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Su Wenzheng, Liu Shutiany. EFFECTIVE COUPLE-STRESS DYNAMIC BEAM MODEL OF A TYPICAL CELLULAR SOLID[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(1): 111-126. DOI: 10.6052/0459-1879-15-210
Citation: Su Wenzheng, Liu Shutiany. EFFECTIVE COUPLE-STRESS DYNAMIC BEAM MODEL OF A TYPICAL CELLULAR SOLID[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(1): 111-126. DOI: 10.6052/0459-1879-15-210
shu

EFFECTIVE COUPLE-STRESS DYNAMIC BEAM MODEL OF A TYPICAL CELLULAR SOLID

  • 1.

    School of Civil and Safety Engineering, Dalian Jiaotong University, Dalian 116028, China

  • 2. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116023, China

  • Received Date: June 08, 2015
  • Revised Date: August 31, 2015
    Graphical Abstract
    • Abstract
  • The e ective continuum beam model can be used to study the dynamic behavior of the one-dimensional cellular solid structure. However, this e ective model will bring the size e ect when the cell size is close to the height dimension of the beam-like structure. The classical continuum model, which has no length scale, cannot describe this size dependent feature. By contrast, the generalized continuum model is pertinent to the description of the size e ect. The purpose of this paper is to develop an e ective Timoshenko continuum beam model for the transverse natural vibration analysis of a periodic cellular solid beam-like structure whose unit cell has a circular void, based on the couple-stress theory. The properties of the e ective couple-stress continuum are generated under the criterion of the equivalent strain energy and the geometrical average by the analysis of a unit cell. These properties are then employed in the Timoshenko beam theory to obtain the dynamics di erential equations. Comparison is made with the prediction of a finite element analysis of the complete cellular structure, which is taken as the benchmark for accuracy. Good agreements both on the frequencies and mode shapes are found by a variety of examples where the method of modal assurance criterion (MAC) is employed for the comparison of the mode shapes. The emphasis is put on the influence of the relative size of the void diameter, the size ratio of the beam height to the cell size, and the aspect ratio of the beam-like structure on the accuracy of the e ective beam model. A series of methods on the natural vibration analysis of a cellular solid beam-like structure is recommended conservatively based on these analyses.
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    • References (33)
  • 1 Gibson LJ, Ashby MF. Cellular Solids: Structure and Properties. Cambridge: Cambidge University Press, 1997
    2 Ashby MF, Evans AG, Fleck NA, et al. Metal Foams: A Design Guide. Boston: Butterworth-Heinemann, 2000
    3 Onck PR, Andrews EW, Gibson LJ. Size e ects in ductile cellular solids. Part I: Modeling. International Journal of Mechanical Sciences,2001, 43(3): 681-699
    4 Andrews EW, Gioux G, Onck P, et al. Size e ects in ductile cellular solids. Part II: Experimental results. International Journal of Mechanical Sciences, 2001, 43(3): 701-713
    5 Dai GM, Zhang WH. Size e ects of basic cell in static analysis of sandwich beams. International Journal of Solids and Structures,2008, 45(9): 2512-2533
    6 Liu S, Su W. E ective couple-stress continuum model of cellular solids and size e ects analysis. International Journal of Solids and Structures, 2009, 46(14-15): 2787-2799
    7 苏文政, 刘书田. 基于偶应力理论的格栅材料等效介质模型. 力 学学报, 2008, 40(6): 776-785 (Su Wenzheng, Liu Shutian. E ective continuum model of grid material based on couple-stress theory. Chinese Journal of Theoretical and Applied Mechanics, 2008,40 (6):776-785 (in Chinese))
    8 蔡园武, 徐亮, 程耿东. 正六角形单胞周期性蜂窝板等效刚度研 究. 大连理工大学学报, 2014, 54(4): 377-383 (Cai Yuanwu, Xu Liang, Cheng Gengdong. Study of e ective sti ness of periodic honeycomb plate with regular hexagonal unit cell. Journal of Dalian University of Technology, 2014, 54(4): 377-383 (in Chinese))
    9 Yi S, Xu L, Cheng G, et al. FEM formulation of homogenization method for e ective properties of periodic heterogeneous beam and size e ect of basic cell in thickness direction. Computers & Structures,2015, 156: 1-11
    10 Burgueno R, Quagliata MJ, Mohanty AK, et al. Hierarchical cellular designs for load-bearing biocomposite beams and plates. Materials Science and Engineering A, 2005, 390(1-2): 178-187
    11 邱克鹏, 吴晨, 张卫红. 蜂窝夹芯结构吸波性能的有限元计算分 析. 中国科学:物理学力学天文学, 2013, 43(9): 1057-1064 (Qiu Kepeng, Wu Chen, Zhang Weihong. Numerical analysis of absorbing property for structural absorbing material (SAM) with honeycomb cores. Scientia Sinica Physica, Mechanica & Astronomica,2013, 43(9): 1057-1064 (in Chinese))
    12 张卫红, 段文东, 许英杰等. 六边形蜂窝等效面外剪切模量预测 及其尺寸效应. 力学学报, 2013, 45(2): 288-292 (Zhang Weihong, Duan Wendong, Xu Yingjie, et al. Predictions of e ective out-plane shear modulus and size e ect of hexagonal honeycomb. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45 (2): 288-292 (in Chinese))
    13 张卫红, 骆金威, 戴高明等. 周期性多孔材料等效剪切模量与尺 寸效应研究. 力学学报, 2011, 43(1): 144-153 (Zhang Weihong, Luo Jinwei, Dai Gaoming, et al. Numerical predictions of e ective shear modulus and size e ect for periodic cellular materials. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43 (1):144-153 (in Chinese))
    14 Dai G, Zhang W. Cell size e ects for vibration analysis and design of sandwich beams. Acta Mechanica Sinica, 2009, 25(3): 353-365
    15 Banerjee S, Bhaskar A. The applicability of the e ective medium theory to the dynamics of cellular beams. International Journal of Mechanical Sciences, 2009, 51(8): 598-608
    16 Su W, Liu S. Vibration analysis of periodic cellular solids based on an e ective couple-stress continuum model. International Journal of Solids and Structures, 2014, 51(14): 2676-2686
    17 Tekoglu C, Onck PR. Size e ects in two-dimensional Voronoi foams: A comparison between generalized continua and discrete models. Journal of the Mechanics and Physics of Solids, 2008,56(12): 3541-3564
    18 孟晗, 辛锋先, 卢天健. 多孔纤维吸声材料填充蜂窝结构的声学 性能. 中国科学: 物理学力学天文学, 2014, 44(6): 599-609 (Meng Han, Xin Fengxian, Lu Tianjian. A coustical properties of honeycomb structures filled with fibrous absorptive materials. Scientia Sinica Physica, Mechanica & Astronomica. 2014, 44 (6): 599-609 (in Chinese))
    19 Yan J, Hu WB, Wang ZH, et al. Size e ect of lattice material and minimum weight design. Acta Mechanica Sinica, 2014, 30(2): 191-197
    20 虞吉林. 考虑微结构的固体力学的进展和若干应用. 力学进展,1985, 15(1): 82-89 (Yu Jilin. Progress and applications of solid mechanics considering microstructure. Advances in Mechanics, 1985,15 (1): 82-89 (in Chinese))
    21 Eringen AC. Microcontinuum Field Theories. New York Springer,1999
    22 胡更开, 刘晓宁, 荀飞. 非均匀微极介质的有效性质分析. 力学进 展, 2004, 34(2): 195-214 (Hu Gengkai, Liu Xiaoning, Xun Fei. Micromechanics of heterogeneous micropolar mediums. Advances in Mechanics, 2004, 34(2): 195-214(in Chinese))
    23 Mindlin RD. Influence of couple-stresses on stress concentrations. Experimental Mechanics, 1963, 3(1): 1-7
    24 任树伟, 辛锋先, 卢天健. 考虑尺度效应的微平板声振耦合特性研 究. 中国科学: 技术科学, 2014, 44(2): 201-208 (Ren Shuwei, Xin Fengxian, Lu Tianjian. Vibroacoustic characteristics of micro-plates considering scale e ect. Science China: Technological Sciences,2014, 44(2): 201-208
    25 王晓明, 王飞, 赵学增等. 基于Cosserat 理论的四边简支自由振动 微平板尺度效应研究. 固体力学学报, 2012, 33(1): 63-68 (Wang Xiaoming, Wang Fei, Zhao Xuezeng, et al. On the size e ects in a freely-vibrating micro-plate with the four edges simply-supported based on the Cosserat theroy. Chinese Journal of Solid Mechanics,2012, 33(1): 63-68 (in Chinese))
    26 Asghari M, Kahrobaiyan MH, Rahaeifard M, et al. Investigation of the size e ects in Timoshenko beams based on the couple stress theory. Archive of Applied Mechanics, 2011, 81(7): 863-874
    27 李莉, 陈万吉, 郑楠. 修正偶应力理论层合薄板稳定性模型及尺度 效应. 工程力学, 2013, 30(5): 1-7 (Li Li, Chen Wanji, Zheng Nan. Model of composite laminated thin plate based on modified couple stress theory and buckling analysis of scale e ects. Engineering Mechanics,2013, 30 (5): 1-7 (in Chinese))
    28 Lakes R, Drugan WJ. Bending of a cosserat elastic bar of square cross section: theory and experiment. Journal of Applied Mechanics,2015, 82(9): 091002
    29 Han SM, Benaroya H, Wei T. Dynamics of transversely vibrating beams using four engineering theories. Journal of Sound and Vibration,1999, 225(5): 935-988
    30 Bigoni D, Drugan WJ. Analytical derivation of cosserat moduli via homogenization of heterogeneous elastic materials. Journal of Applied Mechanics, Transactions ASME, 2007, 74(4): 741-753
    31 夏桂云, 曾庆元. 深梁理论的研究现状与工程应用. 力学与实践,2015, 37(3): 302-316 (Xia Guiyun, Zeng Qingyuan. Timoshenko beam theory and its applications. Mechanics in Engineering, 2015,37(3): 302-316 (in Chinese))
    32 Bouyge F, Jasiuk I, Boccara S, et al. A micromechanically based couple-stress model of an elastic orthotropic two-phase composite. European Journal of Mechanics, A/Solids, 2002, 21(3): 465-481
    33 Ewins DJ. Modal Testing: Theory, Practice and Application. Baldock: Research Studies Press, 2000
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