多层次等效的Mori-Tanaka法预测含空腔点阵增强芯层的等效弹性模量
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摘要
提出了兼具力学和声学性能的夹层吸声复合材料-含空腔点阵增强夹芯结构;为了预测含空腔点阵增强结构芯层的等效弹性模量,建立了包含空腔、点阵增强柱和泡沫基体的三相复合材料的细观力学多层次等效数理模型,结合点阵增强柱和空腔周期性分布的特点建立代表性体积单元,利用Mori-Tanaka方法进行两次单相夹杂等效处理,获取了含空腔点阵增强芯层等效弹性模量的解析解,与试验数据和细观力学有限元法结果对比均吻合较好。采用有限元软件ANSYS建立了含空腔点阵增强夹芯结构的实际模型和等效模型,并将芯层等效模量解析结果作为等效模型芯层的材料参数,计算弯曲变形和固有频率并进行对比分析,弯曲变形位移和中低频固有频率的相对误差不超过2%,满足工程精度要求。进一步利用该等效方法,分别探讨了点阵增强柱和空腔体积比对芯层等效弹性模量的影响规律。结果表明,上述方法能较准确地预测含空腔点阵增强结构芯层的等效弹性模量,且数理模型清晰,公式简单,计算快速。
A lattice-reinforced sandwich structure with cavities was presented,which had prospects of the integration of both mechanical and acoustic properties.In order to predict the equivalent modulus of lattice-reinforced core materials with cavities,a multi-level equivalent micromechanical mathematical model was built,which was made up of cavities,lattice reinforcements and foam matrices.With the reinforcements and cavities distributing periodically in the core,the representative unit of the equivalent model was established.Based on the Mori-Tanaka method,the single-phase inclusion equivalent was performed twice and the equivalent modulus of lattice-reinforced core materials with cavities were obtained which agree well with the experimental results and those determined using the FEM method.The numerical simulation was then conducted via the ANSYS code package to obtain the bending deformations and the natural frequencies of both the actual model and the equivalent mode,and the equivalent modulus of the core was used as the material parameter of the core of the equivalent model.The simulation results conform highly with each other and the relative errors of both the bending deformation displacements and the natural frequencies at low frequency are less than 2%,which satisfy the precision requirement in engineering.On this premise,further research was conducted to investigate the effects of reinforcements and cavities volume ratio on the equivalent modu-lus of the core.The results indicate that the above method can predict equivalent modulus of lattice-reinforced core materials with cavities accurately and quickly with a clear mathematical mode and simple formulas.
A lattice-reinforced sandwich structure with cavities was presented,which had prospects of the integration of both mechanical and acoustic properties.In order to predict the equivalent modulus of lattice-reinforced core materials with cavities,a multi-level equivalent micromechanical mathematical model was built,which was made up of cavities,lattice reinforcements and foam matrices.With the reinforcements and cavities distributing periodically in the core,the representative unit of the equivalent model was established.Based on the Mori-Tanaka method,the single-phase inclusion equivalent was performed twice and the equivalent modulus of lattice-reinforced core materials with cavities were obtained which agree well with the experimental results and those determined using the FEM method.The numerical simulation was then conducted via the ANSYS code package to obtain the bending deformations and the natural frequencies of both the actual model and the equivalent mode,and the equivalent modulus of the core was used as the material parameter of the core of the equivalent model.The simulation results conform highly with each other and the relative errors of both the bending deformation displacements and the natural frequencies at low frequency are less than 2%,which satisfy the precision requirement in engineering.On this premise,further research was conducted to investigate the effects of reinforcements and cavities volume ratio on the equivalent modu-lus of the core.The results indicate that the above method can predict equivalent modulus of lattice-reinforced core materials with cavities accurately and quickly with a clear mathematical mode and simple formulas.
引文
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[17] MORI T,TANAKA K.Average stress in matrix and average elastic energy of materials with misfitting inclusions[J].Acta Metallurgica,1973,21(5):571-574.
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[21]刘文辉,张新明,唐建国,等.一种计算孔洞体积的方法[J].中南大学学报(自然科学版),2007,38(5):815-819.LIU Wenhui,ZHANG xinming,TANG Jianguo,et al.A method of calculating the volume of a hole[J].Journal of Central South University(Science and Technology),2007,38(5):815-819(in Chinese).
[2] DU L,JIAO G.Indentation study of Z-pin rein-forced polymer foam core sandwich structures[J].Composites Part A:Applied Science&Manufacturing,2009,40(6-7):822-829.
[3]黄涛,矫桂琼,李野.缝纫泡沫夹层结构芯子剪切模量研究[J].机械强度,2007,29(1):113-117.HUANG Tao,JIAO Guiqiong,LI Ye.Study on shear modulus of stitched foam core sandwich[J].Journal of Mechanical Strength,2007,29(1):113-117(in Chinese).
[4]李飘,陈美霞,罗琦.横向增强芯材的等效弹性模量研究[J].中国舰船研究,2013,8(2):65-72.LI Piao,CHEN Meixia,LUO Qi.Research on the equivalent modulus of elasticity of transverse reinforced core materials[J].Chinese Journal of Ship Research,2013,8(2):65-72(in Chinese).
[5]商超.消声瓦的吸声机理研究[D].哈尔滨:哈尔滨工业大学,2011.SHANG Chao.The absorption mechanisms of anechoic tile[D].Harbin:Harbin Institute of Technology,2011(in Chinese).
[6]姚熊亮,计方,庞福振,等.隔声去耦瓦声学性能研究[C].船舶水下噪声学术讨论会,2009.YAO Xiongliang,JI Fang,PANG Fuzhen,et al.Study on acoustic performance of sound insulation vibration decoupling tile[C].Symposium on Underwater Noise of Ships,2009(in Chinese).
[7]缪旭弘,王仁乾,顾磊,等.去耦隔声层性能数值分析[J].船舶力学,2005,9(5):125-131.MIAO Xuhong,WANG Renqian,GU Lei,et al.Numerical analysis on the sound insulation performance of decoupling material[J].Journal of Ship Mechanics,2005,9(5):125-131(in Chinese).
[8]卢子兴,高镇同.应用微分方法确定复合泡沫塑料的杨氏模量[J].北京航空航天大学学报,1996(6):692-695.LU Zixing,GAO Zhentong.Determination of young’s modulus of the syntactic foam plastics by differential scheme[J].Journal of Beijing University of Aeronautics and Astronautics,1996(6):692-695(in Chinese).
[9]杜修力,金浏.含孔隙混凝土复合材料有效力学性能研究[J].工程力学,2012,29(6):70-77.DU Xiuli,JIN Liu.Research on effective mechanical properties of concrete composite material with pores[J].Engineering Mechanics,2012,29(6):70-77(in Chinese).
[10]王兵,冯吉才,李庆飞,等.纤维柱增强泡沫夹芯的等效力学性能研究[J].哈尔滨工业大学学报,2012,44(3):29-33.WANG Bing,FENG Jicai,LI Qingfei,et al.Study on the effective mechanical properties of foam core sandwich structure reinforced by fiber composite columns[J].Journal of Harbin Institute of Technology,2012,44(3):29-33(in Chinese).
[11]谢桂兰,赵锦枭,田杰,等.均匀化有限元法预测复合材料层合板宏观有效弹性性能[J].玻璃钢/复合材料,2014(7):23-27.XIE Guilan,ZHAO Jinxiao,TIAN Jie,et al.Study of sealing to prevent oil leakage for the thermoplastic cylinder head cover[J].Fiber Reinforced Plastics/Composites,2014(7):23-27(in Chinese).
[12] SUN C T,VAIDYA R S.Prediction of composite properties from a representative volume element[J].Composites Science&Technology,1996,56(2):171-179.
[13]李艳茹,程忠庆,姜海波.利用外方内圆模型预测单向复合材料的横向弹性模量[J].复合材料学报,2018,35(8):2110-2115.LI Yanru,CHENG Zhongqing,JIANG Haibo.Prediction of transverse elastic modulus of unidirectional composites using the model of circle-in-square[J].Acta Materiae Compoitae Sinica,2018,35(8):2110-2115(in Chinese).
[14] ZHU H,CHEN Q,YAN Z,et al.Micromechanical models for saturated concrete repaired by the electrochemical deposition method[J].Materials&Structures,2014,47(6):1067-1082.
[15] YAN Z,CHEN Q,ZHU H,et al.A multi-phase micromechanical model for unsaturated concrete repaired using the electrochemical deposition method[J].International Journal of Solids&Structures,2013,50(24):3875-3885.
[16]陈庆,朱合华,闫治国,等.基于Mori-Tanaka法的电化学沉积修复饱和混凝土细观描述[J].建筑结构学报,2015,36(1):98-103.CHEN Qing,ZHU Hehua,YAN Zhiguo,et al.Micro-scale description of saturated concrete repaired by electrochemical deposition method based on Mori-Tanaka method[J].Journal of Building Structures,2015,36(1):98-103(in Chinese).
[17] MORI T,TANAKA K.Average stress in matrix and average elastic energy of materials with misfitting inclusions[J].Acta Metallurgica,1973,21(5):571-574.
[18] BENVENISTE Y.A new approach to the application of Mori-Tanaka’s theory in composite materials[J].Mechanics of Materials,1987,6(2):147-157.
[19] ZHAO Y H,TANDON G P,WENG G J.Elastic moduli for a class of porous materials[J].Acta Mechanica,1989,76(1-2):105-131.
[20]沈观林,胡更开,刘彬.复合材料力学[M].北京:清华大学出版社,2013.SHEN Guanlin,HU Gengkai,LIU Bin.Mechanics of composites[M].Beijing:Tsinghua University Press,2013(in Chinese).
[21]刘文辉,张新明,唐建国,等.一种计算孔洞体积的方法[J].中南大学学报(自然科学版),2007,38(5):815-819.LIU Wenhui,ZHANG xinming,TANG Jianguo,et al.A method of calculating the volume of a hole[J].Journal of Central South University(Science and Technology),2007,38(5):815-819(in Chinese).