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弹性地基上自由边矩形板的弯曲、稳定和振动 总被引:3,自引:0,他引:3
本文讨论了在弹性地基上自由边矩形板的弯曲、稳定和振动的问题.本文选择了一个挠曲函数,它不但能满足自由边的全部边界条件,而且也满足了自由角点的条件,从而得到了较好的近似解,文中使用了能量法. 相似文献
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弹性地基上的自由边矩形板 总被引:1,自引:0,他引:1
本文讨论了在弹性地基上的自由边矩形板的弯曲问题.我们讨论了两种情形,诸如在板的中心受到一集中力作用和在板的四个角点上各受到一相等的集中力作用.文中选择了一个挠曲函数,它不但能满足所有自由边上的全部几何边界条件,而且也满足所有的内力边界条件.同时,我们应用了变分法,从而得到了较好的近似解答. 相似文献
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本文在Castigliano原理的基础上推广了单位虚载荷法.据此,用力法直接导出了梁、板和壳一类结构的挠曲面的一般方程.我们导出了具有非齐次位移边界条件的矩形薄板和考虑横向切变形影响的矩形厚板的挠曲面方程.同时给出了相应直梁的挠曲轴方程.推广了互等定理的应用.计算了三个简例. 相似文献
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王子文 《应用数学与计算数学学报》2014,(4):449-453
给出了矩阵函数f(X)=A-BX-(BX)*的秩和最小惯性指数定理,其中*表示矩阵的共轭转置.作为应用,给出了Lyapunov矩阵方程以及矩阵不等式BX+(BX)*≥A和BX+(BX)*≤A可解的若干充要条件. 相似文献
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针对核函数和自由项代数且对数奇异的第一类线性Volterra积分方程,通过Laplace变换导出这类方程的解在零点的渐近展开式,对于方程解的奇异性质给出准确刻画.对于核函数仅代数奇异的情形,还得到方程的解在无穷远点的渐近展开式.这些展开式可以分别作为当自变量变小或变大时方程的近似解.最后,给出实例说明展开式的正确性及有效性. 相似文献
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任意厚度具有自由边叠层板的精确解析解 总被引:1,自引:0,他引:1
自由边问题一直是三维弹性力学中的难题,通常很难满足自由边上一个正应力和两个剪应力都等于0.基于三维弹性力学基本方程和状态空间方法,引入自由边界位移函数并考虑全部弹性常数,建立了正交异性具有自由边单层和叠层板的状态方程.对状态方程中的变量以级数形式展开,通过边界条件的满足精确求解任意厚度具有自由边叠层板的位移和应力,此解满足层间应力和位移的连续条件.算例计算表明,采用引入的位移函数形式,简化了计算过程并且采用较少的级数项可以获得收敛解.与有限元方法计算结果进行了对比,可以得到较高精度的数值结果.其解可以作为其它数值方法和半解析方法的参考解. 相似文献
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以Poisson方程的混合变分形式为基础,采用移动最小二乘方法建立插值形函数空间,给出了Poisson方程的混合无网格方法,理论上证明了Poisson方程混合无网格解的存在唯一性,并给出了误差估计.本质边界条件的处理采用Lagrange乘子法.数值算例表明,在应用相同阶次的基函数条件下,利用混合无网格方法求解Poisson方程所得的解的梯度值优于传统的无网格方法及有限元法. 相似文献
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张新平 《数学的实践与认识》2002,32(2):290-296
给出了在 Lp,2 p<∞ ,范意义下 ,核下自由项均属于 H函数类的多维 Fredholm积分方程类近似解的ε-计算复杂性估计 . 相似文献
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Color degree and monochromatic degree conditions for short properly colored cycles in edge‐colored graphs 下载免费PDF全文
《Journal of Graph Theory》2018,87(3):362-373
For an edge‐colored graph, its minimum color degree is defined as the minimum number of colors appearing on the edges incident to a vertex and its maximum monochromatic degree is defined as the maximum number of edges incident to a vertex with a same color. A cycle is called properly colored if every two of its adjacent edges have distinct colors. In this article, we first give a minimum color degree condition for the existence of properly colored cycles, then obtain the minimum color degree condition for an edge‐colored complete graph to contain properly colored triangles. Afterwards, we characterize the structure of an edge‐colored complete bipartite graph without containing properly colored cycles of length 4 and give the minimum color degree and maximum monochromatic degree conditions for an edge‐colored complete bipartite graph to contain properly colored cycles of length 4, and those passing through a given vertex or edge, respectively. 相似文献
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We model the roadway of a suspension bridge as a thin rectangular plate and we study in detail its oscillating modes. The plate is assumed to be hinged on its short edges and free on its long edges. Two different kinds of oscillating modes are found: longitudinal modes and torsional modes. Then we analyze a fourth order hyperbolic-like equation describing the dynamics of the bridge. In order to emphasize the structural behavior we consider an isolated equation with no forcing and damping. Due to the nonlinear behavior of the cables and hangers, a structural instability appears. With a finite dimensional approximation we prove that the system remains stable at low energies while numerical results show that for larger energies the system becomes unstable. We analyze the energy thresholds of instability and we show that the model allows to give answers to several questions left open by the Tacoma collapse in 1940. 相似文献
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Giovambattista Amendola 《Applicable analysis》2013,92(1):67-87
We consider the linear theory of the electromagnetism characterized by a constitutive equation for the current density with memory effects. We find in the frequency domain a first expression of the minimum free energy, which is the maximum recoverable work we can obtain from a given state of the material. By using another equivalent formulation of the minimum free energy, we give the explicit formulae for the particular case of a discrete spectrum model material response. 相似文献
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狄成宽 《数学的实践与认识》2011,41(23)
Lambert W函数具有的一些性质以及现今成熟的数学软件Maple等使得它能很好地应用于时滞微分方程的稳定性判别中.通过应用Lambert W函数对一阶复系数时滞微分方程渐近稳定性的判别命题,分析了一类参数反馈控制复系数时滞微分方程的稳定性,得到了更加精细的结果.相比已往的方法,新方法更简单、计算更方便并能快速有效的给出判定结果. 相似文献
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In this work, the static stability of a thin plate in axial subsonic airflow is studied using the framework of Possio integral equation. Specifically, we consider the cases when the plate’s leading edge is free and the plate’s trailing edge is either pinned or clamped. We formulate the problem under consideration using a partial differential equations (PDE) model and then linearize the model about the free stream velocity, density, and pressure, to enable analytical treatment. Based on the linearized model, we introduce a new derivation of a Possio integral equation that relates the pressure jump along the thin plate to the plate’s downwash. The steady state solution to the Possio equation is then used to account for the aerodynamic loads in the plate steady state governing equation resulting in a singular differential-integral equation which is transformed to a singular integral equation that represents the static aeroelastic equation of the plate. We verify the solvability of the static aeroelastic equation based on the Fredholm alternative for compact operators in Banach spaces and the contraction mapping theorem. By constructing solutions to the static aeroelastic equation and matching the nonzero boundary conditions at the trailing edge with the zero boundary conditions at the leading edge, we obtain characteristic equations for the free-clamped and free-pinned plates. The minimum solutions to the characteristic equations are the divergence speeds which indicate when static instabilities start to occur. We show analytically that free-pinned plates are statically unstable. We also construct, analytically, flow speed intervals that correspond to static stability regions for free-clamped plates. Furthermore, we resort to numerical computations to obtain an explicit formula for the divergence speed of free-clamped plates. Finally, we apply the obtained results on piezoelectric plates and we show that free-clamped piezoelectric plates are statically more stable than conventional free-clamped plates due to the piezoelectric coupling. 相似文献
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《中国科学 数学(英文版)》2015,(9)
This paper is the first attempt to investigate the risk probability criterion in semi-Markov decision processes with loss rates. The goal is to find an optimal policy with the minimum risk probability that the total loss incurred during a first passage time to some target set exceeds a loss level. First, we establish the optimality equation via a successive approximation technique, and show that the value function is the unique solution to the optimality equation. Second, we give suitable conditions, under which we prove the existence of optimal policies and develop an algorithm for computing ?-optimal policies. Finally, we apply our main results to a business system. 相似文献
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Ovidiu Cârj? 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(10):3382-873
We give here a characterization of a Lyapunov pair for a multi-valued semi-linear evolution equation on a Banach space by means of an appropriate lower contingent derivative. The contingent derivative introduced in this paper is related to a new concept of tangency introduced recently in [O. Cârj?, M. Necula, I.I. Vrabie, Necessary and sufficient conditions for viability for semilinear differential inclusions, Trans. Amer. Math. Soc. 361 (2009) 343-390]. As an application, we give a controllability result and a Lipschitz estimate of the corresponding minimum time function under a Petrov-like condition. 相似文献
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Serge Nicaise 《Mathematical Methods in the Applied Sciences》1994,17(1):21-39
We study some boundary value problems on two-dimensional polygonal topological networks, where on each face, the considered operator is the biharmonic operator. The transmission conditions we impose along the edges are inspired by the models introduced by H. Le Dret [13] and Destuynder and Nevers [9]. The boundary conditions on the external edges are the classical ones. This class of problem contains the boundary value problems for the biharmonic equation in a plane polygon (see [3, 11, 12, 18]). Conforming to the classical results cited above, we prove that the weak solution of our problem admits a decomposition into a regular part and a singular part, the latter being a linear combination of singular functions depending on the domain and the considered boundary value problem. Finally, we give the exact formula for the coefficients of these singularities. 相似文献