正交各向异性旋转扁壳的非线性振动<sup>*</sup>

李东

正交各向异性旋转扁壳的非线性振动^*

李东

上海市应用数学和力学研究所上海工业大学

基金项目: * 国家自然科学基金资助的课题

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出版历程
- 收稿日期: 1991-03-04
- 刊出日期: 1992-04-15

Nonlinear Vibrations of Orthotropic Shallow Shells of Revolution

Li Dong

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University of Technology, Shanghai

摘要

摘要: 本文提出一种时间模态假设,由此导出描述圆柱正交各向异性薄扁球壳和锥壳非线性轴对称自由振动的非线性耦合的代数和微分特征值方程组.我们求出了该方程组的近似解析解,并获得壳体振动的幅频响应关系的渐近展开式.文中还讨论了壳体的几何及材料参量对其振动性态的影响.
- 几何非线性 /
- 振动 /
- 正交各向异性 /
- 扁球壳 /
- 扁锥壳
Abstract: A set of nonlinearly coupled algebraic and differential eigenvalue equations of nonlinear axisymmetric free vibration of orthotropic shallow thin spherical and conical shells are formulated following an assumed time-mode approach suggested in this paper. Analytic solutions are presented and an asymptotic relation for the amplitude-frequency response of the shells is derived. The effects of geometrical and material parameters on vibrations of the shells are investigated.
- geometrical nonlinearity /
- vibration /
- orthotropy /
- shallow conical shell /
- shallow spherical shell

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参考文献(16)

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