功能梯度材料动力学问题的POD模型降阶分析

郑保敬; 梁钰; 高效伟; 朱强华; 吴泽艳

doi:10.6052/0459-1879-18-069

功能梯度材料动力学问题的POD模型降阶分析

1三峡大学水利与环境学院, 湖北宜昌 443002
2大连理工大学航空航天学院工业装备结构分析国家重点实验室, 大连 116024);

基金项目: 国家自然科学基金资助项目(11602129, 11672061).

详细信息

作者简介:
^*郑保敬, 讲师, 主要研究方向: 计算固体力学 . E-mail: zheng _-bj@126. com

通讯作者:
郑保敬

中图分类号: O321;
计量
- 文章访问数: 1980
- HTML全文浏览量: 172
- PDF下载量: 392
出版历程
- 刊出日期: 2018-07-17

ANALYSIS FOR DYNAMIC RESPONSE OF FUNCTIONALLY GRADED MATERIALS USING POD BASED REDUCED ORDER MODEL $N$

1College of Hydraulic and Environmental Engineering, China Three Gorges University, Yichang 443002, Hubei, China

摘要

摘要: 为了快速分析非均质材料结构在复杂载荷作用下的动态响应, 提出一种模型降阶方法, 只需计算结构在简单均质材料情况下的动力学问题, 进而用其计算结果对非均质材料结构进行分析. 首先, 采用结构内部任意一点处的材料参数值作为整个结构的材料参数, 利用有限元分析软件计算该均质材料结构在动态载荷作用下的位移场建立数据库, 该数据库包含计算模型各个节点(自由度为 $L$ )在某时间段内 $L$ 个时刻的位移; 其次, 对数据库中的信息按照时间离散的特定方式组集成瞬像矩阵, 并利用特征正交分解方法对其进行分解, 得到该模型的 $H$ 个特征正交基底, 选取其中能反应模型主要特征的 $H < L ? N$ 个(其中 $~$ )作为一组最优基底, 通过这组基底建立模型的低阶离散控制方程; 最后, 求解低阶离散微分方程组, 得到功能梯度材料结构在复杂载荷作用下的位移场. 文中分别给出二维和三维算例, 比较了降阶模型和全阶模型计算结果, 验证了该方法的有效性, 并且计算效率能提高1 $^{1)}$ 2个数量级.
- 特征正交分解 /
- 模型降阶 /
- 动力响应 /
- 功能梯度材料
Abstract: In order to quickly analysis the response of heterogeneous materials under dynamic loads, a reduced order method was presented in this paper which only needed to compute dynamic characteristics of homogeneous material under sudden load and got the results for analysis complex non-homogeneous material. Firstly, we used the finite element method to compute the displacement field of homogeneous materials under sudden load, and then discretized data samples was obtained to establish a database which including every moment displacement information of all degrees of freedom (order of $L$ ) during a period of time. Secondly, dealing with database by specific way of time discretization, a snapshot matrix was formed. The matrix was decomposed into $H$ orthogonal basis by proper orthogonal decomposition method and we picked up the major $H < L ? N$ basis from that. Till now we achieved the goal that reducing the model ( $H$ ). Finally, the $[4 - 5]$ basis were used to obtain order-reduced governing dynamic equation. Different dynamic loads of time dependent were applied to the model, and the dynamic response of non-homogeneous material would be achieved by solving order-reduced governing dynamic equations. The displacement fields of traditional FEM and proposed ROM were compared. 2D and 3D examples showed that the computing scales reduced one or two orders of magnitude.
- proper orthogonal decomposition /
- reduced order method /
- dynamic response /
- functionally graded materials

HTML全文

参考文献(1)

[1]	Li J, Chen J, Chen X.Aerodynamic response analysis of wind turbines.Journal of Mechanical Science ＆ Technology, 2011, 25(1): 89-95
[2]	Yau JD.Dynamic response analysis of suspended beams subjected to moving vehicles and multiple support excitations.Journal of Sound ＆ Vibration, 2009, 325(4): 907-922
[3]	Larsen A, Larose GL.Dynamic wind effects on suspension and cable-stayed bridges.Journal of Sound ＆ Vibration, 2015, 334(1): 2-28
[4]	邢维巍, 张硕, 樊尚春. 动态轴向载荷下谐振梁振动响应分析. 传感技术学报, 2016, 29(9): 1372-1375
[4]	(Xing Weiwei, Zhang Shuo, Fan Shangchun.Resonant beam vibrating response under dynamic axial load analysis.Chinese Journal of Sensors and Actuators, 2016, 29(9): 1372-1375 (in Chinese))
[5]	华洪良, 廖振强, 张相炎. 轴向移动悬臂梁高效动力学建模及频率响应分析. 力学学报, 2017, 49(6): 1390-1398
[5]	(Hua Hongliang, Liao Zhenqiang, Zhang Xiangyan.An efficient dynamic modeling method of an axially moving cantilever beam and frequency Response Analysis.Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(6): 1390-1398 (in Chinese))
[6]	Schulz U, Peters M, Bach F W, et al.Graded coatings for thermal, wear and corrosion barriers.Materials Science ＆ Engineering A, 2003, 362(1-2): 61-80
[7]	Sadowski T, Pietras D.Heat transfer process in jet turbine blade with functionally graded thermal barrier coating.Solid State Phenomena, 2016, 254(1): 170-175
[8]	Thomas B, Roy T.Vibration analysis of functionally graded carbon nanotube-reinforced composite shell structures.Acta Mechanica, 2016, 227(2): 581-599
[9]	夏巍, 冯浩成. 热过屈曲功能梯度壁板的气动弹性颤振. 力学学报, 2016, 48(3): 609-614
[9]	(Xia Wei, Feng Haocheng.Aeroelastic flutter of post-buckled functionally graded panels.Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(3): 609-614 (in Chinese))
[10]	许新, 李世荣. 功能梯度材料微梁的热弹性阻尼研究.力学学报, 2017, 49(2): 308-316
[10]	(Xu Xin, Li Shirong.Analysis of thermoelastic damping for functionally graded material micro-beam.Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 308-316 (in Chinese))
[11]	赵磊, 胡超. 功能梯度材料应用及动力学分析.飞航导弹, 2011, 1(8): 93-96
[11]	(Zhao Lei, Hu Chao.Dynamic analysis and application of functionally graded material.Winged Missiles Journal, 2011, 1(8): 93-96 (in Chinese))
[12]	Shahba A, Rajasekaran S.Free vibration and stability of tapered Euler-Bernoulli beams made of axially functionally graded materials.Applied Mathematical Modelling, 2012, 36(7): 3094-3111
[13]	Librescu L, Sang YO, Song O.Spinning thin-walled beams made of functionally graded materials: Modeling, vibration and instability.European Journal of Mechanics - A Solids, 2004, 23(3): 499-515
[14]	Thomas B, Roy T.Vibration analysis of functionally graded carbon nanotube-reinforced composite shell structures.Acta Mechanica, 2016, 227(2): 581-599
[15]	仲政, 吴林志, 陈伟球. 功能梯度材料与结构的若干力学问题研究进展. 力学进展, 2010, 40(5): 528-541
[15]	(Zhong Zheng, Wu Linzhi, Chen Weiqiu.Progress in the study on mechanics problems of functionally graded materials and structures.Adv Mech, 2010, 40(5): 528-541 (in Chinese))
[16]	Perez R, Wang XQ, Mignolet MP.Nonlinear reduced-order models for thermoelastodynamic response of isotropic and functionally graded panels.AIAA Journal, 2009, 49(49): 630-641
[17]	Lumley JL.Coherent structures in turbulence.Transition ＆ Turbulence, 1981, 1(1): 215-242
[18]	姚伟刚, 徐敏, 叶茂. 基于特征正交分解的非定常气动力建模技术. 力学学报, 2010, 42(4): 637-637
[18]	(Yao Weigang, Xu Min,Ye Mao.Unsteady aerodynamic force modeling via proper orthogonal decomposition ROM.Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(4): 637-644 (in Chinese))
[19]	Deng S, Pan C, Wang J, et al.POD analysis of the instability mode of a low-speed streak in a laminar boundary layer.Acta Mechanica Sinica, 2017, 33(6): 981-991
[20]	Shankar KA, Pandey M.Nonlinear dynamic analysis of cracked cantilever beam using reduced order model.Procedia Engineering, 2016, 144(1): 1459-1468
[21]	Deng S, Pan C, Wang J, et al.POD analysis of the instability mode of a low-speed streak in a laminar boundary layer.Acta Mechanica Sinica, 2017, 6: 981-991.
[22]	Gao X, Hu J, Huang S.A Proper orthogonal decomposition analysis method for multimedia heat conduction problems.Journal of Heat Transfer, 2016, 138(7): 1-10
[23]	胡金秀, 郑保敬, 高效伟. 基于特征正交分解降阶模型的瞬态热传导分析. 中国科学物理学力学天文学, 2015, 45(1): 73-84
[23]	(Hu Jingxiu, Zheng Baojing, Gao Xiaowei.Reduced order model analysis method via proper orthogonal decomposition for transient heat conduction.Sci Sin-Phys Mech Astron, 2015, 45(1): 73-84 (in Chinese))
[24]	梁钰, 朱强华, 高效伟. 变工况导热问题的POD分析方法//中国航天第三专业信息网第三十八届技术交流会暨第二届空天动力联合会议. 大连, 2017
[24]	(Liang Yu, Zhu Qianghua, Gao Xiaowei.POD reduced analysis method of heat conduction problem under different loads//The 2nd JCAP and 38th APTIS Technical Conference. Dalian, 2017 (in Chinese))
[25]	王勖成. 有限单元法. 北京: 清华大学出版社, 2003
[25]	(Wang Xucheng. Finite Element Method.Beijing: Tsinghua University Press, 2003 (in Chinese))
[26]	Zhang C, Gao XW, Sladek J, et al.Fracture analysis of functionally graded materials.Composites Science ＆ Technology, 2008, 68(5): 1209-1215

施引文献(27)

期刊类型引用(15)

1.	励精为治，刘保国，刘彦旭，张义彬. 模型不确定转子系统动力学降阶模型构建方法. 机电工程. 2025(03): 472-480 . 百度学术
2.	杨彪，黄宏彬，杜庆治，吴照刚，彭飞云，韩泽民. 基于特征正交分解的微波加热过程快速求解方法. 控制与决策. 2024(09): 3059-3068 . 百度学术
3.	桑瑞涓，龚坚，路宽，靳玉林，张康宇，王衡. 高维非线性动力系统降维理论综述. 动力学与控制学报. 2024(09): 1-15 . 百度学术
4.	肖龙辉，裴志勇，徐文君，吴卫国. 船体结构数字孪生技术及应用. 船舶力学. 2023(04): 573-582 . 百度学术
5.	可钊，时永鑫，张鹏，田阔，王博. 基于全局POD降阶模型的复杂薄壁结构减振优化. 航空学报. 2023(13): 148-163 . 百度学术
6.	郭玉杰，吴晗浪，李薇，李迎港，吴剑晨. 基于等几何分析的参数化曲梁结构非线性动力学降阶模型研究. 工程力学. 2022(08): 31-48 . 百度学术
7.	张家铭，杨执钧，黄锐. 基于非线性状态空间辨识的气动弹性模型降阶. 力学学报. 2020(01): 150-161 . 本站查看
8.	朱强华，杨恺，梁钰，高效伟. 基于特征正交分解的一类瞬态非线性热传导问题的新型快速分析方法. 力学学报. 2020(01): 124-138 . 本站查看
9.	熊春宝，胡倩倩，郭颖. 孔隙率各向异性下饱和多孔弹性地基动力响应. 力学学报. 2020(04): 1120-1130 . 本站查看
10.	李杨，秦庆华，张亮亮，高阳. 一维准晶功能梯度层合圆柱壳热电弹性精确解. 力学学报. 2020(05): 1286-1294 . 本站查看
11.	史惠琦，王惠明. 一种新型介电弹性体仿生可调焦透镜的变焦分析. 力学学报. 2020(06): 1719-1729 . 本站查看
12.	戴婷，戴宏亮，李军剑，贺其. 含孔隙变厚度FG圆板的湿热力学响应. 力学学报. 2019(02): 512-523 . 本站查看
13.	何燕丽，赵翔. 曲梁压电俘能器强迫振动的格林函数解. 力学学报. 2019(04): 1170-1179 . 本站查看
14.	杨健鹏，王惠明. 功能梯度球形水凝胶的化学力学耦合分析. 力学学报. 2019(04): 1054-1063 . 本站查看
15.	梁钰，郑保敬，高效伟，吴泽艳，王峰. 基于POD模型降阶法的非线性瞬态热传导分析. 中国科学:物理学力学天文学. 2018(12): 36-45 . 百度学术

其他类型引用(12)

资源附件(0)

计量

文章访问数: 1980
HTML全文浏览量: 172
PDF下载量: 392
被引次数: 27

功能梯度材料动力学问题的POD模型降阶分析

作者简介:
^*郑保敬, 讲师, 主要研究方向: 计算固体力学 . E-mail: zheng _-bj@126. com

通讯作者:
郑保敬

计量

ANALYSIS FOR DYNAMIC RESPONSE OF FUNCTIONALLY GRADED MATERIALS USING POD BASED REDUCED ORDER MODEL $N$

期刊类型引用(15)

其他类型引用(12)

计量

目录

下载中心

作者中心

功能梯度材料动力学问题的POD模型降阶分析

作者简介: *郑保敬, 讲师, 主要研究方向: 计算固体力学 . E-mail: zheng _-bj@126. com

通讯作者: 郑保敬

计量

出版历程

ANALYSIS FOR DYNAMIC RESPONSE OF FUNCTIONALLY GRADED MATERIALS USING POD BASED REDUCED ORDER MODEL N

期刊类型引用(15)

其他类型引用(12)

计量

出版历程

目录

下载中心

作者中心

作者简介:
^*郑保敬, 讲师, 主要研究方向: 计算固体力学 . E-mail: zheng _-bj@126. com

通讯作者:
郑保敬

ANALYSIS FOR DYNAMIC RESPONSE OF FUNCTIONALLY GRADED MATERIALS USING POD BASED REDUCED ORDER MODEL $N$