用正交曲线坐标系中的曲壳单元分析旋转壳的自由振动

本文采用正交曲线坐标系中考虑横向剪切变形的双曲旋转壳单元,对几种不同类型的旋转壳的自由振动进行了分析。为了计算封闭和半封闭的旋转壳,本文用半解析法,由位移连续条件导出旋转壳顶点的两类位移限制条件,并通过结圆自由度的变换,将其转换为齐次形式。当壳体的经线有折角时,我们采用模态综合法分析它的固有振动特性。     

非均匀变厚度梁的动力响应的一般解

在本文中提出一个新方法——阶梯折算法来研究在任意载荷下任意非均匀和任意变厚度伯努利-欧拉梁的动力响应问题.研究了自由振动和强迫振动.新方法需要将区间离散为一定数目的元素,每个元素可看作是均匀和等厚度的.因此均匀、等厚度梁的一般解可在每个元素上应用.然后用初参数表示的整个梁的一般解使之满足相邻二元素间的物理和几何连续条件,这样就可以得到解析形式的自由振动的频率方程和解析形式的强迫振动的最终解,它化为求解二元线性代数方程,与离散元素的数目无关.现在的方法可推广应用至任意非均匀及任意变厚度有粘滞性和其他种类的梁以及其他结构元件问题上去.     

GENERAL ANALYTIC SOLUTION OF DYNAMIC RESPONSE OF BEAMS WITH NONHOMOGENEITY AND VARIABLE CROSS-SECTION

In this paper, a new method, the step-reduction method, is proposed to investigate the dynamic response of the Bernoulli-Euler beams with arbitrary nonhomogeneity and arbitrary variable cross-section under arbitrary loads. Both free vibration and forced vibration of such beams are studied. The new method requires to discretize the space domain into a number of elements. Each element can be treated as a homogeneous one with uniform thickness. Therefore, the general analytical solution of homogeneous beams with uniform cross-section can be used in each element. Then, the general analytic solution of the whole beam in terms of initial parameters can be obtained by satisfying the physical and geometric continuity conditions at the adjacent elements. In the case of free vibration, the frequency equation in analytic form can be obtained, and in the case of forced vibration, a final solution in analytical form can also be obtained which is involved in solving a set of simultaneous algebraic equations with only