偏心冲击荷载作用下薄圆板动力学响应的保结构分析

秦于越; 邓子辰; 胡伟鹏

doi:10.3879/j.issn.1000-0887.2014.08.006

偏心冲击荷载作用下薄圆板动力学响应的保结构分析

doi: 10.3879/j.issn.1000-0887.2014.08.006

¹西北工业大学力学与土木建筑学院,陕西西安 710072;²大连理工大学工业装备结构分析国家重点实验室,辽宁大连 116023

基金项目: 国家自然科学基金(11372252;11172239;11372253)；大连理工大学工业装备结构分析国家重点实验室开放基金(GZ0802;GZ1312)

详细信息

作者简介:
秦于越（1980—），女，重庆人，讲师，博士(E-mail: 769482448@qq.com);邓子辰（1964—），男，辽宁人，教授，博士生导师(通讯作者. E-mail: dweifan@nwpu.edu.cn).

中图分类号: O241.82
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出版历程
- 收稿日期: 2014-04-08
- 修回日期: 2014-06-16
- 刊出日期: 2014-08-15

Dynamic Analysis of Circular Thin Plates Under Eccentric Impact Load With the StructurePreserving Method

¹School of Mechanics and Civil. Engineering and Architecture,Northwestern Polytechnical University, Xi’an 710072, P.R.China;²State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116023, P.R.China

Funds: The National Natural Science Foundation of China(11372252;11172239;11372253)

摘要

摘要: 关注动力学系统的局部几何性质，采用多辛分析方法研究了偏心冲击荷载作用下薄圆板振动特性.在探索偏心冲击荷载作用下薄圆板振动问题动力学控制方程的对称性和守恒律的对应关系基础上，对动力学控制方程在多辛体系下重新描述，并采用显式中点差分离散方法构造其多辛格式，通过对存在不同相对偏心距冲击荷载作用下的薄圆板振动过程的数值模拟，研究了相对偏心距对薄圆板振动特性的影响，同时，数值模拟结果也充分体现了多辛算法的良好保结构性能.该研究结果不仅为由于荷载作用位置误差带来的动力学响应偏差估计提供了依据，而且为偏心冲击动力学问题的研究提供了新的途径.
- Hamilton(哈密尔顿)系统 /
- 多辛 /
- 薄圆板 /
- 偏心冲击荷载
Abstract: Focused on the local geometric properties of the dynamic system, the multi-symplectic method was used to analyze the vibration behavior of the circular thin plate under eccentric impact load. Firstly, the governing equation for the vibration problem of the plate was redescribed in the multi-symplectic framework. And then, the multi-symplectic scheme was constructed with the explicit midpoint method to simulate the dynamic process of the thin plate under impact load with different relative eccentric distances. Finally, the numerical results were presented and discussed in detail, which demonstrated the structure-preserving properties of the multi-symplectic algorithm. Generally, the numerical results not only present a reference for the estimation of the dynamic responses resulting from the acting position error of the load on the structure, but also propose a new way for the study of the eccentrically impacted plate problems.
- Hamilton system /
- multi-symplectic /
- circular thin plate /
- eccentric impact load

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参考文献(9)

[1]	OUYANG Hua-jiang, ZHONG Wan-xie. A finite strip method in Hamiltonian formulation[J].Computers & Structures,1994,53(2): 241-244.
[2]	ZHONG Wan-xie. Some developments of computational solid mechanics in China[J]. Computers & Structures,1988,30(4):783-788.
[3]	秦于越, 邓子辰, 胡伟鹏. 冲击荷载作用下中心对称薄圆板振动的多辛分析[J]. 西北工业大学学报, 2013,31(6): 931-934.(QIN Yu-yue, DENG Zi-chen, HU Wei-peng. Multi-symplectic analysis of vibration of centrosymmetric thin circular plate under impact load[J], Journal of Northwestern Polytechnical University,2013,31(6): 931-934.(in Chinese))
[4]	FENG Kang. On Difference schemes and symplectic geometry[C]// Proceeding of the 1984 Beijing Symposium on Differential Geometry and Differential Equations . Beijing: Science Press, 1984: 42-58.
[5]	钟万勰, 欧阳华江, 邓子辰. 计算结构力学与最优控制[M]. 大连: 大连理工大学出版社, 1993.(ZHONG Wan-xie, OUYANG Hua-jiang, DENG Zi-chen. Computational Structural Mechanics and Optimal Control [M]. Dalian: Dalian University of Technology Press, 1993.(in Chinese))
[6]	Bridges T J. Multi-symplectic structures and wave propagation[J]. Mathematical Proceedings of the Cambridge Philosophical Society,1997,121(1): 147-190.
[7]	HU Wei-peng, DENG Zi-chen, HAN Song-mei, ZHANG Wen-rong. Generalized multi-symplectic integrators for a class of Hamiltonian nonlinear wave PDEs[J]. Journal of Computational Physics,2013,235: 394-406.
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偏心冲击荷载作用下薄圆板动力学响应的保结构分析

doi: 10.3879/j.issn.1000-0887.2014.08.006

作者简介:
秦于越（1980—），女，重庆人，讲师，博士(E-mail: 769482448@qq.com);邓子辰（1964—），男，辽宁人，教授，博士生导师(通讯作者. E-mail: dweifan@nwpu.edu.cn).

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Dynamic Analysis of Circular Thin Plates Under Eccentric Impact Load With the StructurePreserving Method

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偏心冲击荷载作用下薄圆板动力学响应的保结构分析

doi: 10.3879/j.issn.1000-0887.2014.08.006

作者简介: 秦于越（1980—），女，重庆人，讲师，博士(E-mail: 769482448@qq.com);邓子辰（1964—），男，辽宁人，教授，博士生导师(通讯作者. E-mail: dweifan@nwpu.edu.cn).

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出版历程

Dynamic Analysis of Circular Thin Plates Under Eccentric Impact Load With the StructurePreserving Method

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出版历程

目录

作者简介:
秦于越（1980—），女，重庆人，讲师，博士(E-mail: 769482448@qq.com);邓子辰（1964—），男，辽宁人，教授，博士生导师(通讯作者. E-mail: dweifan@nwpu.edu.cn).