基于辛精细积分方法的三维屈曲结构动力学分析

谢雨欣; 毕皓皓; 张欣刚; 姚文莉; 王博

doi:10.21656/1000-0887.460105

基于辛精细积分方法的三维屈曲结构动力学分析

doi: 10.21656/1000-0887.460105

1. 青岛理工大学理学院，山东青岛 266520;^{2. 西北工业大学工程力学系，西安 710072}

基金项目:

国家自然科学基金(12402002；12172282；12272197)；山东省自然科学基金(ZR2024QA062；ZR2022MA066)；青岛市自然科学基金(24-4-4-zrjj-7-jch)

详细信息

作者简介:
谢雨欣(2004—)，女，硕士生(E-mail: xieyuxinnn111@outlook.com);毕皓皓(1993—)，男，讲师，博士，硕士生导师（通信作者. E-mail: bihaohao@mail.nwpu.edu.cn）.

通讯作者:
毕皓皓(1993—)，男，讲师，博士，硕士生导师(通信作者. E-mail: bihaohao@mail.nwpu.edu.cn).

中图分类号: O231|O34
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- 文章访问数: 27
- HTML全文浏览量: 7
- PDF下载量: 2
- 被引次数: 0
出版历程
- 收稿日期: 2026-05-26
- 修回日期: 2026-07-03
- 网络出版日期: 2026-10-31

Dynamic Analysis of 3D Buckling Structures Based on the Symplectic Precise Integration Method

1. School of Science, Qingdao University of Technology, Qingdao, Shandong 266520, P.R. China;^{2. Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an 710072, P.R. China}

Funds:

The National Science Foundation of China(12402002；12172282；12272197)

摘要

摘要: 基于压缩屈曲原理的三维结构在微机电系统中具有巨大应用潜力，精准预测其动力学响应是实现其广泛工程应用需要解决的关键问题之一.本文首先基于能量法计算了“+”型三维屈曲结构的总能量；随后，通过Lagrange方程推导了该结构的线性振动控制方程，并采用辛精细积分方法对其进行数值求解.数值分析表明，辛精细积分法在长时间积分中能有效保持动力学系统的Hamilton能量，其数值解具备长期稳定性，为分析该类三维屈曲的动力学行为提供了一种高效的数值分析方法.数值结果表明，三维屈曲结构的振动响应对结构参数有显著依赖性.本文结果有助于三维屈曲结构的动力学优化设计.
- 三维屈曲结构 /
- 精细积分方法 /
- 辛算法
Abstract: The 3D structures based on the principle of compression-induced buckling possess significant potential in micro-electro-mechanical systems and other engineering applications. Accurately predicting their dynamic response is one of the key challenges in enabling their widespread practical use. The total energy of a “+”-shaped 3D buckling structure is first evaluated with the energy method. Then, the nonlinear vibration governing equation was derived through the Lagrangian formulation and numerically solved with the precise symplectic integration method. Numerical analysis shows that, the symplectic precise integration method can effectively preserve the Hamiltonian energy of dynamical systems over long-term integration. Its numerical solutions remain stable over time, providing an efficient tool for analyzing the dynamic behaviors of such 3D buckling systems. The vibration responses of 3D buckling structures are significantly dependent on structural parameters. The findings contribute to the dynamic optimization design of 3D buckling structures.
- 3D buckling structure /
- precise integration method /
- symplectic algorithm

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参考文献(35)

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基于辛精细积分方法的三维屈曲结构动力学分析

doi: 10.21656/1000-0887.460105

作者简介:
谢雨欣(2004—)，女，硕士生(E-mail: xieyuxinnn111@outlook.com);毕皓皓(1993—)，男，讲师，博士，硕士生导师（通信作者. E-mail: bihaohao@mail.nwpu.edu.cn）.

通讯作者:
毕皓皓(1993—)，男，讲师，博士，硕士生导师(通信作者. E-mail: bihaohao@mail.nwpu.edu.cn).

计量

Dynamic Analysis of 3D Buckling Structures Based on the Symplectic Precise Integration Method

计量

目录

留言板

基于辛精细积分方法的三维屈曲结构动力学分析

doi: 10.21656/1000-0887.460105

作者简介: 谢雨欣(2004—)，女，硕士生(E-mail: xieyuxinnn111@outlook.com);毕皓皓(1993—)，男，讲师，博士，硕士生导师（通信作者. E-mail: bihaohao@mail.nwpu.edu.cn）.

通讯作者: 毕皓皓(1993—)，男，讲师，博士，硕士生导师(通信作者. E-mail: bihaohao@mail.nwpu.edu.cn).

计量

出版历程

Dynamic Analysis of 3D Buckling Structures Based on the Symplectic Precise Integration Method

计量

出版历程

目录

作者简介:
谢雨欣(2004—)，女，硕士生(E-mail: xieyuxinnn111@outlook.com);毕皓皓(1993—)，男，讲师，博士，硕士生导师（通信作者. E-mail: bihaohao@mail.nwpu.edu.cn）.

通讯作者:
毕皓皓(1993—)，男，讲师，博士，硕士生导师(通信作者. E-mail: bihaohao@mail.nwpu.edu.cn).