基于多层次修正的纤维增强复合薄壳动刚度预测
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摘要
采用多层次修正技术对纤维增强复合薄壳的动刚度进行分析与预测。用正弦半波信号来近似模拟脉冲激励信号,并基于Love壳体理论、能量法、哈密顿原理等方法,实现了该类型复合薄壳的动刚度求解。利用多层次修正技术和测试获得的试验数据,对理论模型中复合薄壳的长度、半径、厚度、弹性模量、泊松比及模态阻尼比等参数进行修正,进而获得了较为精准的理论模型。以T300碳纤维/树脂基复合薄壳为例,搭建了振动测试系统,通过力锤施加脉冲信号,并采用激光速度传感器测试了3个响应测点的动刚度,并与相应的预测结果进行了比较。结果表明,动刚度理论预测的误差最大不超过12.2%,处于误差允许的范围内,进而验证了所提出的动刚度预测方法的正确性。
The dynamic stiffnesses of fiber reinforced composite shells were analyzed and predicted based on the multi-level correction method. Firstly, a sinusoidal half-wave signal was used to approximate the impulse excitation signal, and the dynamic stiffnesses of the composite shell were studied based on the Love shell theory, energy method and Hamiltonian principle. Next, in order to obtain a more accurate dynamic stiffness model of the composite thin shells, the multi-level correction technique and the experimental data were employed to correct the length, radius, thickness, elastic modulus, Poisson's ratio and modal damping ratio. Finally, a T300 fiber/epoxy composite thin shell was taken as a study object and a corresponding vibration test system was set up. The pulse signal was applied by a hammer and the dynamic stiffnesses at three response points were tested by the laser speed sensor. The experimental results were compared with the calculated results. It is found that the predicted errors of the dynamic stiffnesses at the above points are less than 12.2%, which are within an acceptable range. Thus, the correctness of the proposed prediction method for dynamic stiffnesses was verified.
The dynamic stiffnesses of fiber reinforced composite shells were analyzed and predicted based on the multi-level correction method. Firstly, a sinusoidal half-wave signal was used to approximate the impulse excitation signal, and the dynamic stiffnesses of the composite shell were studied based on the Love shell theory, energy method and Hamiltonian principle. Next, in order to obtain a more accurate dynamic stiffness model of the composite thin shells, the multi-level correction technique and the experimental data were employed to correct the length, radius, thickness, elastic modulus, Poisson's ratio and modal damping ratio. Finally, a T300 fiber/epoxy composite thin shell was taken as a study object and a corresponding vibration test system was set up. The pulse signal was applied by a hammer and the dynamic stiffnesses at three response points were tested by the laser speed sensor. The experimental results were compared with the calculated results. It is found that the predicted errors of the dynamic stiffnesses at the above points are less than 12.2%, which are within an acceptable range. Thus, the correctness of the proposed prediction method for dynamic stiffnesses was verified.
引文
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[2] 杜善义.先进复合材料与航空航天[J].复合材料学报,2007,24(1):1-12.DU Shanyi.Advanced composite materials and aerospace engineering[J].Journal of Acta Materiae Compositae Sinica,2007,24(1):1-12.
[3] QATU M S,SULLIVAN R W,WANG W.Recent research advances on the dynamic analysis of composite shells:2000-2009[J].Composite Structures,2010,93(1):14-31.
[4] KAW A K.Mechanics of composite materials[M].Boca Raton:The Chemical Rubber Company Press,2005.
[5] 陈辉.复合材料圆柱壳的振动频率分析[J].纤维复合材料学报,1989,12(3):12-21.CHEN Hui.Vibration frequency analysis of composite cylindrical shell[J].Journal of Fiber Composite,1989,12(3):12-21.
[6] MANGALGIRI P D.Composite materials for aerospace applications[J].Bulletin of Materials Science,1999,22(3):657-664.
[7] MORGAN P.Carbon fibers and their composites[M].Boca Raton:The Chemical Rubber Company Press,2005.
[8] WEAVER W,TIMOSHENKO S P,YOUNG D H.Vibration problems in engineering[M].Hoboken:Wiley,1990.
[9] 刘伟,王磊,俞强,等.船舶推力轴承纵向液压减振技术研究[J].舰船科学技术,2016,38(5):59-62.LIU Wei,WANG Lei,YU Qiang,et al.Research of reducing axial vibration with hydraulic shock absorber in ship’s thrust bearing[J].Ship Science and Technology,2016,38(5):59-62.
[10] KAYNIA A M,KAUSEL E.Dynamic stiffness and seismic response of pile groups:R82-03 [R].Washington D.C.:NASA,1982.
[11] MARSH E R,YANTEK D S.Experimental measurement of precision bearing dynamic stiffness[J].Journal of Sound & Vibration,1997,202(1):55-66.
[12] NAKAMURA N.Nonlinear response analysis considering dynamic stiffness with both frequency and strain dependencies[J].Journal of Engineering Mechanics,2008,134(7):530-541.
[13] TILEYLIOGLU S,STEWART J P,NIGBOR R L.Dynamic stiffness and damping of a shallow foundation from forced vibration of a field test structure[J].Journal of Geotechnical & Geoenvironmental Engineering,2011,137(4):344-353.
[14] FRANGOUDIS C,RASHID A,NICOLESCU C M.Experimental analysis of a machining system with adaptive dynamic stiffness[J].Journal of Machine Engineering,2014,13(1):49-63.
[15] 石清鑫,袁奇,胡永康.250 t高速动平衡机摆架的动刚度分析[J].机械工程学报,2011,47(1):75-79.SHI Qingxin,YUAN Qi,HU Yongkang.Analysis of dynamic stiffness of 250 t high speed dynamic balancing machine[J].Journal of Mechanical Engineering,2011,47(1):75-79.
[16] 袁占航.反共振振动筛的几个关键技术及仿真研究[D].沈阳:东北大学,2011.
[17] 李宇菲.复合材料汽车板簧的优化设计及其有限元分析[D].武汉:武汉理工大学,2012.
[18] 欧鸣雄,王岩,严建华,等.立式循环泵结构动刚度对转子振动特性的影响[J].核动力工程,2013,34(6):36-
39.OU Mingxiong,WANG Yan,YAN Jianhua,et al.Influence of structural dynamic stiffness of vertical circulating pump on vibration characteristics of rotor[J].Nuclear Power Enginnering,2013,34(6):36-39.
[19] 邓四二,董晓,崔永存,等.双列角接触球轴承动刚度特性分析[J].兵工学报,2015,36(6):1140-1146.DENG Sier,DONG Xiao,CUI Yongcun,et al.Analysis of dynamic stiffness characteristics of double·row angular contact ball bearings[J].Acta Armam,2015,36(6):1140-1146.
[20] 曹志远.板壳振动理论[M].北京:中国铁道出版社,1989.
[21] LAM K Y,LOY C T.Influence of boundary conditions and fibre orientation on the natural frequencies of thin orthotropic laminated cylindrical shells[J].Composite Structures,1995,31(1):21-30.
[22] LUKE D A.Multilevel modeling[M].New York:SAGE Publications Inc,2004.