弹性厚球壳的有限元动力分析及其应用

• 作 者: 徐燕申 David E.Gilsinn E.clayton Teague
• 机 构: 天津大学,美国NationalInstitute of Standards and Technology,美国NationalInstitute of Standards and Technology
• 出 处: 振动与冲击
• 发表日期: 1990年04期
• 关键词: 球壳 弹性 特征值 动力分析 测量机 固有振动模态 有限元 振型 解析解 对比讨论

本文用三维八节点块单元,进行了弹性厚球壳的动力特性分析,并与相应的弹性动力方程的解析解作了对比讨论。特征值计算表明,两种计算结果是十分接近的。有限元网格形状和单元数的多少,对特征值的计算结果甚有影响。弹性厚球壳的一个特征值,对应着一组模态振型,在文中作了理论上的解释,并出示了两个低阶特征值对应的固有振动模态:五种形态的椭球振动和七种形态的“三角球”形振动。本文为超精密测量机机体的结构动态设计提供了理论依据。

In this paper, the three-dimensional eight-node block element is used to analyze the dynamic characteristics of the elastic thick spherical shell, and compared with the analytical solution of the corresponding elastic dynamic equation. The eigenvalue calculations show that the two calculation results are very close. The number of finite element meshes and the number of elements have an effect on the calculation of the eigenvalues. An eigenvalue of an elastic thick spherical shell corresponds to a set of modal shapes, which is explained theoretically in the text and shows the natural vibration modes corresponding to the two low-order eigenvalues: ellipsoidal vibration in five morphologies. And seven forms of “triangle ball” shape vibration. This paper provides a theoretical basis for the structural dynamic design of the ultra-precision measuring machine body.