非均质变截面折线形梁的面外振动的传递矩阵法

本文根据折线形梁面外二维振动的特点,用传递矩阵法研究其面外振动特性,导出了非均质变截面折线形梁面外振动的频率方程,采用非线性代数方程的搜索求根方法计算固有频率。本文方法具有公式简洁和占计算机内存少的特点,可编制成通用程序在小型微机上分析大型折线形梁的面外振动特性。     

机械荷载与热荷载共同作用下变厚度梁的热弹性力学解

本文研究了两端简支变厚度梁受机械荷载与热荷载共同作用下的热弹性力学解.温度场用调和级数展开,通过求解热传导方程可首先确定温度沿梁厚度方向的非线性分布情况.从二维热弹性力学理论的基本方程出发,导出满足控制微分方程和两端简支边界条件的位移函数的一般解,对上下表面的边界方程作傅立叶正弦级数展开确定待定系数,数值结果与商业有限元软件ANSYS进行了比较,显示出很高的精度.本文方法可直接应用于对应力和位移分析要求较高的工程问题,如航空航天和微型机械的设计.     

微重力状态下旋转对称刚性容器中液体晃动研究

本文研究微重状态下旋转对称刚性容器中液体晃动问题。用摄动迭代法计算静止自由液面,精度较高。利用微幅晃动条件,使运动方程线性化,导出了液体晃动固有频率的计算公式。最后,对园柱形容器进行了具体计算。     

多自由度振动系统的快速控制

研究多自由度振动系统的时间最优控制问题．利用主振型的正交性，将多自由度系统的振动变换为一系列独立的主振动，在分别求得各阶主振动的快速控制表达式后，再由振型变换得整个系统的快速控制解，代入约束条件得最速时间应满足的方程，由计算机数值求得最速时间．     

最小二乘识别的一个改进算法

本文首先研究采样频率对最小二乘识别精度的影响,分析了过高采样频率导致识别失败的原因,然后提出了一种既可充分利用采样数据又简单实用的改进算法,方法对单测点和多测点均适用,最后举例说明本文方法的有效性.     

任意形状弹性薄板弯曲的精确解*

本文提供了一个求解任意形状弹性薄板弯曲的新方法,在求得了极坐标系中弹性薄板弯曲微分方程的精确解后,将解代入薄板的边界条件,利用Fourier级数将边界方程展开,可确定出各待定常数,所得结果是精确的。     

计及表面波的圆环形贮液容器的弯曲自由振动*

本文研究考虑表面波作用的圆环形贮液容器的弯曲自由振动问题,导出了贮液容器与液体耦联振动的振型函数和固有频率的精确计算公式,结果可借助于计算机求解.分析表明,水对容器的振动效应可等效于在内外环体上分别附着一不同的广义分布质量.     

Vibration of arbitrarily shaped membranes with elastical supports at points

This paper presents a new method for solving the vibration of arbitrarily shaped membranes with elastical supports at points. The reaction forces of elastical supports at points are regarded as unknown external forces acting on the membranes. The exact solution of the equation of motion is given which includes terms representing the unknown reaction forces. The frequency equation is derived by the use of the linear relationship of the displacements with the reaction forces of elastical supports at points. Finally the calculating formulae of the frequency equation of circular membranes are analytically performed as examples and the inherent frequencies of circular membranes with symmetric elastical supports at two points are numerically calculated.     

Elasticity solution of clamped-simply supported beams with variable thickness

This paper studies the stress and displacement distributions of continuously varying thickness beams with one end clamped and the other end simply supported under static loads. By introducing the unit pulse functions and Dirac functions, the clamped edge can be made equivalent to the simply supported one by adding the unknown horizontal reactions. According to the governing equations of the plane stress problem, the general expressions of displacements, which satisfy the governing differefitial equations and the boundary conditions attwo ends of the beam, can be deduced. The unknown coefficients in the general expressions are then determined by using Fourier sinusoidal series expansion along the upper and lower boundaries of the beams and using the condition of zero displacements at the clamped edge. The solution obtained has excellent convergence properties. Comparing the numerical results to those obtained from the commercial software ANSYS, excellent accuracy of the present method is demonstrated.