The interaction of cowl shock wave and boundary layer has a crucial effect on the stability,operability and performance of hypersonic inlets.Many studies on inhibiting the sep-aration and managing the strength of the ...The interaction of cowl shock wave and boundary layer has a crucial effect on the stability,operability and performance of hypersonic inlets.Many studies on inhibiting the sep-aration and managing the strength of the interaction of the shock wave and boundary layer with expansion corner have been conducted.However,the expansion waves near the circular arc shoulder to effectively control the interaction and cowl shock arrangement is little investigated.Therefore,the interaction of the cowl shock wave and boundary layer under thefluence of the expansion waves is studied by inviscid and viscous numerical simulations.The results reveal that the expansion waves have an important impact on the interaction between the cowl shock wave and boundary layer and the strength of shock wave,and that there are four types of inter-action processes with the change of the relative impingement positions of cowl shock wave.The expansion waves have a different influence on the shock wave and boundary layer inter-action at different incident points.When the incident point of the cowl shock wave goes far downstream from the end of the circular arc shoulder,the influence of expansion waves is weakened,and the magnitude of separation zone increases.However,when the expansion waves are applied to the interaction of the cowl shock wave and boundary layer on the circular arc shoulder,the separation can be effectively controlled.In particular,while the expansion waves interact with the shock wave and boundary layer in the back half of the circular arc shoulder,the separation is best inhibited.Compared with the upstream and downstream inci-dent points,the scale of separation area in the optimal control region is reduced by 65.3%at most.Furthermore,the total pressure recovery coefficientfirst increases and then decreases when the cowl moves from upstream to downstream,and the total pressure recovery coefficient reaches the maximum value of 68.36%at the incident position of cowl shock wave d Z 8.09d0.展开更多
A class of singular nonlinear boundary value problems arising in the boundary layer behind expansion wave are studied.Sufficient conditions for the existence and uniqueness of positive solutions to the problems are es...A class of singular nonlinear boundary value problems arising in the boundary layer behind expansion wave are studied.Sufficient conditions for the existence and uniqueness of positive solutions to the problems are established by utilizing the monotonic approaching tech- nique.And a theoretical estimate formula for skin friction coefficient is presented.The numerical solution is presented by using the shoot method.The reliability and efficiency of the theoretical prediction are verified by numerical results.展开更多
The valence subband energies and wave functions of a tensile strained quantum well are calculated by the plane wave expansion method within the 6×6 Luttinger Kohn model.The effect of the number and period of pla...The valence subband energies and wave functions of a tensile strained quantum well are calculated by the plane wave expansion method within the 6×6 Luttinger Kohn model.The effect of the number and period of plane waves used for expansion on the stability of energy eigenvalues is examined.For practical calculation,it should choose the period large sufficiently to ensure the envelope functions vanish at the boundary and the number of plane waves large enough to ensure the energy eigenvalues keep unchanged within a prescribed range.展开更多
The super-cell plane wave expansion method is employed to calculate band structures for the design of a siliconbased one-dimensional phononic crystal plate with large absolute forbidden bands. In this method, a low im...The super-cell plane wave expansion method is employed to calculate band structures for the design of a siliconbased one-dimensional phononic crystal plate with large absolute forbidden bands. In this method, a low impedance medium is introduced to replace the free stress boundary, which largely reduces the computational complexity. The dependence of band gaps on structural parameters is investigated in detail. To prove the validity of the super-cell plane wave expansion, the transmitted power spectra of the Lamb wave are calculated by using a finite element method. With the detailed computation, the band-gap of a one-dimensional plate can be designed as required with appropriate structural parameters, which provides a guide to the fabrication of a Lamb wave phononic crystal.展开更多
A theoretical analysis is made, using plane wave expansion, on how the width of the first three band gaps is influenced by filling ratio, dielectric constant ratio, and periodic width in one-dimensional photonic cryst...A theoretical analysis is made, using plane wave expansion, on how the width of the first three band gaps is influenced by filling ratio, dielectric constant ratio, and periodic width in one-dimensional photonic crystals （PhCs）. From simulation and analysis, there are one, two, and three peak points on the first, second and third band gaps respectively with the changes of filling ratio un- der fixed dielectric constant ratio. When filling ratio is fixed, the bandwidth of the first band gap consistently increases with dielectric constant ratio. However, no similar trend is observed in the second and the third band gaps. Because of scaling properties, varying periodic width does not alter the relative bandwidth.展开更多
This paper presents a method for expanding horizontal flow variables in data using the free solutions to the shallow-water system as a basis set. This method for equatorial wave expansion of instantaneous flows（EWEIF...This paper presents a method for expanding horizontal flow variables in data using the free solutions to the shallow-water system as a basis set. This method for equatorial wave expansion of instantaneous flows（EWEIF） uses dynamic constraints in conjunction with projections of data onto parabolic cylinder functions to determine the amplitude of all equatorial waves.EWEIF allows us to decompose an instantaneous wave flow into individual equatorial waves with a presumed equivalent depth without using temporal or spatial filtering a priori.Three sets of EWEIF analyses are presented. The first set is to confirm that EWEIF is capable of recovering the individual waves constructed from theoretical equatorial wave solutions under various scenarios. The other two sets demonstrate the ability of the EWEIF method to derive time series of individual equatorial waves from instantaneous wave fields without knowing a priori exactly which waves exist in the data as well as their spatial and temporal scales using outputs of an equatorial β-channel shallow-water model and ERA-Interim data. The third set of demonstrations shows, for the first time, the continuous evolutions of individual equatorial waves in the stratosphere whose amplitude is synchronized with the background zonal wind as predicted by quasi-biennial oscillation theory.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 study,we design and numerically investigate a novel all optical D flip-flop(AODFF)based on linear photonic crystal(LPhC)structure that is composed of optical waveguides using the finite difference time domain(...In this study,we design and numerically investigate a novel all optical D flip-flop(AODFF)based on linear photonic crystal(LPhC)structure that is composed of optical waveguides using the finite difference time domain(FDTD)method.The proposed structure has the hexagonal close packed of 16×20 circular rods that are suspended in the air substrate with a lattice constant of 606 nm.The plane wave expansion(PWE)method is used to obtain the band diagram for AODFF at an operating wavelength of 1550 nm.The proposed optical flip-flop achieves a low delay time of 0.2 ps and a high contrast ratio(CR)of 10.33 dB.The main advantage of this design is that the input power as low as 1 mW/μm^(2) is sufficient for its operation,since no nonlinear rods are included.In addition,the footprint of the proposed AODFF is 100μm^(2),which is smaller compared to the structures reported in the literature,and it has a fast switching frequency of 5 Tbit/s.展开更多
This paper reports a series solution of wave functions for two-dimensional scattering and diffraction of plane SH waves induced by a symmetrical V-shaped canyon with different shape ratios. A half-space with a symmetr...This paper reports a series solution of wave functions for two-dimensional scattering and diffraction of plane SH waves induced by a symmetrical V-shaped canyon with different shape ratios. A half-space with a symmetrical V-shaped canyon is divided into two sub-regions by using a circular-arc auxiliary boundary. The two sub-regions are represented by global and local cylindrical coordinate systems, respectively. In each coordinate system, the wave field satisfying the Helmholtz equation is represented by the separation of variables method, in terms of the series of both Bessel functions and Hankel functions with unknown complex coefficients. Then, the two wave fields are described in the local coordinate system using the Graf addition theorem. Finally, the unknown coefficients are sought by satisfying the continuity conditions of the auxiliary boundary. To consider the phase characteristics of the wave scattering, a parametric analysis is carried out in the time domain by assuming an incident signal of the Ricker type. Surface and subsurface transient responses demonstrate the characteristics and mechanisms of wave propagating and scattering.展开更多
This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement res...This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement residual and stress residual along the boundaries. Numerical results show that there are notable differences for response amplitudes between a semi-circular cavity and a whole-circular cavity in a half-space.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
The model of a "spring-mass" resonator periodically attached to a piezoelectric/elastic phononic crystal(PC) nanobeam with surface effects is proposed, and the corresponding calculation method of the band st...The model of a "spring-mass" resonator periodically attached to a piezoelectric/elastic phononic crystal(PC) nanobeam with surface effects is proposed, and the corresponding calculation method of the band structures is formulized and displayed by introducing the Euler beam theory and the surface piezoelectricity theory to the plane wave expansion(PWE) method. In order to reveal the unique wave propagation characteristics of such a model, the band structures of locally resonant(LR) elastic PC Euler nanobeams with and without resonators, the band structures of LR piezoelectric PC Euler nanobeams with and without resonators, as well as the band structures of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on PZT-4, with resonators attached on epoxy, and without resonators are compared. The results demonstrate that adding resonators indeed plays an active role in opening and widening band gaps. Moreover, the influence rules of different parameters on the band gaps of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on epoxy are discussed, which will play an active role in the further realization of active control of wave propagations.展开更多
The complete band gaps （CBGs） of shallow water waves propagating over bottoms with periodically drilled holes are investigated numerically by the plane wave expansion method. Four different patterns are considered, ...The complete band gaps （CBGs） of shallow water waves propagating over bottoms with periodically drilled holes are investigated numerically by the plane wave expansion method. Four different patterns are considered, containing triangular, square, hexagonal and circular cross-sectioned holes arranged into triangular lattices. Results show that the width of CBGs can be changed by adjusting the orientation of noncircular holes and the effect of hole shape on the width of the maximal CBGs is discussed.展开更多
The consistent tanh expansion(CTE) method is employed to the(2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada(CDGKS) equation. The interaction solutions between solitons and the cnoidal periodic waves are explic...The consistent tanh expansion(CTE) method is employed to the(2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada(CDGKS) equation. The interaction solutions between solitons and the cnoidal periodic waves are explicitly obtained. Concretely, we discuss a special kind of interaction solution in the form of tanh functions and Jacobian elliptic functions in both analytical and graphical ways. The results show that the profiles of the soliton-cnoidal periodic wave interaction solutions can be designed by choosing different values of wave parameters.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
Band gaps of 2D phononic crystal with orthotropic cylindrical fillers embedded in the isotropic host are studied in this paper. Two kinds of periodic structures, namely, the square lattice and the triangle lattice, ar...Band gaps of 2D phononic crystal with orthotropic cylindrical fillers embedded in the isotropic host are studied in this paper. Two kinds of periodic structures, namely, the square lattice and the triangle lattice, are considered. For anisotropic phononic crystal, band gaps not only depend on the periodic lattice but also the angle between the symmetry axis of orthotropic material and that of the periodic structure. Rotating these cylindrical fillers makes the angle changing continuously; as a result, pass bands and forbidden bands of the phononic crystal are changed. The plane wave expansion method is used to reduce the band gap problem to an eigenvalue problem. The numerical example is given for YBCO/Epoxy composites. The location and the width of band gaps are estimated for different rotating angles. The influence of anisotropy on band gaps is discussed based on numerical results.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
A metamaterial was introduced into the cover of a patch antenna and its band structure was analyzed. The metama- terial cover with correct selection of the working frequency increases by 9.14 dB the patch antenna’s d...A metamaterial was introduced into the cover of a patch antenna and its band structure was analyzed. The metama- terial cover with correct selection of the working frequency increases by 9.14 dB the patch antenna’s directivity. The mechanism of metamaterial cover is completely different from that of a photonic bandgap cover. The mechanism of the metamaterial cover, the number of the cover’s layers, and the distance between the layers, were analyzed in detail. The results showed that the metamaterial cover, which works like a lens, could effectively improve the patch antenna’s directivity. The physical reasons for the improvement are also given.展开更多
The factors affecting one dimensional （1D） and two dimensional （2D） photonic crystals （PhCs） are systemically analyzed in this paper by numerical simulation. Transfer matrix method （TMM） is employed for 1D PCs...The factors affecting one dimensional （1D） and two dimensional （2D） photonic crystals （PhCs） are systemically analyzed in this paper by numerical simulation. Transfer matrix method （TMM） is employed for 1D PCs, both finite difference time domain method （FDTD） and plane wave expansion method （PWE） are employed for 2D PCs. The result shows that the photonic bandgaps （PBG） are directly affected by crystal type, crystal lattice constant, modulation of refractive index and periodicity, and it is should be useful for design of different type photonic crystals with the required PBG and functional devices. Finally, as an example, a near-IR 1D PCs narrow filter was designed.展开更多
It is of great significance to present a photonic crystal lattice structure with a wide photonic bandgap. A two-dimension complex lattice photonic crystal is proposed. The photonic crystal is composed of complex latti...It is of great significance to present a photonic crystal lattice structure with a wide photonic bandgap. A two-dimension complex lattice photonic crystal is proposed. The photonic crystal is composed of complex lattices with triangular structure, and each single cell is surrounded by six scatterers in an hexagon. The photonic band gaps are calculated based on the plane wave expansion (PWE) method. The results indicate that the photonic crystal has tunable large TM polarization band gap, and a gap-midgap ra...展开更多
基金supported by the Project 1912,the National Natural Science Foundation of China (Grant Nos.52125603 and 11972139)the Fundamental Research Funds for the Central Universities (HIT.BRET.2021006 and FRFCU5710094620).
文摘The interaction of cowl shock wave and boundary layer has a crucial effect on the stability,operability and performance of hypersonic inlets.Many studies on inhibiting the sep-aration and managing the strength of the interaction of the shock wave and boundary layer with expansion corner have been conducted.However,the expansion waves near the circular arc shoulder to effectively control the interaction and cowl shock arrangement is little investigated.Therefore,the interaction of the cowl shock wave and boundary layer under thefluence of the expansion waves is studied by inviscid and viscous numerical simulations.The results reveal that the expansion waves have an important impact on the interaction between the cowl shock wave and boundary layer and the strength of shock wave,and that there are four types of inter-action processes with the change of the relative impingement positions of cowl shock wave.The expansion waves have a different influence on the shock wave and boundary layer inter-action at different incident points.When the incident point of the cowl shock wave goes far downstream from the end of the circular arc shoulder,the influence of expansion waves is weakened,and the magnitude of separation zone increases.However,when the expansion waves are applied to the interaction of the cowl shock wave and boundary layer on the circular arc shoulder,the separation can be effectively controlled.In particular,while the expansion waves interact with the shock wave and boundary layer in the back half of the circular arc shoulder,the separation is best inhibited.Compared with the upstream and downstream inci-dent points,the scale of separation area in the optimal control region is reduced by 65.3%at most.Furthermore,the total pressure recovery coefficientfirst increases and then decreases when the cowl moves from upstream to downstream,and the total pressure recovery coefficient reaches the maximum value of 68.36%at the incident position of cowl shock wave d Z 8.09d0.
基金the National Natural Science Foundation of China （No. 50476083）.
文摘A class of singular nonlinear boundary value problems arising in the boundary layer behind expansion wave are studied.Sufficient conditions for the existence and uniqueness of positive solutions to the problems are established by utilizing the monotonic approaching tech- nique.And a theoretical estimate formula for skin friction coefficient is presented.The numerical solution is presented by using the shoot method.The reliability and efficiency of the theoretical prediction are verified by numerical results.
文摘The valence subband energies and wave functions of a tensile strained quantum well are calculated by the plane wave expansion method within the 6×6 Luttinger Kohn model.The effect of the number and period of plane waves used for expansion on the stability of energy eigenvalues is examined.For practical calculation,it should choose the period large sufficiently to ensure the envelope functions vanish at the boundary and the number of plane waves large enough to ensure the energy eigenvalues keep unchanged within a prescribed range.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10874086 and 10834009)the National Basic Research Program of China (Grant No. 2010CB327803)
文摘The super-cell plane wave expansion method is employed to calculate band structures for the design of a siliconbased one-dimensional phononic crystal plate with large absolute forbidden bands. In this method, a low impedance medium is introduced to replace the free stress boundary, which largely reduces the computational complexity. The dependence of band gaps on structural parameters is investigated in detail. To prove the validity of the super-cell plane wave expansion, the transmitted power spectra of the Lamb wave are calculated by using a finite element method. With the detailed computation, the band-gap of a one-dimensional plate can be designed as required with appropriate structural parameters, which provides a guide to the fabrication of a Lamb wave phononic crystal.
基金Supported by the National Natural Science Foundation of China (61036006)
文摘A theoretical analysis is made, using plane wave expansion, on how the width of the first three band gaps is influenced by filling ratio, dielectric constant ratio, and periodic width in one-dimensional photonic crystals （PhCs）. From simulation and analysis, there are one, two, and three peak points on the first, second and third band gaps respectively with the changes of filling ratio un- der fixed dielectric constant ratio. When filling ratio is fixed, the bandwidth of the first band gap consistently increases with dielectric constant ratio. However, no similar trend is observed in the second and the third band gaps. Because of scaling properties, varying periodic width does not alter the relative bandwidth.
基金supported by grants from the National Science Foundation(Grant No.AGS-1354834)the NASA Interdisciplinary Studies Program(Grant No.NNH12ZDA001NIDS)
文摘This paper presents a method for expanding horizontal flow variables in data using the free solutions to the shallow-water system as a basis set. This method for equatorial wave expansion of instantaneous flows（EWEIF） uses dynamic constraints in conjunction with projections of data onto parabolic cylinder functions to determine the amplitude of all equatorial waves.EWEIF allows us to decompose an instantaneous wave flow into individual equatorial waves with a presumed equivalent depth without using temporal or spatial filtering a priori.Three sets of EWEIF analyses are presented. The first set is to confirm that EWEIF is capable of recovering the individual waves constructed from theoretical equatorial wave solutions under various scenarios. The other two sets demonstrate the ability of the EWEIF method to derive time series of individual equatorial waves from instantaneous wave fields without knowing a priori exactly which waves exist in the data as well as their spatial and temporal scales using outputs of an equatorial β-channel shallow-water model and ERA-Interim data. The third set of demonstrations shows, for the first time, the continuous evolutions of individual equatorial waves in the stratosphere whose amplitude is synchronized with the background zonal wind as predicted by quasi-biennial oscillation theory.
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.
文摘In this study,we design and numerically investigate a novel all optical D flip-flop(AODFF)based on linear photonic crystal(LPhC)structure that is composed of optical waveguides using the finite difference time domain(FDTD)method.The proposed structure has the hexagonal close packed of 16×20 circular rods that are suspended in the air substrate with a lattice constant of 606 nm.The plane wave expansion(PWE)method is used to obtain the band diagram for AODFF at an operating wavelength of 1550 nm.The proposed optical flip-flop achieves a low delay time of 0.2 ps and a high contrast ratio(CR)of 10.33 dB.The main advantage of this design is that the input power as low as 1 mW/μm^(2) is sufficient for its operation,since no nonlinear rods are included.In addition,the footprint of the proposed AODFF is 100μm^(2),which is smaller compared to the structures reported in the literature,and it has a fast switching frequency of 5 Tbit/s.
基金National Natural Science Foundation of China Under Grant No.51278382
文摘This paper reports a series solution of wave functions for two-dimensional scattering and diffraction of plane SH waves induced by a symmetrical V-shaped canyon with different shape ratios. A half-space with a symmetrical V-shaped canyon is divided into two sub-regions by using a circular-arc auxiliary boundary. The two sub-regions are represented by global and local cylindrical coordinate systems, respectively. In each coordinate system, the wave field satisfying the Helmholtz equation is represented by the separation of variables method, in terms of the series of both Bessel functions and Hankel functions with unknown complex coefficients. Then, the two wave fields are described in the local coordinate system using the Graf addition theorem. Finally, the unknown coefficients are sought by satisfying the continuity conditions of the auxiliary boundary. To consider the phase characteristics of the wave scattering, a parametric analysis is carried out in the time domain by assuming an incident signal of the Ricker type. Surface and subsurface transient responses demonstrate the characteristics and mechanisms of wave propagating and scattering.
基金supported by National Natural Science Foundation of China (No. 50978183)Tianjin Natural Science Foundation (No. 07JCZDJC10100)
文摘This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement residual and stress residual along the boundaries. Numerical results show that there are notable differences for response amplitudes between a semi-circular cavity and a whole-circular cavity in a half-space.
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(No.11847009)the Natural Science Foundation of Suzhou University of Science and Technology(No.XKQ2018007)。
文摘The model of a "spring-mass" resonator periodically attached to a piezoelectric/elastic phononic crystal(PC) nanobeam with surface effects is proposed, and the corresponding calculation method of the band structures is formulized and displayed by introducing the Euler beam theory and the surface piezoelectricity theory to the plane wave expansion(PWE) method. In order to reveal the unique wave propagation characteristics of such a model, the band structures of locally resonant(LR) elastic PC Euler nanobeams with and without resonators, the band structures of LR piezoelectric PC Euler nanobeams with and without resonators, as well as the band structures of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on PZT-4, with resonators attached on epoxy, and without resonators are compared. The results demonstrate that adding resonators indeed plays an active role in opening and widening band gaps. Moreover, the influence rules of different parameters on the band gaps of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on epoxy are discussed, which will play an active role in the further realization of active control of wave propagations.
基金supported by the National Natural Science Foundation of China (Grant No. 10674032)
文摘The complete band gaps （CBGs） of shallow water waves propagating over bottoms with periodically drilled holes are investigated numerically by the plane wave expansion method. Four different patterns are considered, containing triangular, square, hexagonal and circular cross-sectioned holes arranged into triangular lattices. Results show that the width of CBGs can be changed by adjusting the orientation of noncircular holes and the effect of hole shape on the width of the maximal CBGs is discussed.
基金Supported by the National Natural Science Foundation of China under Grant No.11505154the Zhejiang Provincial Natural Science Foundation of China under Grant No.LQ16A010003the Scientific Research Foundation for Doctoral Program of Zhejiang Ocean University under Grant No.Q1511
文摘The consistent tanh expansion(CTE) method is employed to the(2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada(CDGKS) equation. The interaction solutions between solitons and the cnoidal periodic waves are explicitly obtained. Concretely, we discuss a special kind of interaction solution in the form of tanh functions and Jacobian elliptic functions in both analytical and graphical ways. The results show that the profiles of the soliton-cnoidal periodic wave interaction solutions can be designed by choosing different values of wave parameters.
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.10672019)
文摘Band gaps of 2D phononic crystal with orthotropic cylindrical fillers embedded in the isotropic host are studied in this paper. Two kinds of periodic structures, namely, the square lattice and the triangle lattice, are considered. For anisotropic phononic crystal, band gaps not only depend on the periodic lattice but also the angle between the symmetry axis of orthotropic material and that of the periodic structure. Rotating these cylindrical fillers makes the angle changing continuously; as a result, pass bands and forbidden bands of the phononic crystal are changed. The plane wave expansion method is used to reduce the band gap problem to an eigenvalue problem. The numerical example is given for YBCO/Epoxy composites. The location and the width of band gaps are estimated for different rotating angles. The influence of anisotropy on band gaps is discussed based on numerical results.
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 (No. 2004CB719802) supported by the National Basic Research Program (973) of China
文摘A metamaterial was introduced into the cover of a patch antenna and its band structure was analyzed. The metama- terial cover with correct selection of the working frequency increases by 9.14 dB the patch antenna’s directivity. The mechanism of metamaterial cover is completely different from that of a photonic bandgap cover. The mechanism of the metamaterial cover, the number of the cover’s layers, and the distance between the layers, were analyzed in detail. The results showed that the metamaterial cover, which works like a lens, could effectively improve the patch antenna’s directivity. The physical reasons for the improvement are also given.
基金Sponsored by the Ministerial Level Advanced Research Foundation (1006513002060)
文摘The factors affecting one dimensional （1D） and two dimensional （2D） photonic crystals （PhCs） are systemically analyzed in this paper by numerical simulation. Transfer matrix method （TMM） is employed for 1D PCs, both finite difference time domain method （FDTD） and plane wave expansion method （PWE） are employed for 2D PCs. The result shows that the photonic bandgaps （PBG） are directly affected by crystal type, crystal lattice constant, modulation of refractive index and periodicity, and it is should be useful for design of different type photonic crystals with the required PBG and functional devices. Finally, as an example, a near-IR 1D PCs narrow filter was designed.
基金supported by the Special Foundation for Harb-in Young Scientists (Grant Number 2008RFQXG031)the Ba-sic Research Foundation of Harbin Engineering University.
文摘It is of great significance to present a photonic crystal lattice structure with a wide photonic bandgap. A two-dimension complex lattice photonic crystal is proposed. The photonic crystal is composed of complex lattices with triangular structure, and each single cell is surrounded by six scatterers in an hexagon. The photonic band gaps are calculated based on the plane wave expansion (PWE) method. The results indicate that the photonic crystal has tunable large TM polarization band gap, and a gap-midgap ra...
