任意弹性边界的多段梁自由振动研究

鲍四元; 周静; 陆健炜

doi:10.21656/1000-0887.410045

任意弹性边界的多段梁自由振动研究

doi: 10.21656/1000-0887.410045

苏州科技大学工程力学系, 江苏苏州 215011

基金项目: 国家自然科学基金（11202146）

详细信息

作者简介:
鲍四元（1980—），男，副教授，博士，硕士生导师(通讯作者. E-mail： bsiyuan@126.com).

中图分类号: TU323
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出版历程
- 收稿日期: 2020-01-23
- 修回日期: 2020-03-08
- 刊出日期: 2020-09-01

Free Vibration of MultiSegment Beams With Arbitrary Boundary Conditions

Department of Engineering Mechanics, Suzhou University of Science and Technology, Suzhou, Jiangsu 215011, P.R.China

Funds: The National Natural Science Foundation of China（11202146）

摘要

摘要: 研究了连续多段梁的自由振动特性.为区别于诸简支等传统约束边界，提出了弹性约束边界下多段梁结构的自由振动特性分析方法.首先根据谱几何法，在传统Fourier级数的基础上添加四个辅助函数，构造了多段Euler梁中每段的横向位移函数.其次，将位移函数的假设谱几何形式代入多段梁结构的Lagrange函数得到新的表达式，由Hamilton原理将自由振动问题化成矩阵特征值形式，从而求解出任意弹性边界条件下多段梁的自振频率和模态.针对四个具体算例，通过改变边界处弹簧刚度值可求得不同边界条件下连续多段梁的自振频率和模态.与已有文献的结果比较，充分验证了该文方法的正确性、规范性和高效性.
- 谱几何法 /
- 任意边界 /
- 多段梁 /
- 自由振动
Abstract: The vibration characteristics of continuous multi-segment beams were studied. Other than classical boundary conditions (such as simple supports), the elastic constraints were considered to analyze the free vibration characteristics of multi-segment beams. Firstly, according to the spectro-geometric method, 4 auxiliary functions were added on the basis of the traditional Fourier series to construct the lateral displacement function for each segment of the beam. Secondly, new expressions of the Lagrangian functions for the beam structure were obtained by substitution of the supposed spectro-geometric form into the Lagrangian functions. The free vibration problem was transformed into the standard matrix eigenvalue form from the Hamiltonian principle, and the natural frequencies and modes of the beam under arbitrary boundary conditions were obtained. For 4 numerical examples, the natural frequencies and modes of the continuous multi-segment beams were calculated under different boundary conditions of variant spring stiffness values. Comparison of the results between existing literatures and this work shows correctness, standardization and efficiency of the proposed method.
- spectro-geometric method /
- arbitrary boundary /
- continuous multi-segment beam /
- free vibration

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参考文献(15)

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