基于辛叠加方法的正交各向异性矩形悬臂薄板受迫振动解析解

王森林; 李进宝; 马红艳; 李锐

doi:10.21656/1000-0887.440277

基于辛叠加方法的正交各向异性矩形悬臂薄板受迫振动解析解

doi: 10.21656/1000-0887.440277

大连理工大学工程力学系工业装备结构分析优化与CAE软件全国重点实验室，辽宁大连 116024

基金项目:

国家自然科学基金（12372067；12022209；11972103）

详细信息

作者简介:
王森林（1998—），男，硕士生（E-mail: 2719116256@mail.dlut.edu.cn）；李进宝（1999—），男，硕士生（E-mail: jinbao_li@mail.dlut.edu.cn）；马红艳（1968—），女，教授，博士，硕士生导师（E-mail: mahy@dlut.edu.cn）；李锐（1985—），男，教授，博士，博士生导师（通讯作者. E-mail: ruili@dlut.edu.cn）.

通讯作者:
李锐（1985—），男，教授，博士，博士生导师（通讯作者. E-mail: ruili@dlut.edu.cn）.

中图分类号: O302
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- 被引次数: 0
出版历程
- 收稿日期: 2023-09-20
- 修回日期: 2023-10-06
- 网络出版日期: 2024-09-30

Analytical Forced Vibration Solutions of Orthotropic Cantilever Rectangular Thin Plates With the Symplectic Superposition Method

State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment,Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

Funds:

The National Science Foundation of China(12372067；12022209；11972103)

摘要

摘要: 基于辛叠加方法研究了正交各向异性矩形悬臂薄板在谐载载荷作用下的受迫振动问题.首先从薄板受迫振动的基本方程出发，将问题导入到Hamilton体系，并将原问题拆分为若干子问题，然后在辛空间中利用分离变量和本征展开方法推导出子问题的解析解，最后通过叠加求解出悬臂薄板受迫振动的解析解.辛叠加方法的主要优点是经过逐步严格推导获得解析解，不需要对解的形式做任何假设，突破了传统半逆解法的限制.算例针对不同谐载载荷情况进行了数值计算，并将该文方法与有限元方法获得的结果进行比较，验证了该文方法的可靠性和精确性.
- 辛叠加方法 /
- 正交各向异性薄板 /
- 解析解 /
- 受迫振动
Abstract: The forced vibrations of orthotropic cantilever rectangular thin plates under harmonic loadings were investigated with the symplectic superposition method. The basic equations for the forced vibration of thin plates were introduced into the Hamiltonian system. The original problem was divided into some fundamental subproblems, and the analytical solutions of the subproblems were derived with the method of separation of variables and through eigenvector expansion in the symplectic space. The solution of the original problem was finally obtained by superposition. The main advantage of the symplectic superposition method is that the analytical solution can be obtained by step-by-step rigorous derivation, without any assumptions on the form of the solution, which breaks through the limitations of traditional semi-inverse methods. The numerical results calculated corresponding to different harmonic loads were compared with those obtained via the finite element method to verify the reliability and accuracy of the proposed method.
- symplectic superposition method /
- orthotropic thin plate /
- analytical solution /
- forced vibration

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参考文献(31)

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