EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

功能梯度材料微梁的热弹性阻尼研究

许新 李世荣

许新, 李世荣. 功能梯度材料微梁的热弹性阻尼研究[J]. 力学学报, 2017, 49(2): 308-316. doi: 10.6052/0459-1879-16-369
引用本文: 许新, 李世荣. 功能梯度材料微梁的热弹性阻尼研究[J]. 力学学报, 2017, 49(2): 308-316. doi: 10.6052/0459-1879-16-369
Xu Xin, Li Shirong. ANALYSIS OF THERMOELASTIC DAMPING FOR FUNCTIONALLY GRADED MATERIAL MICRO-BEAM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 308-316. doi: 10.6052/0459-1879-16-369
Citation: Xu Xin, Li Shirong. ANALYSIS OF THERMOELASTIC DAMPING FOR FUNCTIONALLY GRADED MATERIAL MICRO-BEAM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 308-316. doi: 10.6052/0459-1879-16-369

功能梯度材料微梁的热弹性阻尼研究

doi: 10.6052/0459-1879-16-369
基金项目: 

国家自然科学基金资助项目 11272278

国家自然科学基金资助项目 11672260

详细信息
    通讯作者:

    2) 李世荣, 教授, 主要研究方向:结构非线性分析及新型材料结构力学行为.E-mail:srli@yzu.edu.cn

  • 中图分类号: O343

ANALYSIS OF THERMOELASTIC DAMPING FOR FUNCTIONALLY GRADED MATERIAL MICRO-BEAM

  • 摘要: 基于Euler-Bernoulli梁理论和单向耦合的热传导理论,研究了功能梯度材料(functionally graded material,FGM)微梁的热弹性阻尼(thermoelastic damping,TED).假设矩形截面微梁的材料性质沿厚度方向按幂函数连续变化,忽略了温度梯度在轴向的变化,建立了单向耦合的变系数一维热传导方程.热力耦合的横向自由振动微分方程由经典梁理论获得.采用分层均匀化方法将变系数的热传导方程简化为一系列在各分层内定义的常系数微分方程,利用上下表面的绝热边界条件和界面处的连续性条件获得了微梁温度场的分层解析解.将温度场代入微梁的运动方程,获得了包含热弹性阻尼的复频率,进而求得了代表热弹性阻尼的逆品质因子.在给定金属-陶瓷功能梯度材料后,通过数值计算结果定量分析了材料梯度指数、频率阶数、几何尺寸以及边界条件对TED的影响.结果表明:(1)若梁长固定不变,梁厚度小于某个数值时,改变陶瓷材料体积分数可以使得TED取得最小值;(2)固有频率阶数对TED的最大值没有影响,但是频率阶数越高对应的临界厚度越小;(3)不同的边界条件对应的TED的最大值相同,但是随着支座约束刚度增大对应的临界厚度减小;(4)TED的最大值和对应的临界厚度随着金属组分的增大而增大.

     

  • 图  1  FGM微梁的几何尺寸和坐标系

    Figure  1.  Geometry and coordinates of an FGM micro-beam

    图  2  本文所得纯陶瓷微梁的热弹性阻尼解答与文献中的解析解的比较

    Figure  2.  A comparison of the present solution of TED for a pure ceramic microbeam with the analytical solution in the literature

    图  3  前三阶模态下FGM微梁的热弹性阻尼随厚度的变化曲线

    Figure  3.  Curves of the thermoelastic damping of the FGM micro-beam versus thethickness in the first three vibrating modes

    图  4  FGM简支微梁自由振动时的频移和衰减随厚度的变化的关系曲线 (一阶模态)

    Figure  4.  The frequency shift and the attenuation change with the thickness of anS-S FGM micro-beam (in the first mode)

    图  5  给定不同材料梯度指数n时热弹性阻尼$Q^{ - 1}$与厚度h之间的关系曲线 (一阶模态)

    Figure  5.  Thermoelastic damping $Q^{ - 1}$ versus the thickness $h $ of S-S FGMmicro-beam for different values of $n $ (in the first mode)

    图  6  给定不同厚度时FGM微梁的热弹性阻尼$Q^{ -1}$与材料梯度指数n之间的关系曲线 (一阶模态)

    Figure  6.  Thermoelastic damping $Q^{ - 1}$ versus the material gradient $n $ for somespecified values of the thickness (in the first mode)

    图  7  不同边界条件下热弹性阻尼与厚度的关系曲线 (一阶模态)

    Figure  7.  Relationship curves between TED and the thickness under differentboundary conditions (in the first mode)

    表  1  镍和氮化硅的物性参数 ($T_0 = 300$ K)

    Table  1.   The material properties of nickel and silicon nitride ($T_0 =300$ K)

    表  2  一阶频率下FGM微梁不同N对应的$Q^{ - 1}$值 (S-S, $h=3 \mu $m, $l=300 \mu $m, $n=1$)

    Table  2.   Values of the quality factor $Q^{ - 1}$ with numbers of the divided layer of an FGM beam at thefirst order frequency (S-S, $h=3 \mu $m, $l=300 \mu $m, $n=1$)

    表  3  热弹性阻尼最大值$Q_{\max }^{ - 1} (\times 10^{ - 4})$和相应的临界厚度$h_{\rm cr }(\mu $m) 值随材料梯度指数和边界条件的变化 (一阶模态,$l =300 \mu $m)

    Table  3.   Values of the maximum TED, $Q_{\max }^{ - 1} (\times 10^{ - 4})$ and the related critical thickness $h_{\rm cr }(\mu $m) varying with the boundary conditions and for material gradient index n (in the firstmode, $l=300 \mu $m)

  • [1] Prabhakar S, Vengallatore S. Thermoelastic damping in bilayered micromechanical beam resonators. Journal of Micromechanics and Microengineering, 2007, 17:532-538 doi: 10.1088/0960-1317/17/3/016
    [2] Tai YP, Li P, Zuo WL. An entropy based analytical model for thermoelastic damping in micromechanical resonators. Applied Mechanics and Materials, 2012, 159:46-50 doi: 10.4028/www.scientific.net/AMM.159
    [3] Hendou RH, Mohammadi AK. Transient analysis of nonlinear Euler-Bernoulli micro-beam with thermoelastic damping, via nonlinear normal modes. Journal of Sound and Vibration, 2014, 333:6224-6236 doi: 10.1016/j.jsv.2014.07.002
    [4] Lin SM. Analytical solutions for thermoelastic vibrations of beam resonators with viscous damping in non-Fourier model. International Journal of Mechanical Sciences, 2014, 87:26-35 doi: 10.1016/j.ijmecsci.2014.05.026
    [5] Lifshitz R, Roukes ML. Thermoelastic damping in micro-and nanomechanical systems. Physical Review B, 2000, 61(8):5600-5609 doi: 10.1103/PhysRevB.61.5600
    [6] Sun YX, Fang DN, Soh AK. Thermoelastic damping in micro-beam resonators. International Journal of Solids and Structures, 2006, 43:3213-3229 doi: 10.1016/j.ijsolstr.2005.08.011
    [7] Moosapour M, Hajabasi MA, Ehteshami H. Thermoelastic damping effect analysis in micro flexural resonator of atomic force microscopy. Applied Mathematical Modelling, 2014, 38:2716-2733 doi: 10.1016/j.apm.2013.10.067
    [8] Guo X, Yi YB. Suppression of thermoelastic damping in MEMS beam resonators by piezoresistivity. Journal of Sound and Vibration, 2014, 333:1079-1095 doi: 10.1016/j.jsv.2013.09.041
    [9] Vengallatore S. Analysis of thermoelastic damping in laminated composite micromechanical beam resonators. Journal of Micromechanics and Microengineering, 2005, 15:2398-2404 doi: 10.1088/0960-1317/15/12/023
    [10] Khisaeva ZF, Ostoja-Starzewski M. Theroelastic damping in nanomechanical resonators with finite wave speeds. Journal of Thermal Stresses, 2006, 29:201-216 doi: 10.1080/01495730500257490
    [11] Prabhakar S, Vengallatore S. Theory of thermoelastic damping in micromechanical resonators with two-dimensional heat conduction. Journal of Microelectro Mechanical Systems, 2008, 17(2):495-502 https://www.researchgate.net/publication/3330356_Theory_of_Thermoelastic_Damping_in_Micromechanical_Resonators_With_Two-Dimensional_Heat_Conduction
    [12] Parayil DV, Kulkarni SS, Pawaskar DN. Analytical and numerical solutions for thick beams with thermoelastic damping. International Journal of Mechanical Sciences, 2015, 94-95:10-19 doi: 10.1016/j.ijmecsci.2015.01.018
    [13] Karami Mohammadi A, Ale Ali N. Vibrational behavior of an electrically actuated micro-beam with thermoelastic damping. Journal of Mechanics, 2014, 30(3):219-227 doi: 10.1017/jmech.2014.12
    [14] Kakhki EK, Hosseini SM, Tahani M. An analytical solution for thermoelastic damping in a micro-beam based on generalized theory of thermoelasticity and modified couple stress theory. Applied Mathematical Modelling, 2016, 40:3164-3174 doi: 10.1016/j.apm.2015.10.019
    [15] Zener C. Internal friction in solids Ⅰ:theory of internal friction in reeds. Physical Review, 1937, 52:230-235 doi: 10.1103/PhysRev.52.230
    [16] Zener C. Internal friction in solids Ⅱ:general theory of thermoelastic internal friction. Physical Review, 1938, 53:90-99 doi: 10.1103/PhysRev.53.90
    [17] Abbasnejad B, Rezazadeh G, Shabani R. Stability analysis of a capacitive FGM micro-beam using modified couple stress theory. Acta Mechanica Solida Sinica, 2013, 26(4):427-440 doi: 10.1016/S0894-9166(13)60038-5
    [18] Abbasnejad B, Rezazadeh G. Mechanical behavior of a FGM microbeam subjected to a nonlinear electrostatic pressure. International Journal of Mechanics and Materials in Design, 2012, 8:381-392 doi: 10.1007/s10999-012-9202-x
    [19] Rezaee M, Sharafkhani N, Chitsaz A. Electrostatically actuated FGM micro-tweezer under the thermal moment. Microsystem Technologies, 2013, 19:1829-1837 doi: 10.1007/s00542-013-1766-3
    [20] Zamanzadeh M, Rezazadeh G, Jafarsadeghi-poornaki I, et al. Static and dynamic stability modeling of a capacitive FGM micro-beam in presence of temperature changes. Applied Mathematical Modelling, 2013, 37:6964-6978 doi: 10.1016/j.apm.2013.02.034
    [21] Akgoz B, Civalek O. Free vibration analysis of axially functionally graded tapered Bernoulli-Euler microbeams based on the modified couple stress theory. Composite Structures, 2013, 98:314-322 doi: 10.1016/j.compstruct.2012.11.020
    [22] Li YL, Meguid SA, Fu YM, et al. Nonlinear analysis of thermally and electrically actuated functionally graded material microbeam. Proceedings of the Royal Society A, 2013, 470:0473 https://www.researchgate.net/publication/260131810_Nonlinear_analysis_of_thermally_and_electrically_actuated_functionally_graded_material_microbeam
    [23] Jia XL, Zhang SM, Ke LL, et al. Thermal effect on the pull-in instability of functionally graded micro-beams subjected to electrical actuation. Composite Structures, 2014, 116:136-146 doi: 10.1016/j.compstruct.2014.05.004
    [24] Akgoz B, Civalek O. Thermo-mechanical buckling behavior of functionally graded microbeams embedded in elastic medium. International Journal of Engineering Science, 2014, 85:90-104 doi: 10.1016/j.ijengsci.2014.08.011
    [25] Akgoz B, Civalek O. Shear deformation beam models for functionally graded microbeams with new shear correction factors. Composite Structures, 2014, 112:214-225 doi: 10.1016/j.compstruct.2014.02.022
    [26] 李世荣, 刘平.功能梯度梁与均匀梁静动态解间的相似转换.力学与实践, 2010, 32(5):45-49 http://www.cnki.com.cn/Article/CJFDTOTAL-LXYS201005011.htm

    Li Shirong, Liu Ping. Analogous transformation of static and dynamic solutions between functionally graded material beams and uniform beams. Mechanics in Engineering, 2010, 32(5):45-49(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-LXYS201005011.htm
  • 加载中
图(7) / 表(3)
计量
  • 文章访问数:  1272
  • HTML全文浏览量:  186
  • PDF下载量:  982
  • 被引次数: 0
出版历程
  • 收稿日期:  2016-12-08
  • 网络出版日期:  2017-01-11
  • 刊出日期:  2017-03-18

目录

    /

    返回文章
    返回