slabs.The optimized square-lattice PnC slabs,featuring a rounded-cross structure oriented along the`110e directions of silicon,achieve an impressive relative bandgap(RBG)width of 82.2%for in-plane modes.When further tilted by 15° from the (100) directions within the(001)plane,the optimal RBG width is expanded to 91.4%.We fabricate and characterize thin-film piezoelectric-on-silicon LVRs,with or without optimized 2D PnC slabs.The presence of PnC slabs around anchors increases the series and parallel quality factors Q_(s) and Q_(p) from 2240 to 7118 and from 2237 to 7501,respectively,with the PnC slabs oriented along the`110e directions of silicon.展开更多
Enhancing the vibration resistance of micro-electro-mechanical systems(MEMS)resonators in complex environments is a critical issue that urgently needs to be addressed.This paper presents a chip-scale locally resonant ...Enhancing the vibration resistance of micro-electro-mechanical systems(MEMS)resonators in complex environments is a critical issue that urgently needs to be addressed.This paper presents a chip-scale locally resonant phononic crystal(LRPnC)plate based on a folded helical beam structure.Through finite element simulation and theoretical analysis,the bandgap characteristics and vibration suppression mechanisms of this structure were thoroughly investigated.The results show that the structure exhibits a complete bandgap in the frequency range of 9.867-14.605 kHz,and the bandgap can be effectively tuned by adjusting the structural parameters.Based on this,the influence of the number of unit cell layers on the vibration reduction performance was further studied,and a finite periodic LRPnC plate was constructed.Numerical studies have shown that the LRPnC plate can achieve more than-30 dB of vibration attenuation within the bandgap and effectively suppress y-direction coupling vibrations caused by x-direction propagating waves.In addition,its chip-scale size and planar structure design provide new ideas and methods for the engineering application of phononic crystal technology in the field of MEMS vibration isolation.展开更多
By using the plane-wave-expansion method, the band structure of three-dimension phononic crystals was calculated, in which the cuboid scatterers were arranged in a host with a face-centered-cubic （FCC） structure.The...By using the plane-wave-expansion method, the band structure of three-dimension phononic crystals was calculated, in which the cuboid scatterers were arranged in a host with a face-centered-cubic （FCC） structure.The influences of a few factors such as the component materials, the filling fraction of scatterers and the ratio （RHL） of the scatterer＇s height to its length on the band-gaps of phononic crystals were investigated.It is found that in the three-dimension solid phononic crystals with FCC structure, the optimum case to obtain band-gaps is to embed high-velocity and high-density scatterers in a low-velocity and low-density host. The maximum value of band-gap can be obtained when the filling fraction is in the middle value. It is also found that the symmetry of the scatterers strongly influences the band-gaps. For RHL＞1, the width of the band-gap decreases as RHL increases. On the contrary, the width of the band-gap increases with the increase of RHL when RHL is smaller than 1.展开更多
The band structures of both in-plane and anti-plane elastic waves propagating in two-dimensional ordered and disordered （in one direction） phononic crystals are studied in this paper. The localization of wave propag...The band structures of both in-plane and anti-plane elastic waves propagating in two-dimensional ordered and disordered （in one direction） phononic crystals are studied in this paper. The localization of wave propagation due to random disorder is discussed by introducing the concept of the localization factor that is calculated by the plane-wave-based transfer-matrix method. By treating the quasi-periodicity as the deviation from the periodicity in a special way, two kinds of quasi phononic crystal that has quasi-periodicity （Fibonacci sequence） in one direction and translational symmetry in the other direction are considered and the band structures are characterized by using localization factors. The results show that the localization factor is an effective parameter in characterizing the band gaps of two-dimensional perfect, randomly disordered and quasi-periodic phononic crystals. Band structures of the phononic crystals can be tuned by different random disorder or changing quasi-periodic parameters. The quasi phononic crystals exhibit more band gaps with narrower width than the ordered and randomly disordered systems.展开更多
Absolute phononic band gaps can be substantially improved in two-dimensional lattices by using a symmetry reduction approach. In this paper, the propagation of elastic waves in a two-dirnensional hybrid triangular lat...Absolute phononic band gaps can be substantially improved in two-dimensional lattices by using a symmetry reduction approach. In this paper, the propagation of elastic waves in a two-dirnensional hybrid triangular lattice structure consisting of stainless steel cylinders in air is investigated theoretically. The band structure is calculated with the plane wave expansion （PWE） method. The hybrid triangular Bravais lattice is formed by two kinds of triangular lattices. Different from ordinary triangular lattices, the band gap opens at low frequency （between the first and the second bands） regime because of lifting the bands degeneracy at high symmetry points of the Brillouin zone. The location and width of the band gaps can be tuned by the position of the additional rods.展开更多
Based on a better understanding of the lattice vibration modes, two simple spring-mass models are constructed in order to evaluate the frequencies on both the lower and upper edges of the lowest locally resonant band ...Based on a better understanding of the lattice vibration modes, two simple spring-mass models are constructed in order to evaluate the frequencies on both the lower and upper edges of the lowest locally resonant band gaps of the ternary locally resonant phononic crystals. The parameters of the models are given in a reasonable way based on the physical insight into the band gap mechanism. Both the lumped-mass methods and our models are used in the study of the influences of structural and the material parameters on frequencies on both edges of the lowest gaps in the ternary locally resonant phononic crystals. The analytical evaluations with our models and the theoretical predictions with the lumped-mass method are in good agreement with each other. The newly proposed heuristic models are helpful for a better understanding of the locally resonant band gap mechanism, as well as more accurate evaluation of the band edge frequencies.展开更多
Based on the variational theory, a wavelet-based numerical method is developed to calculate the defect states of acoustic waves in two-dimensional phononic crystals with point and line defects. The supercell technique...Based on the variational theory, a wavelet-based numerical method is developed to calculate the defect states of acoustic waves in two-dimensional phononic crystals with point and line defects. The supercell technique is applied. By expanding the displacement field and the material constants （mass density and elastic stiffness） in periodic wavelets, the explicit formulations of an eigenvalue problem for the plane harmonic bulk waves in such a phononic structure are derived. The point and line defect states in solid-liquid and solid-solid systems are calculated. Comparisons of the present results with those measured experimentally or those from the plane wave expansion method show that the present method can yield accurate results with faster convergence and less computing time.展开更多
Periodic arrays of negative capacitance shunted piezoelectric patches are employed to control the band gaps of phononic beams. The location and the extent of induced band gap depend on the mismatch in impedance genera...Periodic arrays of negative capacitance shunted piezoelectric patches are employed to control the band gaps of phononic beams. The location and the extent of induced band gap depend on the mismatch in impedance generated by each patch. The total impedance mismatch is determined by the added mass and stiffness of each patch as well as the shunting electrical impedance. Therefore, the band gap of the shunted phononic beam can be actively tuned by appropriately selecting the value of negative capacitance. The control of the band gap of phononic beam with negative capacitive shunt is demonstrated numerically by employing transfer matrix method. The result reveals that using negative capacitive shunt to tune the band gap is effective.展开更多
In this paper, a method based on the Dirichlet- to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses...In this paper, a method based on the Dirichlet- to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses the scattered fields in a unit cell as the cylindrical wave expansions and imposes the Bloch condition on the boundary of the unit cell. The Dirichlet-to-Neumann （DtN） map is applied to obtain a linear eigenvalue equation, from which the Bloch wave vectors along the irreducible Brillouin zone are calculated for a given frequency. Compared with other methods, the present method is memory-saving and time-saving. It can yield accurate results with fast convergence for various material combinations including those with large acoustic mismatch without extra computational cost. The method is also efficient for mixed fluid-solid systems because it considers the different wave modes in the fluid and solid as well as the proper fluid-solid interface condition.展开更多
In this paper, the elastic wave propagation in a two-dimensional piezoelectric phononic crystal is studied by considering the mechanic-electric coupling. The generalized eigenvalue equation is obtained by the relation...In this paper, the elastic wave propagation in a two-dimensional piezoelectric phononic crystal is studied by considering the mechanic-electric coupling. The generalized eigenvalue equation is obtained by the relation of the mechanic and electric fields as well as the Bloch-Floquet theorem. The band structures of both the in-plane and anti-plane modes are calculated for a rectangular lattice by the planewave expansion method. The effects of the lattice constant ratio and the piezoelectricity with different filling fractions are analyzed. The results show that the largest gap width is not always obtained for a square lattice. In some situations, a rectangular lattice may generate larger gaps. The band gap characteristics are influenced obviously by the piezoelectricity with the larger lattice constant ratios and the filling fractions.展开更多
Periodic arrays of hybrid-shunted piezoelectric patches are used to control the band-gaps of phononic metamaterial beams. Passive resistive-inductive （RL） shunting circuits can produce a narrow resonant band-gap （R...Periodic arrays of hybrid-shunted piezoelectric patches are used to control the band-gaps of phononic metamaterial beams. Passive resistive-inductive （RL） shunting circuits can produce a narrow resonant band-gap （RG）, and active negative capacitive （NC） shunting circuits can broaden the Bragg band-gaps （BGs）. In this article, active NC shunting circuits and passive resonant RL shunting circuits are connected to the same piezoelectric patches in parallel, which are usually called hybrid shunting circuits, to control the location and the extent of the band-gaps. A super-wide coupled band-gap is generated when the coupling between RG and the BG occurs. The attenuation constant of the infinite periodic structure is predicted by the transfer matrix method, which is compared with the vibration transmittance of a finite periodic structure calculated by the finite element method. Numerical results show that the hybrid-shunting circuits can make the band-gaps wider by appropriately selecting the inductances, negative capacitances, and resistances.展开更多
The propagation characteristics of flexural waves in periodic grid structures designed with the idea of phononic crystals are investigated by combining the Bloch theorem with the finite element method. This combined a...The propagation characteristics of flexural waves in periodic grid structures designed with the idea of phononic crystals are investigated by combining the Bloch theorem with the finite element method. This combined analysis yields phase constant surfaces, which predict the location and the extension of band gaps, as well as the directions and the regions of wave propagation at assigned frequencies. The predictions are validated by computation and experimental analysis of the harmonic responses of a finite structure with 11 × 11 unit cells. The flexural wave is localized at the point of excitation in band gaps, while the directional behaviour occurs at particular frequencies in pass bands. These studies provide guidelines to designing periodic structures for vibration attenuation.展开更多
The wave propagation is studied in two-dimensional disordered piezoelectric phononic crystals using the finite-difference time-domain （FDTD） method. For different cases of disorder, the transmission coefficients are...The wave propagation is studied in two-dimensional disordered piezoelectric phononic crystals using the finite-difference time-domain （FDTD） method. For different cases of disorder, the transmission coefficients are calculated. The influences of disorders on band gaps are investigated. The results show that the disorder in the piezoelectric phononic crystals has more significant influences on the band gap in the low frequency regions than in the high frequency ones. The relation between the width of band gap and the direction of position disorder is also discussed. When the position disorder is along the direction perpendicular to the wave transmission, the piezoelectric phononic crystals have wider band gaps at low frequency regions than the case of position disorder being along the wave transmission direction. It can also be found that the effect of. size disorder on band gaps is analogous to that of location disorder. When the perturbation coefficient is big, it has more pronounced effects on the pass bands in the piezoelectric phononic crystals with both size and location disorders than in the piezoelectric phononic crystals with single disorder. In higher frequency regions the piezoelectric effect reduces the transmission coefficients. But for larger disorder degree, the effects of the piezoelectricity will be reduced.展开更多
The bandgap,an important characteristic of the periodic structure,is dispersionrelated,which can be designed by tailoring the layout of materials within the periodic microstructures.A typical example of a periodic str...The bandgap,an important characteristic of the periodic structure,is dispersionrelated,which can be designed by tailoring the layout of materials within the periodic microstructures.A typical example of a periodic structure is phononic crystals (PnCs),which are traditionally fabricated from two-phase materials.Herein,we investigate the topologies of periodic three-phase PnCs.The microstructures of the three-phase PnCs are optimized using a two-stage genetic algorithm,and three case studies are proposed to obtain the following:(1)the maximum relative bandgap width,(2)the maximum absolute bandgap width,and (3)the max- imum bandgap at a specified frequency.More importantly,the three-phase material provides significant advantages compared to the typical two-phase materials,such as a low-frequency bandgap.This research is expected to contribute highly to vibration and noise isolation,elastic wave filters,and acoustic devices.展开更多
A folding beam-type piezoelectric phononic crystal model is proposed to isolate vibration. Two piezoelectric bimorphs are joined by two masses as a folding structure to comprise each unit cell of the piezoelectric pho...A folding beam-type piezoelectric phononic crystal model is proposed to isolate vibration. Two piezoelectric bimorphs are joined by two masses as a folding structure to comprise each unit cell of the piezoelectric phononic crystal. Each bimorph is connected independently by a resistive-inductive resonant shunting circuit. The folding structure extends the propagation path of elastic waves, while its structure size remains quite small. Propagation of coupled extension-flexural elastic waves is studied by the classical laminated beam theory and transfer matrix method. The theoretical model is further verified with the finite element method(FEM). The effects of geometrical and circuit parameters on the band gaps are analyzed. With only 4 unit cells, the folding beam-type piezoelectric phononic crystal generates two Bragg band gaps of 369 Hz to1 687 Hz and 2 127 Hz to 4 000 Hz. In addition, between these two Bragg band gaps, a locally resonant band gap is induced by resonant shunting circuits. Appropriate circuit parameters are used to join these two Bragg band gaps by the locally resonant band gap.Thus, a low-frequency and broad band gap of 369 Hz to 4 000 Hz is obtained.展开更多
基金Project supported by the National Key Research and Development Program of China(Grant No.2024YFF0508503)。
文摘Strong long-wavelength laser pulses enable direct manipulation of atomic lattices for engineering novel quantum states in complex materials.Nonlinear coupling between two infrared-active phonon modes(TO_(1) and TO_(2)),induced by intense terahertz light fields,significantly enhances the amplitude of the TO_(1) mode and facilitates ultrafast control of transient structural distortions.This light-induced distortion reduces the lattice thermal conductivity from 8.1 W·m^(-1)·K^(-1)to 3.0 W·m^(-1)·K^(-1).The reduction originates from the nonlinear coupling,which enhances anharmonic interactions in the lattice potential energy and substantially shortens the phonon lifetime(τ).This work demonstrates a strategy applicable to other perovskite materials and provides a framework for investigating light-induced electrical,optical,and thermodynamic phase transitions.
基金supported by the Basic Science Research Program through the National Research Foundation of Korea,funded by the Ministry of Education(No.2022R1I1A1A01056406)。
文摘Defective phononic crystals(PnCs)have enabled spatial localization and quantitative amplification of elastic wave energy.Most previous research has focused on applications such as narrow-bandpass filters,ultrasonic sensors,and piezoelectric energy harvesters,typically operating under the assumption of an external elastic wave incidence.Recently,a novel approach that uses defective PnCs as ultrasonic actuators to generate amplified waves has emerged.However,the existing studies are limited to the generation of either longitudinal or bending waves,with no research addressing the concurrent generation of both.Hence,this paper proposes a straightforward methodology for the concurrent generation and amplification of both wave types utilizing defect modes at independent defect-band frequencies.Bimorph piezoelectric elements are attached to the defect,with each element connected to independent external voltage sources.By precisely adjusting the magnitude and temporal phase differences between the voltage sources,concurrently amplified wave generation is achieved.The paper highlights the advantages of the proposed analytical model.This model is both computationally time-efficient and accurate,in comparison with the COMSOL simulation results.For instance,in case studies,the analytical model reduces the computational time from one hour to mere seconds,while maintaining acceptable error rates of 1%in peak frequencies.This concurrent wave-generation methodology opens new avenues for applications in rotating machinery fault diagnosis,structural health monitoring,and medical imaging.
基金National Natural Science Foundation of China(No.51705545)。
文摘This paper presents a locally resonant phononic crystal with excellent noise reduction in the low-frequency range as a soundproofing plate in mufflers.A locally resonant phononic crystal is established,and the bandgap range of the phononic crystal is analyzed by using COMSOL software.Taking the partition plate in the muffler as the object,the acoustic-solid coupling is studied to analyze the sound insulation characteristics of the locally resonant phononic crystal.A phononic crystal plate-like structure is established to analyze its noise reduction performance in the muffler.The results indicate that the locally resonant phononic crystal exhibits favorable low-frequency sound insulation performance within a bandgap range below 200 Hz.At 160 Hz,the noise reduction is 15 dB higher than that of ordinary partition plates.As the number of layers of the phononic crystal plate increases,its noise reduction effect gradually enhances,while the magnitude of the noise reduction increment tends to diminish.At 160 Hz,the single-,double-and triple-layer plates achieve peak reductions of 47,53 and 57 dB,respectively.Compared with the double-layer phononic crystal plate,the composite of the locally resonant phononic crystal plate and the steel plate has an average noise reduction of 5 dB higher.Through research and analysis of the composite locally resonant phononic crystal plates,more feasible combined structures can be provided for future muffler structural design.
基金The National Natural Science Foundation of China(No.12002086)。
文摘To analyze the band gap characteristics of phononic crystals,a two-dimensional phononic crystal plate model with an elastic foundation was first established.The plane wave expansion method was used to compute the dispersion curves of this phononic crystal model,and the results were compared with those from the finite element method to verify their accuracy.Subsequently,a parameter study explored the effects of the elastic foundation coeffi-cient and coverage ratio on the band gap.The results indicate that as the coverage ratio of the elastic foundation increases,the band gap significantly expands,reaching its maximum value at 100%coverage.Additionally,as the elastic foundation stiffness increases,the band gap gradually widens and converges toward fixed boundary conditions.The study also investigated the band gap of phononic crystal plates with defects,finding that the vibrational energy concentrates at the defect unit cell.Furthermore,the defect band frequency can be effectively modulated by adjusting the coefficient of the elastic foundation,providing a theoretical basis for achieving efficient energy conversion.
基金Project supported by the National Natural Science Foundation of China(Nos.11872105,12072022,11911530176,and 12202039)。
文摘In this paper,the dispersion,attenuation,and bandgap characteristics of in-plane coupled Bloch waves in one-dimensional piezoelectric semiconductor(PSC)phononic crystals are investigated,emphasizing the influence of positive-negative(PN)junctions.Unlike piezoelectric phononic crystals,the coupled Bloch waves in PSC phononic crystals are attenuated due to their semiconductor properties,and thus the solution of Bloch waves becomes more complicated.The transfer matrix of the phononic crystal unit cell is obtained using the state transfer equation.By applying the Bloch theorem for periodic structures,the dispersion relation of the coupled Bloch waves is derived,and the dispersion,attenuation,and bandgap are obtained in the complex wave number domain.It is found that the influence of the PN junction cannot be neglected.Moreover,the effects of the PN junction under different apparent wave numbers and steady-state carrier concentrations are provided.This indicates the feasibility of adjusting the propagation characteristics of Bloch waves through the regulation of the PN heterojunction.
基金supported by the National Natural Science Foundation of China(Grant No.52175552)the National Key RD Program of China(Grant Nos.2022YFB3205400 and 2022YFB3204300).
文摘Two-dimensional phononic crystal(PnC)slabs have shown advantages in enhancing the quality factors Q of piezoelectric laterally vibrating resonators(LVRs)through topology optimization.However,the narrow geometries of most topology-optimized silicon–air 2D PnC slabs face significant fabrication challenges owing to restricted etching precision,and the anisotropic nature of silicon is frequently overlooked.To address these issues,this study employs the finite element method with appropriate discretization numbers and the genetic algorithm to optimize the structures and geometries of 2D silicon–air PnC slabs.The optimized square-lattice PnC slabs,featuring a rounded-cross structure oriented along the`110e directions of silicon,achieve an impressive relative bandgap(RBG)width of 82.2%for in-plane modes.When further tilted by 15° from the (100) directions within the(001)plane,the optimal RBG width is expanded to 91.4%.We fabricate and characterize thin-film piezoelectric-on-silicon LVRs,with or without optimized 2D PnC slabs.The presence of PnC slabs around anchors increases the series and parallel quality factors Q_(s) and Q_(p) from 2240 to 7118 and from 2237 to 7501,respectively,with the PnC slabs oriented along the`110e directions of silicon.
基金supported by National Natural Science Foundation of China(No.62271262).
文摘Enhancing the vibration resistance of micro-electro-mechanical systems(MEMS)resonators in complex environments is a critical issue that urgently needs to be addressed.This paper presents a chip-scale locally resonant phononic crystal(LRPnC)plate based on a folded helical beam structure.Through finite element simulation and theoretical analysis,the bandgap characteristics and vibration suppression mechanisms of this structure were thoroughly investigated.The results show that the structure exhibits a complete bandgap in the frequency range of 9.867-14.605 kHz,and the bandgap can be effectively tuned by adjusting the structural parameters.Based on this,the influence of the number of unit cell layers on the vibration reduction performance was further studied,and a finite periodic LRPnC plate was constructed.Numerical studies have shown that the LRPnC plate can achieve more than-30 dB of vibration attenuation within the bandgap and effectively suppress y-direction coupling vibrations caused by x-direction propagating waves.In addition,its chip-scale size and planar structure design provide new ideas and methods for the engineering application of phononic crystal technology in the field of MEMS vibration isolation.
基金This work was supported by the Natural Science Foundation of Hu＇nan Province （Grant No. 00JJY2072） the Foundation of Educational Committee of Hu＇nan Province （Grant No. 01B019）.
文摘By using the plane-wave-expansion method, the band structure of three-dimension phononic crystals was calculated, in which the cuboid scatterers were arranged in a host with a face-centered-cubic （FCC） structure.The influences of a few factors such as the component materials, the filling fraction of scatterers and the ratio （RHL） of the scatterer＇s height to its length on the band-gaps of phononic crystals were investigated.It is found that in the three-dimension solid phononic crystals with FCC structure, the optimum case to obtain band-gaps is to embed high-velocity and high-density scatterers in a low-velocity and low-density host. The maximum value of band-gap can be obtained when the filling fraction is in the middle value. It is also found that the symmetry of the scatterers strongly influences the band-gaps. For RHL＞1, the width of the band-gap decreases as RHL increases. On the contrary, the width of the band-gap increases with the increase of RHL when RHL is smaller than 1.
基金supported by the National Natural Science Foundation of China(No.10632020).
文摘The band structures of both in-plane and anti-plane elastic waves propagating in two-dimensional ordered and disordered （in one direction） phononic crystals are studied in this paper. The localization of wave propagation due to random disorder is discussed by introducing the concept of the localization factor that is calculated by the plane-wave-based transfer-matrix method. By treating the quasi-periodicity as the deviation from the periodicity in a special way, two kinds of quasi phononic crystal that has quasi-periodicity （Fibonacci sequence） in one direction and translational symmetry in the other direction are considered and the band structures are characterized by using localization factors. The results show that the localization factor is an effective parameter in characterizing the band gaps of two-dimensional perfect, randomly disordered and quasi-periodic phononic crystals. Band structures of the phononic crystals can be tuned by different random disorder or changing quasi-periodic parameters. The quasi phononic crystals exhibit more band gaps with narrower width than the ordered and randomly disordered systems.
基金supported by the National Natural Science Foundation of China(No.10632020).
文摘Absolute phononic band gaps can be substantially improved in two-dimensional lattices by using a symmetry reduction approach. In this paper, the propagation of elastic waves in a two-dirnensional hybrid triangular lattice structure consisting of stainless steel cylinders in air is investigated theoretically. The band structure is calculated with the plane wave expansion （PWE） method. The hybrid triangular Bravais lattice is formed by two kinds of triangular lattices. Different from ordinary triangular lattices, the band gap opens at low frequency （between the first and the second bands） regime because of lifting the bands degeneracy at high symmetry points of the Brillouin zone. The location and width of the band gaps can be tuned by the position of the additional rods.
基金Project supported by the National Natural Science Foundation of China （Grant No 50575222） and the State Key Development Program for Basic Research of China （Grant No 51307）.
文摘Based on a better understanding of the lattice vibration modes, two simple spring-mass models are constructed in order to evaluate the frequencies on both the lower and upper edges of the lowest locally resonant band gaps of the ternary locally resonant phononic crystals. The parameters of the models are given in a reasonable way based on the physical insight into the band gap mechanism. Both the lumped-mass methods and our models are used in the study of the influences of structural and the material parameters on frequencies on both edges of the lowest gaps in the ternary locally resonant phononic crystals. The analytical evaluations with our models and the theoretical predictions with the lumped-mass method are in good agreement with each other. The newly proposed heuristic models are helpful for a better understanding of the locally resonant band gap mechanism, as well as more accurate evaluation of the band edge frequencies.
基金the National Natural Science Foundation of China(No.10632020)the German Research Foundation(No.ZH 15/11-1)jointly by the China Scholarship Council and the German Academic Exchange Service(No.D/08/01795).
文摘Based on the variational theory, a wavelet-based numerical method is developed to calculate the defect states of acoustic waves in two-dimensional phononic crystals with point and line defects. The supercell technique is applied. By expanding the displacement field and the material constants （mass density and elastic stiffness） in periodic wavelets, the explicit formulations of an eigenvalue problem for the plane harmonic bulk waves in such a phononic structure are derived. The point and line defect states in solid-liquid and solid-solid systems are calculated. Comparisons of the present results with those measured experimentally or those from the plane wave expansion method show that the present method can yield accurate results with faster convergence and less computing time.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.50875255 and 10902123)
文摘Periodic arrays of negative capacitance shunted piezoelectric patches are employed to control the band gaps of phononic beams. The location and the extent of induced band gap depend on the mismatch in impedance generated by each patch. The total impedance mismatch is determined by the added mass and stiffness of each patch as well as the shunting electrical impedance. Therefore, the band gap of the shunted phononic beam can be actively tuned by appropriately selecting the value of negative capacitance. The control of the band gap of phononic beam with negative capacitive shunt is demonstrated numerically by employing transfer matrix method. The result reveals that using negative capacitive shunt to tune the band gap is effective.
基金supported by the National Natural Science Foundation of China(51178037,10632020)the 973 State Key Development Program for Basic Research of China(2010CB732104)
文摘In this paper, a method based on the Dirichlet- to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses the scattered fields in a unit cell as the cylindrical wave expansions and imposes the Bloch condition on the boundary of the unit cell. The Dirichlet-to-Neumann （DtN） map is applied to obtain a linear eigenvalue equation, from which the Bloch wave vectors along the irreducible Brillouin zone are calculated for a given frequency. Compared with other methods, the present method is memory-saving and time-saving. It can yield accurate results with fast convergence for various material combinations including those with large acoustic mismatch without extra computational cost. The method is also efficient for mixed fluid-solid systems because it considers the different wave modes in the fluid and solid as well as the proper fluid-solid interface condition.
基金the National Natural Science Foundation of China (10672017 and 10632020)
文摘In this paper, the elastic wave propagation in a two-dimensional piezoelectric phononic crystal is studied by considering the mechanic-electric coupling. The generalized eigenvalue equation is obtained by the relation of the mechanic and electric fields as well as the Bloch-Floquet theorem. The band structures of both the in-plane and anti-plane modes are calculated for a rectangular lattice by the planewave expansion method. The effects of the lattice constant ratio and the piezoelectricity with different filling fractions are analyzed. The results show that the largest gap width is not always obtained for a square lattice. In some situations, a rectangular lattice may generate larger gaps. The band gap characteristics are influenced obviously by the piezoelectricity with the larger lattice constant ratios and the filling fractions.
基金supported by the National Natural Science Foundation of China(Grant Nos.51275519 and 51175501)
文摘Periodic arrays of hybrid-shunted piezoelectric patches are used to control the band-gaps of phononic metamaterial beams. Passive resistive-inductive （RL） shunting circuits can produce a narrow resonant band-gap （RG）, and active negative capacitive （NC） shunting circuits can broaden the Bragg band-gaps （BGs）. In this article, active NC shunting circuits and passive resonant RL shunting circuits are connected to the same piezoelectric patches in parallel, which are usually called hybrid shunting circuits, to control the location and the extent of the band-gaps. A super-wide coupled band-gap is generated when the coupling between RG and the BG occurs. The attenuation constant of the infinite periodic structure is predicted by the transfer matrix method, which is compared with the vibration transmittance of a finite periodic structure calculated by the finite element method. Numerical results show that the hybrid-shunting circuits can make the band-gaps wider by appropriately selecting the inductances, negative capacitances, and resistances.
基金Project supported by the National Natural Science Foundation of China (Grant No 50875255)
文摘The propagation characteristics of flexural waves in periodic grid structures designed with the idea of phononic crystals are investigated by combining the Bloch theorem with the finite element method. This combined analysis yields phase constant surfaces, which predict the location and the extension of band gaps, as well as the directions and the regions of wave propagation at assigned frequencies. The predictions are validated by computation and experimental analysis of the harmonic responses of a finite structure with 11 × 11 unit cells. The flexural wave is localized at the point of excitation in band gaps, while the directional behaviour occurs at particular frequencies in pass bands. These studies provide guidelines to designing periodic structures for vibration attenuation.
基金supported by the National Natural Science Foundation of China(Nos.10672017 and 10632020).supports provided by the China Postdoctoral Science Foundation,Heilongjiang Province Postdoctoral Science Foundation
文摘The wave propagation is studied in two-dimensional disordered piezoelectric phononic crystals using the finite-difference time-domain （FDTD） method. For different cases of disorder, the transmission coefficients are calculated. The influences of disorders on band gaps are investigated. The results show that the disorder in the piezoelectric phononic crystals has more significant influences on the band gap in the low frequency regions than in the high frequency ones. The relation between the width of band gap and the direction of position disorder is also discussed. When the position disorder is along the direction perpendicular to the wave transmission, the piezoelectric phononic crystals have wider band gaps at low frequency regions than the case of position disorder being along the wave transmission direction. It can also be found that the effect of. size disorder on band gaps is analogous to that of location disorder. When the perturbation coefficient is big, it has more pronounced effects on the pass bands in the piezoelectric phononic crystals with both size and location disorders than in the piezoelectric phononic crystals with single disorder. In higher frequency regions the piezoelectric effect reduces the transmission coefficients. But for larger disorder degree, the effects of the piezoelectricity will be reduced.
基金National Natural Science Foundation of China (Nos.11672187, 11302135,11502149and 51308357)Natural Science Foundation of Liaoning Province (Nos.201602572,201602573and 201602627)+1 种基金and Program for Liaoning Excellent Talents in University (LNET,No.LJQ2014019)The financial contri- butions are gratefully acknowledged.
文摘The bandgap,an important characteristic of the periodic structure,is dispersionrelated,which can be designed by tailoring the layout of materials within the periodic microstructures.A typical example of a periodic structure is phononic crystals (PnCs),which are traditionally fabricated from two-phase materials.Herein,we investigate the topologies of periodic three-phase PnCs.The microstructures of the three-phase PnCs are optimized using a two-stage genetic algorithm,and three case studies are proposed to obtain the following:(1)the maximum relative bandgap width,(2)the maximum absolute bandgap width,and (3)the max- imum bandgap at a specified frequency.More importantly,the three-phase material provides significant advantages compared to the typical two-phase materials,such as a low-frequency bandgap.This research is expected to contribute highly to vibration and noise isolation,elastic wave filters,and acoustic devices.
基金Project supported by the National Natural Science Foundation of China(Nos.11272126,51435006,and 51121002)the Fundamental Research Funds for the Central Universities(Nos.HUST:2016JCTD114 and HUST:2015TS121)
文摘A folding beam-type piezoelectric phononic crystal model is proposed to isolate vibration. Two piezoelectric bimorphs are joined by two masses as a folding structure to comprise each unit cell of the piezoelectric phononic crystal. Each bimorph is connected independently by a resistive-inductive resonant shunting circuit. The folding structure extends the propagation path of elastic waves, while its structure size remains quite small. Propagation of coupled extension-flexural elastic waves is studied by the classical laminated beam theory and transfer matrix method. The theoretical model is further verified with the finite element method(FEM). The effects of geometrical and circuit parameters on the band gaps are analyzed. With only 4 unit cells, the folding beam-type piezoelectric phononic crystal generates two Bragg band gaps of 369 Hz to1 687 Hz and 2 127 Hz to 4 000 Hz. In addition, between these two Bragg band gaps, a locally resonant band gap is induced by resonant shunting circuits. Appropriate circuit parameters are used to join these two Bragg band gaps by the locally resonant band gap.Thus, a low-frequency and broad band gap of 369 Hz to 4 000 Hz is obtained.
