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本文给出了变系数曲线支承的Ambarsumian矩形厚板自由振动问题的级数解,将位移和剪力在板域内展成重傅里叶级数,将其导数在边界上展成单傅里叶级数,通过傅里叶变换将控制微分方程和边界条件转化成关于位移级数的系数的一组无穷线性代数方程,最终将板的自由振动问题转化为矩阵特征值问题。 相似文献
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弹性半空间地基上正交异性矩形板弯曲通解 总被引:2,自引:0,他引:2
本文先对受任意边界约束的正交各向异性矩形薄板,在各种形式荷载作用下的弯曲问题,构造了四次逐项可导的带有补充项的双重正弦傅里叶级数新通解.该解析解既不需要叠加,对不同的物性参数又不需要分类,而且待定系数少又具有明确的物理含义,这使得正交各向异性矩形薄板的弯曲问题求解统一化、简单化、规律化.然后将新通解与弹性半空间受任意竖向荷载作用下的静力位移积分变换解相结合,得出弹性半空间地基上受任意边界约束的正交各向异性矩形板,在任意竖向荷载作用下的弯曲解析解.本文还给出了算例分析,其结果与文献吻合良好,证明本文的方法是切实可行的. 相似文献
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选取带有补充项的双重正弦傅里叶级数作为振型函数通解,来解析研究带裂纹矩形板的自由振动特性。先将带裂纹矩形板分割成若干小矩形板,利用各小矩形板的边界条件,并结合振型函数中待定常数的物理意义,简化得到各小矩形板的振型函数,再结合各板的控制方程、未使用的边界条件、公共边协调条件及本文提出公共自由角点的协调条件,建立求解频率的代数方程组,然后将其转化为广义特征值问题来求解带裂纹矩形板的无量纲频率;最后选取具体参数进行计算并与文献结果对比,吻合良好,证明了本文采用的研究方法以及所提出公共角点协调条件的正确性和合理性。由于该振型函数能满足矩形板的任意边界约束,且其中的待定常数具有明确的物理意义,所以可使矩形板问题的求解统一化、简单化和规律化。 相似文献
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Green函数法解点支承任意板自由振动频率 总被引:2,自引:0,他引:2
1 引言板是工程中经常采用的结构形式之一.沿边界呈对称点支承的悬臂板在土木工程中不乏常见.这种板的自由振动构成了典型板自振问题的一种特殊形式,由于解析法对自由边界条件及支承点的约束条件难以满足,所以常令科技人员感到棘手.H.T.Saliba 曾用4种级数迭加对这种板进行过分析、计算,得出几组计算结果.计算中每个级数取30 相似文献
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本文用样条边界元法分析轴对称圆形基础板的非线性非光滑接触。除事先给出外力与地基表面位移的对应关系外,地基的模型、板的厚薄(Reissner/Kirchhoff型)和外荷载沿径向的分布均可是任意的。文中将地基反力看作板的外载,对变量沿径向采用不等距祥条插值,并用无地基效应的板基本解。算例表明本文方法只要用少量自由度,便可得到令人满意的结果。 相似文献
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将富里叶-贝塞尔级数引入积分方程[1],推导出一种研究含振子及弹性支承圆板振动特性的新方法,根据积分方程和富里叶-贝塞尔级数理论,首先用第一类贝塞尔函数构造圆板的格林函数,然后由叠加原理将圆板的自由振动问题转化为积分方程的特征值问题;进面将积分方程形式的特征值问题转化为无穷阶矩阵的标准特征值问题,计算时根据精度的要求,截取无穷阶矩阵的标准特征值为有限阶矩阵的标准特征值问题,采用Q-R算法,计算实践表明,本方法不仅具有运算简捷,精度高,适用性强的特点,而且能从整体上对系统的动态性加以研究,从而为这类系统的优化设计提供有;力的 工具。 相似文献
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Nonlinear bending of simply supported symmetric laminated cross-ply rectangular plates 总被引:4,自引:0,他引:4
Based on the von Kármán-type theory of plates,nonlinear bending problems of simplysupported symmetric laminated cross-ply rectangular plates under the combined action ofpressure and inplane load are investigated in this paper.The solution which satisfies thegoverning equations and boundary conditions is obtained by using the double Fourier seriesmethod. 相似文献
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自由正交异性矩形厚板的动态稳定 总被引:3,自引:0,他引:3
对在一条边上作用着均匀分布的非保守跟随力的四边自由正交异性矩形厚板的动态稳定进行了分析,通过把位移和剪力展成重傅立叶级数解,把微分方程简化成了代数方程。计算表明厚度的微小变化会引起颤振载荷明显的减小。这个明显减小是因为存在剪切变形。 相似文献
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弹性地基上四边自由的各向异性矩形板 总被引:4,自引:2,他引:4
通过叠加法得到了弹性地基上的各向异性矩形板的一般解。每个叠加解被展成重傅立叶级数,其自身或其一阶导数在边界上的值被展成单傅立叶级数。利用控制微分方程和一些边界条件,每个叠加解被简化成用边界值的级数的系数表示的傅立叶级数。文后给出了弹性地基上的方板的挠曲面图。 相似文献
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Based on the three-dimensional elasticity equations, this paper studies the elastic bending response of a transversely isotropic functionally graded solid circular plate subject to transverse biharmonic forces applied on its top surface. The material properties can continuously and arbitrarily vary along the thickness direction. By virtue of the generalized England’s method, the problem can be solved by determining the expressions of four analytic functions. Expanding the transverse load in Fourier series along the circumferential direction eases the theoretical construction of the four analytic functions for a series of important biharmonic loads. Certain boundary conditions are then used to determine the unknown constants that are involved in the four constructed analytic functions. Numerical examples are presented to validate the proposed method. Then, we scrutinize the asymmetric bending behavior of a transversely isotropic functionally graded solid circular plate with different geometric and material parameters. 相似文献
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本文根据势能驻值原理,建立了均匀受压矩形管的大挠度弹性屈曲理论,用于分析屈曲后相邻板件间的相互约束作用,即屈曲后板组效应。该方法通过引入拉格朗日乘子,使系统总势能取驻值的同时,形函数能满足一系列基本的,但非完备的边界条件;在此基础上采用增量法将非线性方程组线性化,从而确定给定荷载下矩形管的受力状态及变形。由于系统总势能是以解析式的形式给出,且仅需取有限的级数项就可达到满意的精度,故该半解析法具有计算效率高的特点。目前许多国家的钢结构设计规范中,在计算受压板件的有效宽度时,常采用板组约束系数来考虑板组效应。由于有效宽度法本身考虑了板的屈曲后强度,而约束系数多数却是建立在小挠度弹性屈曲理论上的,故有必要分析板件的屈曲后板组效应。本文详细讨论了矩形管的屈曲后板组效应,并与小挠度理论给出的计算结果进行比较,得出了均匀受压矩形管屈曲后板组效应减弱的结论。 相似文献
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On the basis of anisotropic mathematical elasticity, using multiple conformal representations, the stress functions of multiple
complex variables for an infinite multiply-connected anisotropic plate are derived. The functions are developed in Fourier
series on unit circles, and the unknown coefficients of the functions are determined by undetermined coefficients method.
Then the stresses in the plate can be calculated. A plate containing multiple elliptical holes or cracks is discussed, and
the corresponding FORTRAN77 program is developed. Five examples are given. The results show that this method is very effective
and convenient.
The project supported by Aeronautical Science Foundation of China 相似文献
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Based on the first-order shear deformation plate theory with von Karman non-linearity, the non-linear axisymmetric and asymmetric behavior of functionally graded circular plates under transverse mechanical loading are investigated. Introducing a stress function and a potential function, the governing equations are uncoupled to form equations describing the interior and edge-zone problems of FG plates. This uncoupling is then used to conveniently present an analytical solution for the non-linear asymmetric deformation of an FG circular plate. A perturbation technique, in conjunction with Fourier series method to model the problem asymmetries, is used to obtain the solution for various clamped and simply supported boundary conditions. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. The results are verified by comparison with the existing results in the literature. The effects of non-linearity, material properties, boundary conditions, and boundary-layer phenomena on various response quantities in a solid circular plate are studied and discussed. It is found that linear analysis is inadequate for analysis of simply supported FG plates which are immovable in radial direction even in the small deflection range. Furthermore, the responses of FG materials under a positive load and a negative load of identical magnitude are not the same. It is observed that the boundary-layer width is approximately equal to the plate thickness with the boundary-layer effect in clamped FG plates being stronger than that in simply supported plates. 相似文献