A GENERAL ANALYTICAL SOLUTION FOR ELASTIC VIBRATION OF RECTANGULAR THIN PLATES

A general solution of differential equation for lateral displacement function of rectangular elastic thin plates in free vibration is established in this paper. It can be used to solve the vibration problem of rectangular plate with arbitrary boundaries. As an example. the frequency and its vibration mode of a rectangular plate with four edges free have been Solved.     

正交异性矩形板弯曲问题的解析解

本文对求解正交异性矩形板弯曲问题,采用先建立微分方程的一般解,然后根据边界条件确定积分常数,求解了特征方程为复数根的情形。     

大曲率圆环壳对称变形的应力公式

压力容器封头顶点开孔接管处,为了减小应力集中,常做成半径很小的圆角,如图1所示.因此应将接管处看成是包含有经向曲率半径R_1很小的圆环壳.当采用薄壳结构力学方法求得圆环壳的内力和内矩后,如仍采用薄壳的应力公式来计算最大应力,则误差将随着R_1的减小而更加增大.本文参照大曲率杆的应力计算方法建立了大曲率圆环壳对称变形的应力公式,可以较精确地计算出圆角处的局部应力.如图2所示,圆环壳子午面微段中面以及距离中面为z 沿经线的长分别为     

FREE VIBRATION OF ANISOTROPIC RECTANGULAR PLATES BY GENERAL ANALYTICAL METHOD

According to the differential equation for transverse displacement function of anisotropic rectangular thin plates in free vibration, a general analytical solution is established. This general solution, composed of the composite solutions of trigonometric function and hyperbolic function, can satisfy the problem of arbitrary boundary conditions along four edges. The algebraic polynomial with double sine series solutions can also satisfy the problem of boundary conditions at four corners. Consequently, this general solution can be used to solve the vibration problem of anisotropic rectangular plates with arbitrary boundaries accurately. The integral constants can be determined by boundary conditions of four edges and four corners. Each natural frequency and vibration mode can be solved by the determinate of coefficient matrix from the homogeneous linear algebraic equations equal to zero. For example, a composite symmetric angle ply laminated plate with four edges clamped has been calculated and discussed.     

轴对称载荷作用下迭层复合材料旋转壳的分段解析法

纤维缠绕旋转壳体结构具有重量轻、强度高、易加工等优点,这样的壳体在宇航技术中应用最多,这样的壳体沿子午线的刚度是变化的,但通常是正交异性的,且壳壁很薄,因而可以用分段解析法求得近似解。即把壳体沿其旋转轴分成许多个截壳单元,对每一截壳用解析法求 ...     

ANALYSIS OF SYMMETRIC LAMINATED RECTANGULAR PLATES IN PLANE STRESS

Symmetric laminated plates used usually are anisotropic plates. Based on the fundamental equation for anisotropic rectangular plates in plane stress problem, a general analytical solution is established accurately by method of stress function. Therefore the general formula of stress and displacement in plane is given. The integral constants in general formula can be determined by boundary conditions. This general solution is composed of solutions made by trigonometric function and hyperbolic function, which can satisfy the problem of arbitrary boundary conditions along four edges, and the algebraic polynomial solutions which can satisfy the problem of boundary conditions at four corners. Consequently this general solution can be used to solve the plane stress problem with arbitrary boundary conditions. For example, a symmetric laminated square plate acted with uniform normal load, tangential load and nonuniform normal load on four edges is calculated and analyzed.     

对称迭层矩形板的平面应力分析

常用的对称迭层板为各向异性板．根据平面应力问题的基本方程精确地用应力函数解法求得了各向异性板的一般解析解．推导出平面内应力和位移的一般公式，其中积分常数由边界条件来决定．一般解包括三角函数和双曲函数组成的解，它能满足4个边为任意边界条件的问题．还有代数多项式解，它能满足4个角的边界条件．因此一般解可用以求解任意边界条件下的平面应力问题．以4边承受均匀法向和切向载荷以及非均匀法向载荷的对称迭层方板为例，进行了计算和分析．     

镁铁水滑石的制备及其对小球藻油脂合成生物柴油的催化性能

用改良尿素法制备了镁铁水滑石(MgFe-LDH),对其在小球藻油脂合成生物柴油反应中的催化性能进行了研究。利用XRD、FT-IR、SEM及FT-IR拟合、去卷积分析等技术对所制备的MgFe-LDH进行了表征,考察了pH值、Mg/Fe摩尔比、反应温度和时间对其结构和性能的影响。结果表明,Mg/Fe摩尔比为3或4、pH值为9.5,在110 ℃条件下反应10 h,所制备的MgFe-LDH(Mg3Fe或Mg4Fe)结晶度最高,粒径均匀,结构规整。与Mg/Fe摩尔比为2的MgFe-LDH(Mg2Fe)相比,Mg3Fe或Mg4Fe在完全分解焙烧时,其层板结构保持稳定,具有较高的晶体结晶度、较多的催化活性位和较高的催化活性。以Mg3Fe金属氧化物为催化剂,在醇/油摩尔比为6时反应1.5 h,生物柴油产率可达87％;该催化剂循环使用3次,仍具一定催化活性。     

各向异性矩形薄板弯曲问题的一般解

给出了各向异性矩形薄板弯曲问题微分方程的一般解。可以求解任意载荷作用下各种边界的弯曲问题。以四边固支的正方形板为例进行了数值计算。     

基于调和分析法的全球地形球谐系数模型构建

针对当前全球地形球谐系数模型构建表达精度不高、计算效率较低等问题,研究推导了Gauss-Legendre积分法、矩形离散积分法求解球谐系数公式,提出了联合FFT技术和基于OpenMP多核并行技术的计算优化策略,实现了全球2160阶地形球谐系数模型的高效构建.利用模型Earth2012对两种方法进行了对比分析,结果表明:...