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中文核心期刊
Volume 54 Issue 6
May  2022
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Li Shirong. Thermoelastic damping in functionally graded Mindlin rectangular micro plates. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(6): 1601-1612 doi: 10.6052/0459-1879-22-055
Citation: Li Shirong. Thermoelastic damping in functionally graded Mindlin rectangular micro plates. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(6): 1601-1612 doi: 10.6052/0459-1879-22-055

THERMOELASTIC DAMPING IN FUNCTIONALLY GRADED MINDLIN RECTANGULAR MICRO PLATES

doi: 10.6052/0459-1879-22-055
  • Received Date: 2022-01-28
  • Accepted Date: 2022-03-19
  • Available Online: 2022-03-20
  • Publish Date: 2022-06-18
  • Accurately modelling and evaluating of thernoelastic damping (TED) in functionally graded material (FGM) micro plates are challenging novel topics in the study on the responses of thermoelastic coupled vibration of this kind of new type micro resonators. In this paper, TED in a simply supported FGM rectangular micro plate with moderate thickness is investigated by means of mathematical analysis. Based on the Mindlin plate theory and the one-way coupled heat conduction theory, differential equations governing the thermal-elastic free vibration of the FGM micro plates with the material properties varying continuously along with the thickness direction are established. Under the adiabatic boundary conditions at the top and the bottom surfaces, analytical solution of the temperature field expressed by the kinematic parameters is obtained by using layer-wise homogenization approach. As a result, the structural vibration equation including the thermal membrane force and moment is transformed into a partial differential equation only in terms of the amplitude of the deflection. Then, by using the mathematical similarity between the eigenvalue problems an analytical solution of the complex frequency for an FGM Mindlin micro plate with the four edges simply supported is arrived at, from which the inverse quality factor representing the TED is extracted. Finally, numerical results of TED for the FGM rectangular micro plate made of ceramic-metal constituents with the material properties varying in the thickness as power functions are presented. Effects of the transverse shear deformation, the gradient of the material property and the geometric parameters on the TED are quantitatively investigated in detail. The numerical results show that the TED evaluated by the Mindlin plate theory is smaller than that by the Kirchhoff plate theory and that the difference in the values predicted by the two plate theories becomes significant along with the increase of the thickness-to-side length ratio.

     

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  • [1]
    Zener C. Internal fraction in solids I. Theory of internal fraction in reeds. Physical Review, 1937, 53: 90-99
    [2]
    Bishop GE, Kinra V. Equivalence of the mechanical and entropic description of elastothermodynamics in composite materials. Mechanics of Composite Materials and Structures, 1996, 3: 83-95
    [3]
    Bishop GE, Kinra V. Elastothermaldynamic damping in laminated composites. International Journal of Solids and Structures, 1997, 34: 1075-1092
    [4]
    Lifshitz R, Roukes ML. Thermoelastic damping in micro- and nano-mechanical systems. Phys. Rev. B, 2000, 61: 5600-5609
    [5]
    Nayfeh AH, Younis MI. Modeling and simulations of thermoelastic damping in microplates. Journal of Micromechanics and Microengineering, 2024, 14: 1711-1717
    [6]
    Sun YX, Tohmyoh H. Thermoelastic damping of the axisymmetric vibration of circular plate resonator. Journal of Sound and Vibration, 2009, 319: 392-405
    [7]
    Sun YX, Saka M. Thermoelastic damping in micro-scale circular plate resonators. Journal of Sound and Vibration, 2010, 329: 328-337
    [8]
    Ali NA, Mohammadi AK. Thermoelastic damping in clamped-clamped annular microplate. Applied Mechanics and Materials, 2012, 110-116: 1870-1878
    [9]
    Salajeghe S, Khadem SE, Rasekh M. Nonlinear analysis of thermoelastic damping in axisymmetric vibration of micro circular thin-plate resonators. Applied Mathematical Modelling, 2012, 36: 5991-6000
    [10]
    Li P, Fang YM, Hu RF. Thermoelastic damping in rectangular and circular microplate resonators. Journal of Sound and Vibration, 2012, 331: 721-733
    [11]
    Fang YM, Li P, Wang ZL. Thermoelastic damping in the axisymmetric vibration of circular micro plate resonators with two-dimensional heat conduction. Journal of Thermal Stresses, 2013, 36: 830-850
    [12]
    Fang YM, Li P, Zhou HY, et al. Thermoelastic damping in rectangular microplate resonators with three-dimensional heat conduction. International Journal of Mechanical Sciences, 2017, 133: 578-589
    [13]
    马航空, 周晨阳, 李世荣. Mindlin 矩形微板的热弹性阻尼解析解. 力学学报, 2020, 52(5): 1383-1393

    Ma Hangkong Zhou Chenyang, Li Shirong. Analytical solution of thermoelastic damping in Mindlin rectangular plate. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1383-1393 (in Chinese)
    [14]
    Sharma JN, Sharma R. Damping in micro-scale generalized thermoelastic circular plate resonators. Ultrasonics, 2011, 51: 352-358
    [15]
    Sharma JN, Grover D. Thermoelastic vibration analysis of MEMS/NEMS plate resonators with voids. Acta Mechanica, 2012, 223: 167-187
    [16]
    Guo FL, Song J, Wang GQ, et al. Analysis of thermoelastic dissipation in circular micro-plate resonators using the generalized thermoelasticity theory. Journal of Sound and Vibration, 2014, 333: 2465-2474
    [17]
    Grover D. Damping in thin circular viscothermoelastic plate resonators. Canadian Journal of Physics, 2015, 93: 1597-1605
    [18]
    Chugh N, Partap G. Study of thermoelastic damping in microstrecth thermoelastic thin circular plate. Journal of Vibration Engineering and Technologies, 2021, 9: 105-114
    [19]
    Wang YW, Li XF. Synergistic effect of memory-size-microstructure on thermoelastic damping of a micro-plate. International Journal of Heat and Mass Transfer, 2021, 181: 122031 doi: 10.1016/j.ijheatmasstransfer.2021.122031
    [20]
    Sun YX, Jiang Y, Yang JL. Thermoelastic damping of the axisymmetric vibration of laminated trilayered circular plate resonators. Canada Journal of Physics, 2014, 92: 1026-1032
    [21]
    Zuo WL, Li P, Zhang JR, et al. Analytical modeling of thermoelastic damping in bilayered microplate resonators. International Journal of Mechanical Science, 2016, 106: 128-137
    [22]
    Zuo WL, Li P, Du JK, et al. Thermoelastic damping in trilayered microplate resonators. International Journal of Mechanical Sciences, 2019, 151: 595-608
    [23]
    Liu SB, Ma JX, Yang XF, et al. Theoretical analysis of thermoelastic damping in bilayered circular plate resonators with two-dimensional heat conduction. International Journal of Mechanical Sciences, 2018, 135: 114-123
    [24]
    Liu SB, Ma JX, Yang XF, et al. Theoretical 3D model of thermoelastic damping in laminated rectangular plate resonators. International Journal of Structural Stability and Dynamics, 2018, 18: 1850158
    [25]
    Emami AA, Alibeigloo A. Thermoelastic damping analysis of FG Mindlin microplates using strain gradient theory. Journal of Thermal Stresses, 2016, 39: 1499-1522
    [26]
    Li SR, Chen S, Xiong P. Thermoelastic damping in functionally graded material circular micro plates. Journal of Thermal Stresses, 2018, 41: 1396-1413
    [27]
    Li SR, Ma HK. Analysis of free vibration of functionally graded material micro-plates with thermoelastic damping. Archive Applied Mechanics, 2020, 90: 1285-1304
    [28]
    李世荣, 张靖华, 徐华. 功能梯度与均匀圆板弯曲解的线性转换关系, 力学学报, 2011, 43(5): 871-877

    Li Shirong, Zhang Jinghua, Xu Hua. Linear transformation between the bending solutions of functionally graded and homogenous circular plates based on the first-order shear deformation theory, Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(5): 871-877 (in Chinese)
    [29]
    许新, 李世荣. 功能梯度材料微梁的热弹性阻尼研究, 力学学报, 2017, 49(2): 308-316

    Xu Xin, Li Shirong. Analysis of elastic damping of functionally graded micro- beams. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 308-316 (in Chinese)
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