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Symplectic electrothermomechanical buckling solutions for two-dimensional decagonal piezoelectric quasicrystal cylindrical shells 认领 引用
1
作者 Xin SU Yuhang LI +3 位作者 Jufang JIA Xinsheng XU Andi LAI Zhenhuan ZHOU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2026年第7期1549-1568,共20页
Piezoelectric quasicrystals(PQCs),characterized by unique phonon-phason coupling and piezoelectric effects,exhibit significant potential for use in next-generation smart structural devices.However,their complex electr... Piezoelectric quasicrystals(PQCs),characterized by unique phonon-phason coupling and piezoelectric effects,exhibit significant potential for use in next-generation smart structural devices.However,their complex electrothermomechanical buckling behavior remains a challenging analytical problem.This paper presents a symplectic electrothermomechanical buckling model for two-dimensional(2D)decagonal PQC cylindrical shells.By using the symplectic mathematics and Donnell's thin shell theory,the governing buckling equations for axially compressed PQC cylindrical shells are reformulated into a Hamiltonian system.Consequently,the original buckling problem is transformed into a symplectic eigenproblem that can be solved directly,obviating the necessity of trial functions.By use of the symplectic eigenfunction expansion,analytical symplectic buckling equations are obtained,allowing the critical buckling loads and buckling mode shapes to be solved simultaneously.The results indicate that,in addition to the geometry,voltage,and temperature,the phonon-phason-electric coupling inherent in PQC materials significantly influences the critical buckling loads.These analytical results provide a reliable reference for validating other computational approaches. 展开更多
关键词 piezoelectric quasicrystal(PQC)cylindrical shell buckling symplectic method analytical solution
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A Schur-Horn Type Theorem for Symplectic Matrices 认领 引用
2
作者 Shaowu Huang Yimin Wei 《Communications in Mathematical Research》 CSCD 2025年第3期287-295,共9页
In this note,we establish a new version of Schur-Horn type theorem for symplectic matrices.Meanwhile,we establish a necessary and sufficient condition for the equality to hold in the above result.
关键词 Positive definite matrix symplectic matrix equality doubly stochastic matrix
Symplectic solutions for orthotropic micropolar plane stress problem 认领 引用
3
作者 Long Chen Zhaofei Tang +1 位作者 Qiong Wu Qiang Gao 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2025年第1期106-127,共22页
The symplectic approach was utilized to derive solutions to the orthotropic micropolar plane stress problem.The Hamiltonian canonical equation was first obtained by applying Legendre’s transformation and the Hamilton... The symplectic approach was utilized to derive solutions to the orthotropic micropolar plane stress problem.The Hamiltonian canonical equation was first obtained by applying Legendre’s transformation and the Hamiltonian mixed energy variational principle.Then,by using the method of separation of variables,the eigenproblem of the corresponding homogeneous Hamiltonian canonical equation was derived.Subsequently,the corresponding eigensolutions for three kinds of homogeneous boundary conditions were derived.According to the adjoint symplectic orthogonality of the eigensolutions and expansion theorems,the solutions to this plane stress problem were expressed as a series expansion of these eigensolutions.The numerical results for the orthotropic micropolar plane stress problem under various boundary conditions were presented and validated using the finite element method,which confirmed the convergence and accuracy of the proposed approach.We also investigated the relationship between the size-dependent behaviour and material parameters using the proposed approach.Furthermore,this approach was applied to analyze lattice structures under an equivalent micropolar continuum approximation. 展开更多
关键词 Symplectic approach Micropolar Orthotropic materials Size effect Analytical solution
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Symplectic symmetry approach to clustering in atomic nuclei:the case of 24Mg 认领 引用
4
作者 H G Ganev 《Communications in Theoretical Physics》 SCIE CAS CSCD 2025年第5期118-130,共13页
Symplectic symmetry approach to clustering(SSAC)in atomic nuclei,recently proposed,is modified and further developed in more detail.It is firstly applied to the light two-cluster20Ne+αsystem of24Mg,the latter e... Symplectic symmetry approach to clustering(SSAC)in atomic nuclei,recently proposed,is modified and further developed in more detail.It is firstly applied to the light two-cluster20Ne+αsystem of24Mg,the latter exhibiting well developed low-energy Kπ=01+,kπ=21+ and ππ=01- rotational bands in its spectrum.A simple algebraic Hamiltonian,consisting of dynamical symmetry,residual and vertical mixing parts is used to describe these three lowest rotational bands of positive and negative parity in24Mg.A good description of the excitation energies is obtained by considering only the SU(3)cluster states restricted to the stretched many-particle Hilbert subspace,built on the leading Pauli allowed SU(3)multiplet for the positive-and negative-parity states,respectively.The coupling to the higher cluster-model configurations allows us to describe the known low-lying experimentally observed B(E2)transition probabilities within and between the cluster states of the three bands under consideration without the use of an effective charge. 展开更多
关键词 symplectic symmetry approach to clustering algebraic cluster model microscopic cluster model
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Symplectic Schemes for Birkhoffian System 认领 引用 被引量：12
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作者 SUHong-Ling QINMeng-Zhao 《Communications in Theoretical Physics》 SCIE CAS 2004年第3期329-334,共6页
A universal symplectic structure for a Newtonian system including nonconservative cases can be constructed in the framework of Birkhoffian generalization of Hamiltonian mechanics. In this paper the symplectic geometry... A universal symplectic structure for a Newtonian system including nonconservative cases can be constructed in the framework of Birkhoffian generalization of Hamiltonian mechanics. In this paper the symplectic geometry structure of Birkhoffian system is discussed, then the symplecticity of Birkhoffian phase flow is presented. Based on these properties we give a way to construct symplectic schemes for Birkhoffian systems by using the generating function method. 展开更多
关键词 Birkhoffran system symplectic structure generating function method symplectic scheme
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Symplectic perturbation series methodology for non-conservative linear Hamiltonian system with damping 认领 引用 被引量：4
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作者 Zhiping Qiu Haijun Xia 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2021年第6期983-996,I0002,共14页
In this paper,the symplectic perturbation series methodology of the non-conservative linear Hamiltonian system is presented for the structural dynamic response with damping.Firstly,the linear Hamiltonian system is bri... In this paper,the symplectic perturbation series methodology of the non-conservative linear Hamiltonian system is presented for the structural dynamic response with damping.Firstly,the linear Hamiltonian system is briefly introduced and its conservation law is proved based on the properties of the exterior products.Then the symplectic perturbation series methodology is proposed to deal with the non-conservative linear Hamiltonian system and its conservation law is further proved.The structural dynamic response problem with eternal load and damping is transformed as the non-conservative linear Hamiltonian system and the symplectic difference schemes for the non-conservative linear Hamiltonian system are established.The applicability and validity of the proposed method are demonstrated by three engineering examples.The results demonstrate that the presented methodology is better than the traditional Runge–Kutta algorithm in the prediction of long-time structural dynamic response under the same time step. 展开更多
关键词 Symplectic perturbation series methodology Non-conservative Hamiltonian system Structural dynamic response Symplectic difference scheme
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Multi-symplectic wavelet splitting method for the strongly coupled Schrodinger system 认领 引用 被引量：2
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作者 钱旭 陈亚铭 +1 位作者 高二 宋松和 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第12期16-22,共7页
We propose a multi-symplectic wavelet splitting equations. Based on its mu]ti-symplectic formulation, method to solve the strongly coupled nonlinear SchrSdinger the strongly coupled nonlinear SchrSdinger equations can... We propose a multi-symplectic wavelet splitting equations. Based on its mu]ti-symplectic formulation, method to solve the strongly coupled nonlinear SchrSdinger the strongly coupled nonlinear SchrSdinger equations can be split into one linear multi-symplectic subsystem and one nonlinear infinite-dimensional Hamiltonian subsystem. For the linear subsystem, the multi-symplectic wavelet collocation method and the symplectic Euler method are employed in spatial and temporal discretization, respectively. For the nonlinear subsystem, the mid-point symplectic scheme is used. Numerical simulations show the effectiveness of the proposed method during long-time numerical calculation. 展开更多
关键词 multi-symplectic wavelet splitting method symplectic Euler method strongly couplednonlinear SchrSdinger equations
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Symplectic Approach on the Wave Propagation Problem for Periodic Structures with Uncertainty 认领 引用 被引量：1
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作者 Yan Zhao Hui Liang +1 位作者 Youwei Zhang Jiahao Lin 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2019年第3期287-297,共11页
An effective method is proposed in this paper for the symplectic eigenvalue problem of a periodic structure with uniform stochastic properties. Since structural parameters are uncertain, the symplectic transfer matrix... An effective method is proposed in this paper for the symplectic eigenvalue problem of a periodic structure with uniform stochastic properties. Since structural parameters are uncertain, the symplectic transfer matrix of a typical substructure, which is described in the state space, also has sto chastic proper ties. An effec tive spec tral st ochastic finite elemen t method is adopted to ensure the symplectic orthogonality of the random symplectic matrix on the premise of certain precision. By means of the Rayleigh quotient method, the symplectic eigenvalue problem of random symplectic matrix is investigated. On the basis of this, the mean value and the standard deviation of the random eigenvalues are fully discussed. The comparison between the numerical results derived from the proposed method and the Monte-Carlo simulation indicates that the proposed method has high precision. This research provides a useful guidance for the dynamic analysis of periodic structures with stochastic properties. 展开更多
关键词 Periodic structures Spectrum method Random symplectic matrix Symplectic eigenvalue
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Analytical and numerical methods of symplectic system for Stokes flow in two-dimensional rectangular domain 认领 引用
9
作者 徐新生 王尕平 孙发明 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第6期705-714,共10页
In this paper, a new analytical method of symplectic system, Hamiltonian system, is introduced for solving the problem of the Stokes flow in a two-dimensional rectangular domain. In the system, the fundamental problem... In this paper, a new analytical method of symplectic system, Hamiltonian system, is introduced for solving the problem of the Stokes flow in a two-dimensional rectangular domain. In the system, the fundamental problem is reduced to an eigenvalue and eigensolution problem. The solution and boundary conditions can be expanded by eigensolutions using adjoint relationships of the symplectic ortho-normalization between the eigensolutions. A closed method of the symplectic eigensolution is presented based on completeness of the symplectic eigensolution space. The results show that fundamental flows can be described by zero eigenvalue eigensolutions, and local effects by nonzero eigenvalue eigensolutions. Numerical examples give various flows in a rectangular domain and show effectiveness of the method for solving a variety of problems. Meanwhile, the method can be used in solving other problems. 展开更多
关键词 Hamiltonian system symplectic eigenvalues symplectic eigensolutions,Stokes flow rectangular domain
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Self-dual Codes with Symplectic Inner Product 认领 引用
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作者 Nan Ji-zhu Yu Xue-min Du Xian-kun 《Communications in Mathematical Research》 CSCD 2015年第4期345-350,共6页
In this paper, we discuss a kind of Hermitian inner product - symplectic inner product, which is different from the original inner product - Euclidean inner product. According to the definition of symplectic inner pro... In this paper, we discuss a kind of Hermitian inner product - symplectic inner product, which is different from the original inner product - Euclidean inner product. According to the definition of symplectic inner product, the codes under the symplectic inner product have better properties than those under the general Hermitian inner product. Here we present the necessary and sufficient condition for judging whether a linear code C over Fp with a generator matrix in the standard form is a symplectic self-dual code. In addition, we give a method for constructing a new symplectic self-dual codes over Fp, which is simpler than others. 展开更多
关键词 symplectic inner product symplectic self-dual code symplectic circu- lant code
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Linear Operators Preserving Symplectic Group over a Field Consisting of at Least Four Elements 认领 引用
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作者 游宏 刘绍武 《Northeastern Mathematical Journal》 2006年第2期219-232,共14页
Suppose F is a field consisting of at least four elements. Let Mn（F） and SP2n（F） be the linear space of all n × n matrices and the group of all 2n × 2n symplectic matrices over F, respectively. A linear ... Suppose F is a field consisting of at least four elements. Let Mn（F） and SP2n（F） be the linear space of all n × n matrices and the group of all 2n × 2n symplectic matrices over F, respectively. A linear operator L ： M2n（F） → M2n（F） is said to preserve the symplectic group if L（SP2n（F）） = SP2n（F）. It is shown that L is an invertible preserver of the symplectic group if and only if L takes the form （i） L（X） = QPXP^-1 for any X ∈ M2n（F） or （ii） L（X） = QPX^TP^-1 for any X ∈M2n（F）, where Q ∈ SP2n（F） and P is a generalized symplectic matrix. This generalizes the result derived by Pierce in Canad J. Math., 3（1975）, 715-724. 展开更多
关键词 linear preserver symplectic group symplectic matrix generalized symplectic matrix linear operator
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SYMPLECTIC ANALYSIS FOR WAVE PROPAGATION OF HIERARCHICAL HONEYCOMB STRUCTURES 认领 引用 被引量：4
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作者 Kai Zhang Zichen Deng +2 位作者 Xiaojian Xu Xiuhui Hou Junmiao Meng 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2015年第3期294-304,共11页
Wave propagation in two-dimensional hierarchical honeycomb structures with two- order hierarchy is investigated by using the symplectic algorithm. By applying the variational prin- ciple to the dual variables, the wav... Wave propagation in two-dimensional hierarchical honeycomb structures with two- order hierarchy is investigated by using the symplectic algorithm. By applying the variational prin- ciple to the dual variables, the wave propagation problem is transformed into a two-dimensional symplectie eigenvalue problem. The band gaps and spatial filtering phenomena are examined to find the stop bands and directional stop bands. Special attention is directed to the effects of the relative density and the length ratio on the band gaps and phase constant surfaces. This work provides new opportunities for designing hierarchical honeycomb structures in sound insulation applications. 展开更多
关键词 hierarchical honeycomb structures wave propagation band gap phase constant surface symplectic analysis
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THE HAMILTONIAN SYSTEM AND COMPLETENESS OF SYMPLECTIC ORTHOGONAL SYSTEM 认领 引用 被引量：12
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作者 张鸿庆 阿拉坦仓 钟万勰 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1997年第3期237-237,239-242,共1页
In this paper, a new Banach space ZH is defined, and it is proved that there is completeness of eigenfunction system (symplectic orthogonal system) of a class of Hamiltonian system in ZH space. We have also proved the... In this paper, a new Banach space ZH is defined, and it is proved that there is completeness of eigenfunction system (symplectic orthogonal system) of a class of Hamiltonian system in ZH space. We have also proved the following results: ZH space can be continuously imbedded to L-2[0,1] X L-2[0,1], but ZH not equal L-2[0,1] X L-1[0,1]. 展开更多
关键词 Hamiltonian system completeness symplectic orthogonal system
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Double Symplectic Eigenfunction Expansion Method of Free Vibration of Rectangular Thin Plates 认领 引用 被引量：10
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作者 WANG Hua Alatancang HUANG Jun-Jie 《Communications in Theoretical Physics》 SCIE CAS 2009年第12期1087-1092,共6页
The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonia... The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonian. Moreover, the existence and completeness of normed symplectic orthogonal eigenfunction systems of these two block operators are demonstrated. Based on the completeness, the general solution of the free vibration of rectangular thin plates is given by double symplectie eigenfunction expansion method. 展开更多
关键词 free vibration of rectangular thin plate double symplectic eigenfunction expansion method upper triangular matrix differential system general solution
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New exact solutions for free vibrations of rectangular thin plates by symplectic dual method 认领 引用 被引量：17
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作者 Yufeng Xing Bo Liu 《Acta Mechanica Sinica》 SCIE EI CAS 2009年第2期265-270,共6页
The separation of variables is employed to solve Hamiltonian dual form of eigenvalue problem for transverse free vibrations of thin plates,and formulation of the natural mode in closed form is performed.The closed-for... The separation of variables is employed to solve Hamiltonian dual form of eigenvalue problem for transverse free vibrations of thin plates,and formulation of the natural mode in closed form is performed.The closed-form natural mode satisfies the governing equation of the eigenvalue problem of thin plate exactly and is applicable for any types of boundary conditions.With all combinations of simplysupported(S)and clamped(C)boundary conditions applied to the natural mode,the mode shapes are obtained uniquely and two eigenvalue equations are derived with respect to two spatial coordinates,with the aid of which the normal modes and frequencies are solved exactly.It was believed that the exact eigensolutions for cases SSCC,SCCC and CCCC were unable to be obtained,however,they are successfully found in this paper.Comparisons between the present results and the FEM results validate the present exact solutions,which can thus be taken as the benchmark for verifying different approximate approaches. 展开更多
关键词 Classical theory of thin plate Frequency Free vibrations Symplectic dual method Exact solution
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Perfect plane-wave source for a high-order symplectic finite-difference time-domain scheme 认领 引用 被引量：5
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作者 王辉 黄志祥 +1 位作者 吴先良 任信钢 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第11期365-370,共6页
The method of splitting a plane-wave finite-difference time-domain （SP-FDTD） algorithm is presented for the initiation of plane-wave source in the total-field / scattered-field （TF/SF） formulation of high-order sy... The method of splitting a plane-wave finite-difference time-domain （SP-FDTD） algorithm is presented for the initiation of plane-wave source in the total-field / scattered-field （TF/SF） formulation of high-order symplectic finite- difference time-domain （SFDTD） scheme for the first time. By splitting the fields on one-dimensional grid and using the nature of numerical plane-wave in finite-difference time-domain （FDTD）, the identical dispersion relation can be obtained and proved between the one-dimensional and three-dimensional grids. An efficient plane-wave source is simulated on one-dimensional grid and a perfect match can be achieved for a plane-wave propagating at any angle forming an integer grid cell ratio. Numerical simulations show that the method is valid for SFDTD and the residual field in SF region is shrinked down to -300 dB. 展开更多
关键词 splitting plane-wave finite-difference time-domain high-order symplectic finite-differencetime-domain scheme plane-wave source
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Highly accurate symplectic element based on two variational principles 认领 引用 被引量：20
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作者 Guanghui Qing Jia Tian 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2018年第1期151-161,共11页
For the stability requirement of numerical resultants, the mathematical theory of classical mixed methods are relatively complex. However, generalized mixed methods are automatically stable, and their building process... For the stability requirement of numerical resultants, the mathematical theory of classical mixed methods are relatively complex. However, generalized mixed methods are automatically stable, and their building process is simple and straightforward. In this paper, based on the seminal idea of the generalized mixed methods, a simple, stable, and highly accurate 8-node noncompatible symplectic element(NCSE8) was developed by the combination of the modified Hellinger-Reissner mixed variational principle and the minimum energy principle. To ensure the accuracy of in-plane stress results, a simultaneous equation approach was also suggested. Numerical experimentation shows that the accuracy of stress results of NCSE8 are nearly the same as that of displacement methods, and they are in good agreement with the exact solutions when the mesh is relatively fine. NCSE8 has advantages of the clearing concept, easy calculation by a finite element computer program, higher accuracy and wide applicability for various linear elasticity compressible and nearly incompressible material problems. It is possible that NCSE8 becomes even more advantageous for the fracture problems due to its better accuracy of stresses. 展开更多
关键词 Modified H-R mixed variational principle Partial-mixed element Noncompatible symplectic element Finite element method Nearly incompressible material
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Symplectic partitioned Runge-Kutta method based onthe eighth-order nearly analytic discrete operator and its wavefield simulations 认领 引用 被引量：3
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作者 张朝元 马啸 +1 位作者 杨磊 宋国杰 《Applied Geophysics》 SCIE CSCD 2014年第1期89-106,117,118,共18页
We propose a symplectic partitioned Runge-Kutta （SPRK） method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this te... We propose a symplectic partitioned Runge-Kutta （SPRK） method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this technique uses an eighth-orderaccurate nearly analytic discrete （NAD） operator to discretize high-order spatial differentialoperators and employs a second-order SPRK method to discretize temporal derivatives.The stability criteria and numerical dispersion relations of the eighth-order NSPRK methodare given by a semi-analytical method and are tested by numerical experiments. We alsoshow the differences of the numerical dispersions between the eighth-order NSPRK methodand conventional numerical methods such as the fourth-order NSPRK method, the eighth-order Lax-Wendroff correction （LWC） method and the eighth-order staggered-grid （SG）method. The result shows that the ability of the eighth-order NSPRK method to suppress thenumerical dispersion is obviously superior to that of the conventional numerical methods. Inthe same computational environment, to eliminate visible numerical dispersions, the eighth-order NSPRK is approximately 2.5 times faster than the fourth-order NSPRK and 3.4 timesfaster than the fourth-order SPRK, and the memory requirement is only approximately47.17% of the fourth-order NSPRK method and 49.41% of the fourth-order SPRK method,which indicates the highest computational efficiency. Modeling examples for the two-layermodels such as the heterogeneous and Marmousi models show that the wavefields generatedby the eighth-order NSPRK method are very clear with no visible numerical dispersion.These numerical experiments illustrate that the eighth-order NSPRK method can effectivelysuppress numerical dispersion when coarse grids are adopted. Therefore, this methodcan greatly decrease computer memory requirement and accelerate the forward modelingproductivity. In general, the eighth-order NSPRK method has tremendous potential value forseismic exploration and seismology research. 展开更多
关键词 Symplectic partitioned Runge-Kutta method Nearly analytic discrete operator Numerical dispersion Wavefield simulation
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On the symplectic superposition method for free vibration of rectangular thin plates with mixed boundary constraints on an edge 认领 引用 被引量：3
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作者 Dian Xu Zhuofan Ni +4 位作者 Yihao Li Zhaoyang Hu Yu Tian Bo Wang Rui Li 《Theoretical & Applied Mechanics Letters》 CAS CSCD 2021年第5期273-279,共7页
A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years.The method has yielded many new analytic solutions due to its rigorousness.In this study,the first e... A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years.The method has yielded many new analytic solutions due to its rigorousness.In this study,the first endeavor is made to further developed the symplectic superposition method for the free vibration of rectangular thin plates with mixed boundary constraints on an edge.The Hamiltonian system-based governing equation is first introduced such that the mathematical techniques in the symplectic space are applied.The solution procedure incorporates separation of variables,symplectic eigen solution and superposition.The analytic solution of an original problem is finally obtained by a set of equations via the equivalence to the superposition of some elaborated subproblems.The natural frequency and mode shape results for representative plates with both clamped and simply supported boundary constraints imposed on the same edge are reported for benchmark use.The present method can be extended to more challenging problems that cannot be solved by conventional analytic methods. 展开更多
关键词 Symplectic superposition method Free vibration Plates Mixed boundary constraints
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Symplectic analysis for elastic wave propagation in two-dimensional cellular structures 认领 引用 被引量：5
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作者 Xiu-Hui Hou Zi-Chen Deng +1 位作者 Jia-Xi Zhou Tie-Quan Liu 《Acta Mechanica Sinica》 SCIE EI CAS 2010年第5期711-720,共10页
On the basis of the finite element analysis, the elastic wave propagation in cellular structures is investigated using the symplectic algorithm. The variation principle is first applied to obtain the dual variables an... On the basis of the finite element analysis, the elastic wave propagation in cellular structures is investigated using the symplectic algorithm. The variation principle is first applied to obtain the dual variables and the wave propagation problem is then transformed into two-dimensional （2D） symplectic eigenvalue problems, where the extended Wittrick-Williams algorithm is used to ensure that no phase propagation eigenvalues are missed during computation. Three typical cellular structures, square, triangle and hexagon, are introduced to illustrate the unique feature of the symplectic algorithm in higher-frequency calculation, which is due to the conserved properties of the structure-preserving symplectic algorithm. On the basis of the dispersion relations and phase constant surface analysis, the band structure is shown to be insensitive to the material type at lower frequencies, however, much more related at higher frequencies. This paper also demonstrates how the boundary conditions adopted in the finite element modeling process and the structures＇ configurations affect the band structures. The hexagonal cells are demonstrated to be more efficient for sound insulation at higher frequencies, while the triangular cells are preferred at lower frequencies. No complete band gaps are observed for the square cells with fixed-end boundary conditions. The analysis of phase constant surfaces guides the design of 2D cellular structures where waves at certain frequencies do not propagate in specified directions. The findings from the present study will provide invaluable guidelines for the future application of cellular structures in sound insulation. 展开更多
关键词 Cellular structures Symplectic analysis Dispersion relation - Phase constant surface Sound insulation
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