The plane wave numerical technique is recast from Ampere’s and Faraday’s laws for materials that are characterized with a bianisotropic form of the constitutive relations. The populating expressions are provided for...The plane wave numerical technique is recast from Ampere’s and Faraday’s laws for materials that are characterized with a bianisotropic form of the constitutive relations. The populating expressions are provided for the eigenvalue matrix system that can be directly solved for the angular frequencies and field profiles when bianisotropy is included. To demonstrate the computation process and expected state diagrams and field profiles, numerical computation examples are provided for a bianisotropic Bragg Array with central defect. It is shown that the location of the magnetoelectric tensor elements has a significant effect on the eigenstates of an equivalent isotropic (anisotropic) structure. One form of the magnetoelectric tensor (diagonal elements only) leads to the observation of merging states and the formation of exceptional points. The numerical approach presented can be implemented as an add-on to the familiar plane wave numerical technique.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 plan...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
A 1D finite element method in time domain is developed in this paper and applied to calculate in-plane wave motions of free field exited by SV or P wave oblique incidence in an elastic layered half-space. First, the l...A 1D finite element method in time domain is developed in this paper and applied to calculate in-plane wave motions of free field exited by SV or P wave oblique incidence in an elastic layered half-space. First, the layered half-space is discretized on the basis of the propagation characteristic of elastic wave according to the Snell law. Then, the finite element method with lumped mass and the central difference method are incorporated to establish 2D wave motion equations, which can be transformed into 1D equations by discretization principle and explicit finite element method. By solving the 1D equations, the displacements of nodes in any vertical line can be obtained, and the wave motions in layered half-space are finally determined based on the characteristic of traveling wave. Both the theoretical analysis and the numerical results demonstrate that the proposed method has high accuracy and good stability.展开更多
The dynamic soil-tunnel interaction is studied by indirect boundary element method (IBEM), using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subj...The dynamic soil-tunnel interaction is studied by indirect boundary element method (IBEM), using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subjected to incident plane SH waves. The accuracy of the results is verified through comparison with the analytical solution. It is shown that soil-tunnel interaction in layered half-space is larger than that in homogeneous half-space and this interaction mechanism is essentially different from that of soil-foundation-superstructure interaction.展开更多
This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method (IBEM). A free field response analysis is performed to provide the d...This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method (IBEM). A free field response analysis is performed to provide the displacements and stresses on the boundary of the canyon where fictitious uniform moving loads are applied to calculate the Green's fi.mctions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The free field displacements are added to the fictitious uniform moving loads induced displacements and the total response is obtained. Numerical calculations are performed for a canyon with homogenous and in one layer over bedrock. The effects of the thickness and stiffness of the layer on the amplification are studied and discussed.展开更多
An impedance analytical method (IAM) is developed to study the interaction of plane water wave with a slotted-wall caisson breakwater. The non-linear boundary condition at the slotted-wall is expressed in terms of f...An impedance analytical method (IAM) is developed to study the interaction of plane water wave with a slotted-wall caisson breakwater. The non-linear boundary condition at the slotted-wall is expressed in terms of flow resistance. A set of algebraic expressions are obtained for free surface elevation inside and outside chamber, and reflection coefficient. The prediction of the reflection coefficients shows that the relative widths of the chamber inducing the minimum reflection coefficient for a slotted-wall caisson breakwater are in a range of 0.10~0.20, which are smaller than that (0.15~0.25) for a perforated-wall caisson breakwater. The reflection coefficients and free surface elevation obtained by the present model are compared with that of laboratory experiments carried out by previous researchers.展开更多
Several types of acoustic metamaterial(AM)plates have been developed to achieve low-frequency and wide bandgaps,which are adjusted by their geometric configurations and material properties.This paper combines the clas...Several types of acoustic metamaterial(AM)plates have been developed to achieve low-frequency and wide bandgaps,which are adjusted by their geometric configurations and material properties.This paper combines the classical plate theory and the characteristics of piezoelectric materials,and uses the plane wave expansion method(PWEM)to derive the bandgap theoretical model of plate-type metastructures.The dispersion curves of the structures composed of elastic materials,piezoelectric materials,and functionally graded(FG)materials are compared and studied,and verified with the finite element simulation results.Then,the effects of temperatures,piezoelectric parameters,scatterer shapes,scatterer distributions,scatterer tapers,rubber layers,and spiral groove configurations on the bandgap of plate-type metastructures are discussed,and the material and geometric parameters are optimized with the genetic algorithm(GA).This study provides a reference for the design of low-frequency broadband structures.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
Abstract This paper studies three-dimensional diffraction of obliquely incident plane SH waves by twin infinitely long cylindrical cavities in layered poroelastic half-space using indirect boundary element method. The...Abstract This paper studies three-dimensional diffraction of obliquely incident plane SH waves by twin infinitely long cylindrical cavities in layered poroelastic half-space using indirect boundary element method. The approach is validated by comparison with the literature, and the effects of cavity interval, incident frequency, and boundary drainage condition on the diffraction are studied through numerical examples. It is shown that, the interaction between two cavities is significant and surface displacement peaks become large when two cavities are close, and the surface displacement may be significantly amplified by twin cavities, and the influence range with large amplification can be as wide as 40 times of the cavity radius. Surface displacements in dry poroelastic case and saturated poroelastic cases with drained and undrained boundaries are evidently different under certain circumstances, and the differences may be much larger than those in the free-field response.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
In this paper, we propose a method to improve anti-radiation capability by coating heavy metal X-ray protection glass with compound photonic crystal layers, based on the unique property of photonic crystal that light ...In this paper, we propose a method to improve anti-radiation capability by coating heavy metal X-ray protection glass with compound photonic crystal layers, based on the unique property of photonic crystal that light cannot be propagated within the range of band gaps. Using the plane wave expansion method,we made a theoretical study of parameters affecting the band gap structures of one-dimensional photonic crystals. Based on the findings, we chose appropriate materials and compound structure of photonic crystal so as to get high X-ray reflection coating photonic crystal layers. By this method, the reflection rate within X-ray wavelength can reach the maximum value of 100%, and the average value of over 90%. Even low-cost heavy metal X-ray protection glass of absorption coefficient value can achieve the desired effect. Thus, this method greatly decreases the anti-radiation requirements of heavy X-ray protection glass.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
摘要The plane wave numerical technique is recast from Ampere’s and Faraday’s laws for materials that are characterized with a bianisotropic form of the constitutive relations. The populating expressions are provided for the eigenvalue matrix system that can be directly solved for the angular frequencies and field profiles when bianisotropy is included. To demonstrate the computation process and expected state diagrams and field profiles, numerical computation examples are provided for a bianisotropic Bragg Array with central defect. It is shown that the location of the magnetoelectric tensor elements has a significant effect on the eigenstates of an equivalent isotropic (anisotropic) structure. One form of the magnetoelectric tensor (diagonal elements only) leads to the observation of merging states and the formation of exceptional points. The numerical approach presented can be implemented as an add-on to the familiar plane wave numerical technique.
摘要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the National Natural Science Foundation of China(50478014)the National 973 Program(2007CB714200)the Beijing Natural Science Foundation(8061003).
摘要A 1D finite element method in time domain is developed in this paper and applied to calculate in-plane wave motions of free field exited by SV or P wave oblique incidence in an elastic layered half-space. First, the layered half-space is discretized on the basis of the propagation characteristic of elastic wave according to the Snell law. Then, the finite element method with lumped mass and the central difference method are incorporated to establish 2D wave motion equations, which can be transformed into 1D equations by discretization principle and explicit finite element method. By solving the 1D equations, the displacements of nodes in any vertical line can be obtained, and the wave motions in layered half-space are finally determined based on the characteristic of traveling wave. Both the theoretical analysis and the numerical results demonstrate that the proposed method has high accuracy and good stability.
基金National Natural Science Foundation of China under Grant 51378384Key Project of Natural Science Foundation of Tianjin Municipality under Grant 12JCZDJC29000
摘要The dynamic soil-tunnel interaction is studied by indirect boundary element method (IBEM), using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subjected to incident plane SH waves. The accuracy of the results is verified through comparison with the analytical solution. It is shown that soil-tunnel interaction in layered half-space is larger than that in homogeneous half-space and this interaction mechanism is essentially different from that of soil-foundation-superstructure interaction.
基金National Natural Science Foundation of China Under Grant No.50908156 and 50978183Tianjin Natural Science Foundation Under Grant No. 07JCZDJC10100
摘要This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method (IBEM). A free field response analysis is performed to provide the displacements and stresses on the boundary of the canyon where fictitious uniform moving loads are applied to calculate the Green's fi.mctions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The free field displacements are added to the fictitious uniform moving loads induced displacements and the total response is obtained. Numerical calculations are performed for a canyon with homogenous and in one layer over bedrock. The effects of the thickness and stiffness of the layer on the amplification are studied and discussed.
摘要An impedance analytical method (IAM) is developed to study the interaction of plane water wave with a slotted-wall caisson breakwater. The non-linear boundary condition at the slotted-wall is expressed in terms of flow resistance. A set of algebraic expressions are obtained for free surface elevation inside and outside chamber, and reflection coefficient. The prediction of the reflection coefficients shows that the relative widths of the chamber inducing the minimum reflection coefficient for a slotted-wall caisson breakwater are in a range of 0.10~0.20, which are smaller than that (0.15~0.25) for a perforated-wall caisson breakwater. The reflection coefficients and free surface elevation obtained by the present model are compared with that of laboratory experiments carried out by previous researchers.
摘要Several types of acoustic metamaterial(AM)plates have been developed to achieve low-frequency and wide bandgaps,which are adjusted by their geometric configurations and material properties.This paper combines the classical plate theory and the characteristics of piezoelectric materials,and uses the plane wave expansion method(PWEM)to derive the bandgap theoretical model of plate-type metastructures.The dispersion curves of the structures composed of elastic materials,piezoelectric materials,and functionally graded(FG)materials are compared and studied,and verified with the finite element simulation results.Then,the effects of temperatures,piezoelectric parameters,scatterer shapes,scatterer distributions,scatterer tapers,rubber layers,and spiral groove configurations on the bandgap of plate-type metastructures are discussed,and the material and geometric parameters are optimized with the genetic algorithm(GA).This study provides a reference for the design of low-frequency broadband structures.
基金supported by the National Natural Science Foundation of China (Grant No. 10674032)
摘要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 National Natural Science Foundation of China under grant 51378384Key Project of Natural Science Foundation of Tianjin Municipality under Grant 12JCZDJC29000
摘要Abstract This paper studies three-dimensional diffraction of obliquely incident plane SH waves by twin infinitely long cylindrical cavities in layered poroelastic half-space using indirect boundary element method. The approach is validated by comparison with the literature, and the effects of cavity interval, incident frequency, and boundary drainage condition on the diffraction are studied through numerical examples. It is shown that, the interaction between two cavities is significant and surface displacement peaks become large when two cavities are close, and the surface displacement may be significantly amplified by twin cavities, and the influence range with large amplification can be as wide as 40 times of the cavity radius. Surface displacements in dry poroelastic case and saturated poroelastic cases with drained and undrained boundaries are evidently different under certain circumstances, and the differences may be much larger than those in the free-field response.
基金the National Natural Science Foundation of China(No.11847009)the Natural Science Foundation of Suzhou University of Science and Technology(No.XKQ2018007)。
摘要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.
摘要In this paper, we propose a method to improve anti-radiation capability by coating heavy metal X-ray protection glass with compound photonic crystal layers, based on the unique property of photonic crystal that light cannot be propagated within the range of band gaps. Using the plane wave expansion method,we made a theoretical study of parameters affecting the band gap structures of one-dimensional photonic crystals. Based on the findings, we chose appropriate materials and compound structure of photonic crystal so as to get high X-ray reflection coating photonic crystal layers. By this method, the reflection rate within X-ray wavelength can reach the maximum value of 100%, and the average value of over 90%. Even low-cost heavy metal X-ray protection glass of absorption coefficient value can achieve the desired effect. Thus, this method greatly decreases the anti-radiation requirements of heavy X-ray protection glass.
基金The National Natural Science Foundation of China(No.12002086)。
摘要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.