修正Timoshenko梁系统的归一化与对偶关系

蔡汶秀; 郑罡; 唐宇; 孙测世; 叶念雨; 薛文琪

doi:10.21656/1000-0887.450292

修正Timoshenko梁系统的归一化与对偶关系

doi: 10.21656/1000-0887.450292

1. 重庆交通大学省部共建山区桥梁及隧道工程国家重点实验室，重庆 400074;
2. 重庆交通大学土木工程学院，重庆 400074;
3. 四川路桥华东建设有限责任公司，成都 610299

基金项目:

国家自然科学基金（52378284）

详细信息

作者简介:
蔡汶秀(1997—)，女，博士生；郑罡(1972—)，男，研究员，博士，博士生导师(E-mail: zhenggang@cqjtu.edu.cn).

通讯作者:
郑罡(1972—)，男，研究员，博士，博士生导师(E-mail: zhenggang@cqjtu.edu.cn).

中图分类号: Q342
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- 文章访问数: 10
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- 被引次数: 0
出版历程
- 收稿日期: 2024-10-28
- 修回日期: 2025-11-17
- 网络出版日期: 2025-12-31

Normalization and Duality Relations of Modified Timoshenko Beams

1. State Key Laboratory of Mountain Bridge and Tunnel Engineering,Chongqing Jiaotong University, Chongqing 400074, P.R.China;
2. School of Civil Engineering, Chongqing Jiaotong University, Chongqing 400074, P.R.China;
3. Sichuan Road & Bridge East China Construction Co., Ltd., Chengdu 610299, P.R.China

Funds:

The National Science Foundation of China(52378284)

摘要

摘要: 为研究修正Timoshenko梁系统的对偶条件和分类，讨论其理论意义.首先通过引入时间和空间缩放变换，实现了对修正Timoshenko梁动力学方程的标准化；其次，基于该归一化方程，论证了在任意相同边界条件下参数型对偶关系的存在性；然后，探讨了不同截面类型参数型对偶关系的特点；最后，在固支铰支、固支固支和固支自由这三种边界条件下，求解标准化方程，提出了构造对偶梁的方法，并通过文献算例展示了修正Timoshenko梁参数型对偶性的特征.结果表明：归一化算法求解修正Timoshenko对偶梁的频率完全相同，且基于该算法可论证其修正Timoshenko梁的参数型对偶条件.动力学特性的参数型对偶关系为修正Timoshenko梁的一种本质属性，时空缩放变换为揭示该特性的有效方法.
- 修正Timoshenko梁 /
- 对偶关系 /
- 归一化算法 /
- 动力学方程
Abstract: The duality conditions and classification of the modified Timoshenko beam systems were investigated, with its theoretical significance highlighted. First, the modified dynamic equations for the Timoshenko beam were normalized through time and space scaling transformations. Based on the normalized equations, the existence of parametric duality relations was established under arbitrary identical boundary conditions. Next, the parametric dual characteristics corresponding to different cross-sectional geometries were analyzed. Finally, under clamped-hinged, clamped-clamped, and clamped-free boundary conditions, the normalized equations were solved, to develop a novel method for building dual beams. Through examples from the literatures, the parametric dual characteristics of modified Timoshenko beams were further elucidated. The results demonstrate that, the frequencies of the modified Timoshenko dual beams derived via the normalization algorithm are identical, which confirms the parametric dual conditions of the modified beams. This study reveals that the parametric duality of dynamic properties is an intrinsic feature of modified Timoshenko beams, and the time and space scaling transformations provide a robust framework for uncovering these properties.
- modified Timoshenko beam /
- duality relation /
- normalization algorithm /
- dynamic equation

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参考文献(18)

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