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1.
Stokes流问题中的辛本征解方法 总被引:8,自引:0,他引:8
通过引入哈密顿体系,将二维Stokes流问题归结为哈密顿体系下的本
征值和本征解问题. 利用辛本征解空间的完备性,建立一套封闭的求解问题方法. 研究结果
表明零本征值本征解描述了基本的流动,而非零本征值本征解则显示着端部效应影响特点.
数值算例给出了辛本征值和本征解的一些规律和具体例子. 这些数值例子说明了端部非规则
流动的衰减规律. 为研究其它问题提供了一条路径. 相似文献
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对在热环境中功能梯度材料(FGM)输流管道流固耦合热横向振动问题,基于哈密顿原理和Euler-Bernoulli梁理论,建立了端部不可移简支FGM输流管道的力学模型和运动微分方程。引入量纲为一的量,把运动微分方程离散为以量纲归一化广义坐标表达的常微分方程组。应用哈密顿对偶体系理论,得到了哈密顿正则方程,通过分离变量法得到了哈密顿体系下系统的热本征值和本征解的表达式。算例表明,端部不可移简支FGM输流管道的量纲为一的复频率虚部随着梯度指标的增大而增大,随着量纲为一的温度轴力的增大而减小。 相似文献
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圆柱型正交各向异性弹性楔体顶端受有集中力偶的经典解,当顶角满足一定关系时,其应力成为无穷大,这是个佯谬.该文在哈密顿体系下将该问题进行重新求解,即利用极坐标各向异性弹性力学哈密顿体系.在原变量和其对偶变量组成的辛几何空间求解特殊本征值的约当型本征解,从而直接给出该佯谬问题的解析解.结果再次表明经典力学中的弹性楔佯谬解对应的是哈密顿体系下辛几何的约当型解. 相似文献
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功能梯度材料平面问题的辛弹性力学解法 总被引:3,自引:0,他引:3
将辛弹性力学解法推广用于功能梯度材料平面问题的分析,考虑沿长度方向弹性模量为指数函数变化而泊松比为常数的矩形域平面弹性问题,给出了具体的求解步骤. 提出了移位Hamilton矩阵的新概念,建立起相应的辛共轭正交关系;导出了对应特殊本征值的本征解,发现材料的非均匀特性使特殊本征解的形式发生明显的变化. 相似文献
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平面问题中弹性压电材料的本构关系及应用 总被引:6,自引:0,他引:6
本文在三维压电材料本构方程的基础上,推导出二维压电材料的机电耦合方程系统,并分析了受轴向力,弯矩作用时的位移和电势分布情况。 相似文献
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According to the Hellinger-Reissner variational principle and introducing proper transformation of variables , the problem on elastic wedge dissimilar materials can be led to Hamiltonian system, so the solution of the problem can be got by employing the separation of variables method and symplectic eigenfunction expansion under symplectic space, which consists of original variables and their dual variables . The eigenvalue - 1 is a special one of all symplectic eigenvalue for Hamiltonian system in polar coordinate . In general, the eigenvalue - 1 is a single eigenvalue, and the classical solution of an elastic wedge dissimilar materials subjected to a unit concentrated couple at the vertex is got directly by solving the eigenfunction vector for eigenvalue - 1. But the eigenvalue - 1 becomes a double eigenvalue when the vertex angles and modulus of the materials satisfy certain definite relationships and the classical solution for the stress distribution becomes infinite at this moment, that is, the para 相似文献
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《International Journal of Solids and Structures》2006,43(7-8):2126-2145
This paper investigates the fracture problem of a piezoelectric cylinder with a periodic array of embedded circular cracks. An electro-mechanical fracture mechanics model is established first. The model is further used to the thermal fracture analysis of a piezoelectric cylinder subjected to a sudden heating on its outer surface. The temperature field and the associated thermal stresses and electric displacements are obtained and are added to the crack surface to form a mixed-mode boundary value problem for the electro-mechanical coupling fracture. The stress and stress intensities are investigated for the effect of crack spacing. Strength evaluation of piezoelectric materials under the transient thermal environment is made and thermal shock resistance of the medium is given. 相似文献
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Gyroscopic dynamic system can be introduced to Hamiltonian system.Based on an adjoint symplectic subspace iteration method of Hamiltonian gyroscopic system, an adjoint symplectic subspace iteration method of indefinite Hamiltonian function gy- roscopic system was proposed to solve the eigenvalue problem of indefinite Hamiltonian function gyroscopic system.The character that the eigenvalues of Hamiltonian gyroscopic system are only pure imaginary or zero was used.The eigenvalues that Hamiltonian function is negative can be separated so that the eigenvalue problem of positive definite Hamiltonian function system was presented,and an adjoint symplectic subspace iteration method of positive definite Hamiltonian function system was used to solve the separated eigenvalue problem.Therefore,the eigenvalue problem of indefinite Hamiltonian function gyroscopic system was solved,and two numerical examples were given to demonstrate that the eigensolutions converge exactly. 相似文献
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《International Journal of Solids and Structures》2003,40(20):5353-5370
The electro-elastic interaction between a piezoelectric screw dislocation located either outside or inside inhomogeneity and circular interfacial rigid lines under anti-plane mechanical and in-plane electrical loads in linear piezoelectric materials is dealt with in the framework of linear elastic theory. Using Riemann–Schwarz’s symmetry principle integrated with the analysis of singularity of complex functions, the general solution of this problem is presented in this paper. For a special example, the closed form solutions for electro-elastic fields in matrix and inhomogeneity regions are derived explicitly when interface containing single rigid line. Applying perturbation technique, perturbation stress and electric displacement fields are obtained. The image force acting on piezoelectric screw dislocation is calculated by using the generalized Peach–Koehler formula. As a result, numerical analysis and discussion show that soft inhomogeneity can repel screw dislocation in piezoelectric material due to their intrinsic electro-mechanical coupling behavior and the influence of interfacial rigid line upon the image force is profound. When the radian of circular rigid line reaches extensive magnitude, the presence of interfacial rigid line can change the interaction mechanism. 相似文献
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Hui-Ming Wang 《Archive of Applied Mechanics (Ingenieur Archiv)》2014,84(4):491-503
Based on the electro-mechanical coupling theory and the laminate elasticity theory, an electro-elastic solution is obtained for the fiber-reinforced cylindrical composites with integrated piezoelectric actuators when subjected to mechanical and electrical loadings. The hybrid composite is composed of three parts: internal piezoelectric actuator, fiber-reinforced laminated interlayer, and external piezoelectric actuator. The general solution in each piezoelectric smart layer is obtained by introducing three undetermined constants, and the general solutions in the fiber-reinforced laminated interlayer are obtained by means of the state-space method. The mechanical behaviors of the hybrid fiber-reinforced cylindrical composites are investigated. The illustrative examples show that the fiber’s angle, the stacking sequence as well as the applied electric loading strongly affect the physical fields in the fiber-reinforced multilayered cylindrical composites. 相似文献
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Symplectic solution system for reissner plate bending 总被引:3,自引:0,他引:3
Based on the Hellinger-Reissner variatonal principle for Reissner plate bendingand introducing dual variables, Hamiltonian dual equations for Reissner plate bending werepresented. Therefore Hamiltonian solution system can also be applied to Reissner platebending problem, and the transformation from Euclidian space to symplectic space and fromLagrangian system to Hamiltonian system was realized. So in the symplectic space whichconsists of the original variables and their dual variables, the problem can be solved viaeffective mathematical physics methods such as the method of separation of variables andeigenfunction-vector expansion. All the eigensolutions and Jordan canonical formeigensolutions for zero eigenvalue of the Hamiltonian operator matrix are solved in detail, and their physical meanings are showed clearly. The adjoint symplectic orthonormal relation of the eigenfunction vectors for zero eigenvalue are formed. It is showed that the alleigensolutions for zero eigenvalue are basic solutions of the Saint-Venant problem and theyform a perfect symplectic subspace for zero eigenvalue. And the eigensolutions for nonzeroeigenvalue are covered by the Saint-Venant theorem. The symplectic solution method is notthe same as the classical semi-inverse method and breaks through the limit of the traditional semi-inverse solution. The symplectic solution method will have vast application. 相似文献
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《International Journal of Solids and Structures》2007,44(7-8):2540-2552
This paper presents the general solutions of antiplane electro-mechanical field solutions for a piezoelectric finite wedge subjected to a pair of concentrated forces and free charges. The boundary conditions on the circular segment are considered as fixed and grounded. Employing the finite Mellin transform method, the stress and electrical displacement at all fields of the piezoelectric finite wedge are derived analytically. In addition, the singularity orders and intensity factors of stress and electrical displacement can also be obtained. These parameters can be applied to examine the fracture behavior of the wedge structure. After being reduced to the problem of an antiplane edge crack or an infinite wedge in a piezoelectric medium, the results compare well with those of previous studies. 相似文献
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《International Journal of Solids and Structures》2006,43(5):943-956
The recent developments in smart structures technology have stimulated renewed interest in the fundamental theory and applications of linear piezoelectricity. In this paper, we investigate the decay of Saint-Venant end effects for plane deformations of a piezoelectric semi-infinite strip. First of all, we develop the theory of plane deformations for a general anisotropic linear piezoelectric solid. Just as in the mechanical case, not all linear homogeneous anisotropic piezoelectric cylindrical solids will sustain a non-trivial state of plane deformation. The governing system of four second-order partial differential equations for the two in-plane displacements and electric potential are overdetermined in general. Sufficient conditions on the elastic and piezoelectric constants are established that do allow for a state of plane deformation. The resulting traction boundary-value problem with prescribed surface charge is an oblique derivative boundary-value problem for a coupled elliptic system of three second-order partial differential equations. The special case of a piezoelectric material transversely isotropic about the poling axis is then considered. Thus the results are valid for the hexagonal crystal class 6mm. The geometry is then specialized to be a two-dimensional semi-infinite strip and the poling axis is the axis transverse to the longitudinal direction. We consider such a strip with sides traction-free, subject to zero surface charge and self-equilibrated conditions at the end and with tractions and surface charge assumed to decay to zero as the axial variable tends to infinity. A formulation of the problem in terms of an Airy-type stress function and an induction function is adopted. The governing partial differential equations are a coupled system of a fourth and third-order equation for these two functions. On seeking solutions that exponentially decay in the axial direction one obtains an eigenvalue problem for a coupled system of fourth and second-order ordinary differential equations. This problem is the piezoelectric analog of the well-known eigenvalue problem arising in the case of an anisotropic elastic strip. It is shown that the problem can be uncoupled to an eigenvalue problem for a single sixth-order ordinary differential equation with complex eigenvalues characterized as roots of transcendental equations governing symmetric and anti-symmetric deformations and electric fields. Assuming completeness of the eigenfunctions, the rate of decay of end effects is then given by the real part of the eigenvalue with smallest positive real part. Numerical results are given for PZT-5H, PZT-5, PZT-4 and Ceramic-B. It is shown that end effects for plane deformations of these piezoceramics penetrate further into the strip than their counterparts for purely elastic isotropic materials. 相似文献
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Hamilton体系下环扇形域的Stokes流动问题 总被引:1,自引:0,他引:1
基于极坐标下Stokes流的基本方程,将径向坐标模拟为时间坐标,推导了Hamilton体系下Stokes流动问题的对偶方程,采用本征向量展开法对环扇形域Stokes流动问题进行了分析,并给出了相应的实际算例,其结果说明了本文方法的有效性。 相似文献