金属学报  2012, Vol. 48 Issue (8): 995-1004    DOI: 10.3724/SP.J.1037.2012.00235

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Al质蜂窝夹芯板非线性动力学分析

张英杰1,2,颜云辉1,李永强2,李锋2

1. 东北大学机械工程与自动化学院, 沈阳 110819 2. 东北大学理学院, 沈阳 110819

NONLINEAR DYNAMICS ANALYSIS OF ALUMINUM HONEYCOMB SANDWICH PLATE WITH COMPLETED CLAMPED SUPPORTED

ZHANG Yingjie 1,2, YAN Yunhui 1, LI Yongqiang 2, LI Feng 2

1. School of Mechanical and Automation, Northeastern University, Shenyang 110819 2. College of Sciences, Northeastern University, Shenyang 110819

张英杰 颜云辉 李永强 李锋. Al质蜂窝夹芯板非线性动力学分析[J]. 金属学报, 2012, 48(8): 995-1004.
, , , . NONLINEAR DYNAMICS ANALYSIS OF ALUMINUM HONEYCOMB SANDWICH PLATE WITH COMPLETED CLAMPED SUPPORTED[J]. Acta Metall Sin, 2012, 48(8): 995-1004.

摘要 参考文献 相关文章 Metrics 全文: PDF(2407 KB)   摘要: 基于经典叠层板理论和几何大变形理论, 研究了四边固支Al质蜂窝夹芯板的非线性动力学问题. 在考虑横向阻尼的影响下, 利用Hamilton变分原理建立了蜂窝夹芯板受横向激振力作用时的受迫振动微分方程, 通过振型正交化将 蜂窝夹芯板的受迫振动微分方程简化为双模态下的动力学控制方程, 同时利用Runge-Kutta法数值模拟了系统的非线性动力学行为. 结果表明: 由于芯层六角形胞元结构的影响, 使得蜂窝夹芯板的振动对横向激振力幅值的变化非常敏感; 第一阶模态下的最大振幅总要大于第二阶模态下的最大振幅, 横向激振力幅值在不同的取值范围时, 蜂窝夹芯板存在不同性质的动力学现象, 在横向激振力幅值较小阶段, 系统总是呈现单倍周期运动. 当横向激振力幅值增加到一定数值时, 系统呈现出从周期运动向倍周期及混沌等复杂运动形式的转换.通过相应的弯曲振动响应实验, 对数值分析结果进行了实验验证. 关键词 ： 蜂窝夹芯板,  受迫振动,  非线性动力学,  混沌     Abstract：Study on the dynamics of aluminum honeycomb sandwich plates of composite structure material plays a key role for the special applications of the aerospace and automotive engineering. The nonlinear dynamics of honeycomb sandwich plate is explored. According to the classical plate theory and the large deformation, the governing equations of motion are established for the honeycomb sandwich plate subjected to the transversal excitation force by using the Hamilton’s law of variation principle. The transversal damping is taken into consideration. The method of normalization is utilized to transform the nonlinear vibration equations to nonlinear system with double modes of freedom. Numerical simulation is used directly to investigate the nonlinear responses of the honeycomb sandwich plate. The results indicates that the change of transversal excitation force has a significant effect on the vibration of honeycomb sandwich plate because the hexagon cell of core and the amplitude of the first modal are bigger than the second modal. In the different ranges of transversal excitation force, the honeycomb sandwich plate exists different dynamical phenomena. Single periodic motion appears when the force value is small, and periodic motion, multi–period motion, chaotic motion appears with the increase of force. Experiments are conducted to validate the numerical simulation results. Key words： honeycomb sandwich    forced vibration    nonlinear dynamics    chaotic motion 收稿日期: 2012-04-27      ZTFLH:  TB331   基金资助: 国家自然科学基金资助项目50574019 作者简介: 张英杰, 女, 1980年生, 讲师, 博士生 服务 把本文推荐给朋友 加入引用管理器 E-mail Alert RSS 作者相关文章 张英杰 颜云辉 李永强 李锋 44.8K 链接本文: https://www.ams.org.cn/CN/10.3724/SP.J.1037.2012.00235      或      https://www.ams.org.cn/CN/Y2012/V48/I8/995 [1] Abd El–Sayed F K, Jones R, Burgess I W. Composites, 1979; 10: 209 [2] Gibson L J, Ashby M F, Schajer G S, Robertson C I. P Roy Soc A–Math Phy, 1982; 6: 25 [3] Wang Y J. Acta Sci Nat Univ Peking, 1991; 27: 302  (王颖坚. 北京大学学报, 1991; 27: 302) [4] Silva M J, Hayes W C, Gibson L J. Int J Mech Sci, 1995; 37: 1161 [5] Torquato S, Gibiansky L V, Silva M J, Gibson L J. Int J Mech Sci, 1998; 40: 71 [6] Thompson R W, Matthews F L, O’Rourke B P. Mater Des, 1995; 16: 131 [7] Paik J K, Thayamballi A K, Kim G S. Thin Wall Struct, 1999; 35: 205 [8] Millar D. In: Ferguson N S, Wolfe H F, Mei C, eds., Proc 6th Int Conf on Recent Advances in Structural Dynamics, Southampton: Elsevier Applied Science, 1997: 995 [9] Sharma N, Gibson R F, Ayorinde E O. J Sandw Struct Mater, 2006; 8: 263 [10] Zou G P, Lu J, Cao Y, Liu B J. Acta Metall Sin, 2011; 47: 1181 (邹广平, 芦颉, 曹扬, 刘宝君. 金属学报, 2011; 47: 1181) [11] Meo M, Vignjevic R, Marengo G. Int J Mech Sci, 2005; 47: 1301 [12] Staal R A, Mallinson G D, Jayaraman K, Horrigan D P W. J Sandw Struct Mater, 2009; 11: 203 [13] Horrigan D P W, Staal R A. J Sandw Struct Mater, 2011; 13: 111 [14] Saito T, Parbery R D, Okuno S. J Sound Vib, 1997; 208: 271 [15] Lai L. PhD Thesis, University of Toronto, 2002 [16] Nilsson E, Nilsson A C. J Sound Vib, 2002; 251: 409 [17] Ruzzene M. J Sound Vib, 2004; 277: 741 [18] Chen A, Davalos J F. Int J Solids Struct, 2005; 42: 2711 [19] Li Y Q, Jin Z Q, Wang W, Liu J. Chin J Mech Eng, 2008, 44: 165 (李永强, 金志强, 王薇, 刘杰. 机械工程学报, 2008; 44: 165) [20] Li Y Q, Jin Z Q. Compos Struct, 2008; 83: 154 [21] Li Y Q, Zhu D W. Compos Struct, 2009; 88: 33 [22] Li Y Q, Li F, Zhu D W. Compos Struct, 2010; 92: 1110 [23] Sun J, Zhang W, Chen L H, Yao M H. J Dynam Control, 2008; 6: 150 (孙佳, 张伟, 陈丽华, 姚明辉. 动力学与控制学报, 2008; 6: 150) [24] Fu M H, Yin J R. Acta Mech Sin, 1999; 31: 113 [25] Gorman D J. Free Vibration Analysis of Rectangular Plates. New York: Elsevier North Holland Inc, 1982: 75 [1] 刘政,张嘉艺,罗浩林,邓可月. 混沌对流下的半固态A356铝合金初生相形貌演变研究*[J]. 金属学报, 2016, 52(2): 177-183. [2] 曹保胜; 张志鹏; 雷明凯 . 二元非均匀体系非线性动力学扩散模型的相关性[J]. 金属学报, 2008, 44(3): 281-286 . [3] 郜传厚; 周志敏; 邵之江 . 高炉铁水含硅量的混沌局部线性预测[J]. 金属学报, 2005, 41(4): 433-436 . [4] 李学良; 鲁道荣; 朱云贵; 何建波; 王华林 . 表面部分成膜金属阳极溶解模型及其振荡与混沌行为[J]. 金属学报, 2001, 37(5): 493-498 . Viewed Full text Abstract Cited   Shared      Discussed