具有摩擦支承边界的非线性板,梁结构的阻尼特性分析

本文研究了具有纵向干摩擦支承的矩形板和梁的非线性强迫振动,文中采用双线性迟滞弹簧摩擦模型表示边界摩擦力,按照该模型,随位移幅值增加,板和梁的摩擦面相继经历粘住,瞬态滑动,粘住－滑动三种运动状态,由Ｇａｌｅｒｋｉｎ法和一阶ＨＢＭ法求板和梁的稳态响应,通过对摩擦力参数变化时的典型幅频曲线的数值仿真,揭示在软,硬弹簧非线性的综合影响下,系统的振动性态及其摩擦阻尼的作用机理,此外,文中还导出边界干摩擦力的     

弹性地基上自由边矩形板弯曲问题的研究

本文对于弹性地基上自由边矩形板弯曲问题构造了满足全部自由边界条件和自由角点条件的特殊挠度函数，然后应用能量原理得出该问题的挠度解答。通过算例验算了该方法的正确性，计算结果表明，该方法具有简便，精度高的优点，是工程结构计算的有效方法。     

四角点支承四边自由矩形板自振分析新方法

四角点支承四边自由矩形板振形函数表达式由四边自由板所固有的基本振形和角点力所激发的附加振形组成。振形函数要满足振动微分方程和板挠度与角点力间的微分关系。为表示矩形板双向振动规律,基本振形在二个坐标轴方向分别有各自的表达式,并符合对应方向边界所限定的变形和受力特征：在对应自由边界上振幅不为零而剪力分布为零值,在自由角点处对应的四个角点力均为零值。而附加振形在角点处的振幅与角点力要符合板弯曲理论中的微分关系,在四个自由边界上对应的剪力分布均为零值。这种方法克服了现有解法中的理论缺陷,计算理念更合理。     

转动弹性支承矩形板自由振动的一般解析解法

转动弹性支承边与简支边,平夹边均有不同,一方面板边均能防止上下移动,即其挠度均为零。而转动弹性支承边,由于在边界装有均匀分布的转动弹簧使边界弯矩受到斜度的制约而与板边的斜度成正比。采用矩形薄板自由振动横向位移函数的微分方程建立了一般性的解析解,该一般解包括三角函数和双曲线函数组成的解,它能满足4个边为任意边界条件的问题。解中的待定常数可由4边的边界条件来确定,由此得出的齐次线性代数方程系数矩阵行列式等于零可以精确地求得各阶固有频率及其振型。由于矩形板对中间轴具有对称性,利用对称和反对称条件可使求解大大简化。对于正方形板还可利用对角线的对称性而毫无遗漏地找出最低的各阶频率及其振型。以四边均为转动弹性支承方板为例进行计算和讨论。     

二邻边及对角点支承的矩形板弯曲

本文采用叠加法求出二邻边及对角点支承的三种矩形板在板面，板边布荷载和的下弯曲解，计算表明，这种解法速度快，计算精度高。     

板柱结构矩形弹性板弯曲精确解法

板柱结构是工程中经常采用的受力体系,但至今尚无一种精确解法分析板中内力分布。将板柱结构矩形板的弯曲划分为广义静定和广义超静定二类。对于前者利用静力平衡条件确定柱支反力后撤去柱支座,柱支条件下板的弯曲即转换为四边自由矩形板在原荷载和柱支反力共同作用下的弯曲。挠度表达式采用了新的通解形式,其变形曲线符合四边自由边界所限定的变形特征,并采用组合特解,即特解同时满足平衡微分方程,自由边界上剪力分布条件及自由角点上作用力条件,从而可以利用四边边界条件和柱支座处的位移条件直接求解。对于广义超静定弯曲需要利用叠加法求解。这种解法可以分析板柱结构在任意柱支条件下和任意荷载作用下板的弯曲。通过逆向分析验证法真实地说明了本解法具有很高的计算精度。     

四边支承矩形板弯曲统一求解方法──兼论纳维叶解与李维解法的统一性

本文的统一解法可以解决四边支承的矩形板在任意荷载作用下的弯曲．这种解法沟通了纳维叶解与李维解法的内在联系,并解释了经典解法存在局限性的原因．这种求解方法思路清晰,收敛速度快,计算精度高,适用范围广。     

一对边支承一对边自由的矩形板弯曲统一求解方法

根据边界条件的相近性,本文对一对边支承一对边自由的矩形板提出了一种统一的弯曲挠度表达式。该表达式切合板边界所能激发出的弯曲变形形态和角点位时所导致的非弯曲变形特点。它可以计算矩形板在任意荷载作用下和板边界发生任意支座位移时的弯曲。该方法求解思路清晰,收敛速度快,计算精度高。     

边界粘弹性支承对矩形板强迫振动响应的影响

提出边界粘弹性支承对矩形板强迫振动响应影响的分析方法。该方法基于阻尼复模态分析,利用阻尼复模态的正交性,导出了板的完全解耦的模态方程;通过算例研究和讨论了粘弹性边界支承对板的振动响应的影响。     

双模量矩形板的大挠度弯曲计算分析

双模量矩形板在外载荷作用下,会形成各向同性的拉伸区和压缩区,把双模量矩形板看成两种各向同性材料组成的层合板,采用弹性力学理论建立了双模量矩形板在外载荷作用下的静力平衡方程,利用静力平衡方程确定了双模量矩形板的中性面位置,推导出了双模量矩形板的大挠度弯曲变形微分方程。用加权残值法求得了双模量矩形板的大挠度弯曲变形时板中点挠度,把该方法计算结果与有限元计算结果进行了比较,说明了该计算方法是可靠的,并讨论分析了双模量对矩形板大挠度弯曲变形的影响。     

The problem of isotropic rectangular plate with four clamped edges

The examination of the exact solution of the governing equation of the rectangular plate is important for many reasons. This report discusses in exact solution of the governing equation of an isotropic rectangular plate with four clamped edges. A numerical method for clamped isotropic rectangular plate under distributed loads and an exact solution of the governing equation in terms of trigonometric and hyperbolic function are given. Finally, an illustrative example is given and the results are compared with those reported earlier. This method is found to be easier and effective. The results show reasonable agreement with other available results, but with a simpler and practical approach.     

19英寸显示器110°矩形偏转线圈的设计

设计了用于 19英寸显示器、具有 110°偏转角的一种新型的矩形偏转线圈。这种矩形偏转线圈可节省偏转能量 ,提高偏转灵敏度。由于采用了一种简单新颖的设计方法 ,不仅避免了复杂的三维电磁场计算和优化 ,而且还可利用现有的旋转对称偏转线圈的计算结果 ,因此可节省大量的时间。文中给出了相应的设计结果。结果表明 ,采用该方法所设计的新型矩形偏转线圈具有很好的偏转性能 ,进一步证明了所用方法是一种行之有效的方法。该方法不仅可用于非旋转对称矩形线圈的设计 ,而且还可用于其它的电磁场问题。     

Random field of initial deflections and strength of thin rectangular plates

The use of an integral measure of initial deflections of thin plates, based on the strain energy, has proved to be of importance in studying the influence of the imperfections on the strength of plates subjected to in-plane compression. The energy measure allows for a straightforward definition of compound modes and for a computational determination of the lower bound strength. The last quantity may be essential for assessment of plate design strength considering the imperfections as a random field.     

一种便捷的新型矩形偏转线圈的设计方法

针对新型矩形偏转线圈的设计提出了一种简单新颖的设计方法。该方法不仅可以避免复杂的三维电磁场计算和优化,而且还可以利用现有的旋转对称偏转线圈的计算结果,因此可节省大量的时间。此外,该方法不仅可用于非旋转对称矩形线圈的设计,还可用于其它的电磁场问题。文中采用一简单的偏转线圈结构模型,从数值计算和实验验证两方面证明了该方法的正确性和可行性。     

矩形偏转系统的近似多极场模型

提出了可以应用于矩形偏转系统的近似多极场模型,并给出了应用该模型进行偏转系统优化设计的方法,计算比较了旋转对称多极场模型和矩形近似多极场模型的磁场分布,应用近似多极场模型对矩形偏转系统的偏转像差进行了优化计算,得到了较好的像差校正效果。     

Artificial neural network model of the strength of thin rectangular plates with weld induced initial imperfections

Probabilistic assessment of post-buckling strength of thin plate is a difficult problem because of computational effort needed to evaluate single collapse load. The difficulties arise from the nonlinear behaviour of an in-plane loaded plate showing up multiple equilibrium states with possible bifurcations, snap-through or smooth transitions of states. The plate strength depends heavily on the shape of geometrical imperfection of the plate mid-surface. In this paper, an artificial neural network (ANN) is employed to approximate the collapse strength of plates as a function of the geometrical imperfections. For the training set, mainly theoretical imperfections with the corresponding collapse loads of plate calculated by FEM are considered. The ANN validation is based on the measured imperfections of ship plating and FEM strength.     

Large deflection behavior of functionally graded plates under pressure loads

Large deflection analysis of rectangular functionally graded plates is studied in this paper. It is assumed that the mechanical properties of the plate, graded through the thickness, are described by a simple power law distribution in terms of the volume fractions of constituents. The plate is assumed to be under pressure load. The fundamental equations for rectangular plates of FGM are obtained using the Von-Karman theory for large deflection and the solution is obtained by minimization of the total potential energy. Numerical results for rectangular functionally graded plates are given in dimensionless graphical forms. The effects of material properties on the stress field through the thickness are determined and discussed.     

Nonlinear static response of laminated composite plates by discrete singular convolution method

In this paper, large deflection analysis of laminated composite plates is analysed. Nonlinear governing equation for bending based on first-order shear deformation theory (FSDT) in the von Karman sense is presented. These equations have been solved by the method of discrete singular convolution (DSC). Regularized Shannon’s delta (RSD) kernel and Lagrange delta sequence (LDS) kernel are selected as singular convolution to illustrate the present algorithm. The effects of plate aspect ratio, fiber orientation, boundary conditions, thickness-to-side ratio, and applied load on the nonlinear static response of the laminated plate are investigated.     

EJMA标准矩形波纹管计算公式探讨

美国膨胀节制造商协会标准（简称EJMA）从1985年修订第五版就给出了矩形波纹管的计算公式,其推导过程原理是按照材料力学超静定方法,将波纹部分的受力变成两端固支的两个梁的叠加,从而推导出计算公式,矩形波纹管实际的推导原理应按照长短边不等的框架处理,这样EJMA给出的公式与实际有很大误差。本文按照EJMA及实际情况分别给出了各个计算公式,从而判定了EJMA中计算公式的不准确。     

Hygrothermal effects on the bending of angle-ply composite plates using a sinusoidal theory

The sinusoidal shear deformation plate theory is presented to study the response of multilayered angle-ply composite plates due to a variation in temperature and moisture concentrations. The classical, uniform and parabolic shear deformation plate theories are also considered. The effects of temperature and moisture concentrations on the material properties and the hygrothermal response of multilayered angle-ply composite plates are studied. A number of examples are solved to illustrate the numerical results concerning bending response of multilayered angle-ply composite plates subjected to hygro-thermo-mechanical effects. Hygrothermal response due to a variation in temperature and moisture concentrations has been investigated for different material types sensitive to changing hygrothermal environment conditions. Numerical results suggest that temperature-dependent and/or moisture-dependent material properties ought to be used in the analysis of laminated plates subjected to hygrothermal loads.