| 基于辛理论的Bernoulli-Euler梁波散射分析 |
| |
| 引用本文： | 郑罡,唐宇,蔡汶秀,曾广榕.基于辛理论的Bernoulli-Euler梁波散射分析[J].科学技术与工程,2023,23(32):13674-13680. |
| |
| 作者姓名： | 郑罡 唐宇 蔡汶秀 曾广榕 |
| |
| 作者单位： | 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 |
| |
| 基金项目： | 国家自然科学基金(51978112) |
| |
| 摘 要： | 为研究辛对偶力学体系下Bernoulli-Euler梁波的散射问题，通过构造Lagrange乘子以解除泛函约束，引入对偶变量，提出了Bernoulli-Euler梁的Hamilton对偶方程。综合运用本征向量展开法、辛Gram-Schmidt正交算法，以及精细积分法等方法剥离了Bernoulli-Euler梁能带结构中的禁带部分，获得了端部散射体的散射矩阵。结果表明：辛体系下Bernoulli-Euler梁的状态向量是由一对通带本征向量和一对禁带本征向量所组成的，其端部散射体的散射矩阵是一阶酉矩阵，入射波的功率流等于反射波的功率流，满足功率流守恒。
|
| 关 键 词： | Bernoulli-Euler梁，能带，散射，辛理论 |
| 收稿时间： | 2022/12/21 0:00:00 |
| 修稿时间： | 2023/8/18 0:00:00 |
Analyzing the Wave Scattering in Bernoulli-Euler Beam Based on the Symplectic Theory |
| |
| Zheng Gang,Tang Yu,Cai Wenxiu,Zeng Guangrong.Analyzing the Wave Scattering in Bernoulli-Euler Beam Based on the Symplectic Theory[J].Science Technology and Engineering,2023,23(32):13674-13680. |
| |
| Authors: | Zheng Gang Tang Yu Cai Wenxiu Zeng Guangrong |
| |
| Affiliation: | State Key Laboratory of Mountain Bridge and Tunnel Engineering, Chongqing Jiaotong University |
| |
| Abstract: | In order to study the wave scattering problem of Bernoulli-Euler beam in the symplectic dual mechanics system, the Hamiltonian dual equation of Bernoulli-Euler beam was proposed by constructing Lagrange multipliers to release functional constraints and introducing dual variables. The scattering matrix of the end scatterer was obtained by combining the eigenvector expansion method, the symplectic Gram-Schmidt orthogonal algorithm, and the precise integral method to strip the stopband part of the energy band structure of the Bernoulli-Euler beam. The results show that the state vector of the Bernoulli-Euler beam in the symplectic system is composed of a pair of passband eigenvectors and a pair of stopband eigenvectors. The scattering matrix is a first-order unitary matrix, and the power flow of the incident wave is equal to the power flow of the reflected wave, which satisfies the power flow conservation. |
| |
| Keywords: | |
|
| 点击此处可从《科学技术与工程》浏览原始摘要信息 |
|
点击此处可从《科学技术与工程》下载全文 |
