Volume 43 Issue 3
Mar.  2024
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YANG Yongqiang, YANG Ping, ZHANG Xule. Instability Analysis of Rotating Convex and Concave Circular Nanoplate by Considering Surface Residual Stress[J]. Mechanical Science and Technology for Aerospace Engineering, 2024, 43(3): 409-415. doi: 10.13433/j.cnki.1003-8728.20220266
Citation: YANG Yongqiang, YANG Ping, ZHANG Xule. Instability Analysis of Rotating Convex and Concave Circular Nanoplate by Considering Surface Residual Stress[J]. Mechanical Science and Technology for Aerospace Engineering, 2024, 43(3): 409-415. doi: 10.13433/j.cnki.1003-8728.20220266

Instability Analysis of Rotating Convex and Concave Circular Nanoplate by Considering Surface Residual Stress

doi: 10.13433/j.cnki.1003-8728.20220266
  • Received Date: 2022-02-17
  • Publish Date: 2024-03-25
  • Based on the theory of the surface residual stress of nanomaterials and small deflection of elastic plate, the transverse vibration differential equation of rotating convex-concave circular nanoplate was established. The variation of dimensionless complex frequency of convex-concave circular nanoplate with dimensionless angular speed and surface residual stress under different conditions was obtained by using the differential quadrature method. The results show that the first-order divergence instability of rotating convex-concave circular nanoplate was observed in both clamped and simply supported conditions. When other parameters are constant, the critical instability angular speed of the clamped concave circular nanoplate is smaller than that of the convex circular nanoplate, and the critical instability angular speed of the simply supported concave circular nanoplate is greater than that of the convex circular nanoplate. The critical instability angular speed increases with the increasing of surface residual stress, and the critical surface residual stress increases with the increasing of dimensionless angular speed.
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  • [1]
    FAN K Q, LIU J, CAI M L, et al. Exploiting ultralow-frequency energy via vibration-to-rotation conversion of a rope-spun rotor[J]. Energy Conversion and Management, 2020, 225: 113433. doi: 10.1016/j.enconman.2020.113433
    [2]
    张大鹏, 雷勇军, 段静波. 基于非局部理论的黏弹性基体上压电纳米板热-机电振动特性研究[J]. 振动与冲击, 2020, 39(20): 32-41.

    ZHANG D P, LEI Y J, DUAN J B. Thermo-electro-mechanical vibration responses of piezoelectric nanoplates embedded in viscoelastic medium via nonlocal elasticity theory[J]. Journal of Vibration and Shock, 2020, 39(20): 32-41. (in Chinese)
    [3]
    SAHMANI A S, BAHRAMI M, ANSAR R.Surface effects on the free vibration behavior of post buckled circular higher-order shear deformable nanoplates including geometrical nonlinearity[J]. Acta Astronautica, 2014, 105: 417-427.
    [4]
    王平远, 李成, 姚林泉. 基于非局部应变梯度理论功能梯度纳米板的弯曲和屈曲研究[J]. 应用数学和力学, 2021, 42(1): 15-26.

    WANG P Y, LI C, YAO L Q. Bending and buckling of functionally graded nanoplates based on the nonlocal strain gradient theory[J]. Applied Mathematics and Mechanics, 2021, 42(1): 15-26. (in Chinese)
    [5]
    滕兆春, 刘露, 衡亚洲. 弹性地基上受压矩形纳米板的自由振动与屈曲特性[J]. 振动与冲击, 2019, 38(16): 208-216. doi: 10.13465/j.cnki.jvs.2019.16.030

    TENG Z C, LIU L, HENG Y Z. Free vibration and buckling characteristics of compressed rectangular nanoplates resting on elastic foundation[J]. Journal of Vibration and Shock, 2019, 38(16): 208-216. (in Chinese) doi: 10.13465/j.cnki.jvs.2019.16.030
    [6]
    WANG W J, LI P, JIN F, et al. Vibration analysis of piezoelectric ceramic circular nanoplates considering surface and nonlocal effects[J]. Composite Structures, 2016, 140: 758-775. doi: 10.1016/j.compstruct.2016.01.035
    [7]
    DUAN W H, WANG C M. Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on nonlocal plate theory[J]. Nanotechnology, 2007, 18(38): 385704. doi: 10.1088/0957-4484/18/38/385704
    [8]
    BEDROUD M, HOSSEINI-HASHEMI S, NAZEMNEZHAD R. Buckling of circular/annular Mindlin nanoplates via nonlocal elasticity[J]. Acta Mechanica, 2013, 224(11): 2663-2676. doi: 10.1007/s00707-013-0891-5
    [9]
    ANJOMSHOA A, TAHANI M. Vibration analysis of orthotropic circular and elliptical nano-plates embedded in elastic medium based on nonlocal Mindlin plate theory and using Galerkin method[J]. Journal of Mechanical Science and Technology, 2016, 30(6): 2463-2474. doi: 10.1007/s12206-016-0506-x
    [10]
    DASTJERDI S, JABBARZADEH M. Non-linear bending analysis of multi-layer orthotropic annular/circular graphene sheets embedded in elastic matrix in thermal environment based on non-local elasticity theory[J]. Applied Mathematical Modelling, 2017, 41: 83-101. doi: 10.1016/j.apm.2016.08.022
    [11]
    赵德敏, 龚宇龙. 考虑表面效应的纳米圆形薄板振动[J]. 中国石油大学学报(自然科学版), 2017, 41(5): 153-158.

    ZHAO D M, GONG Y L. Surface effects on vibration of circular thin nano-plate[J]. Journal of China University of Petroleum, 2017, 41(5): 153-158. (in Chinese)
    [12]
    ASSADI A, FARSHI B. Vibration characteristics of circular nanoplates[J]. Journal of Applied Physics, 2010, 108(7): 074312. doi: 10.1063/1.3486514
    [13]
    YAN Z. Size-dependent bending and vibration behaviors of piezoelectric circular nanoplates[J]. Smart Materials and Structures, 2016, 25(3): 035017. doi: 10.1088/0964-1726/25/3/035017
    [14]
    LIU C, RAJAPAKSE R K N D. A size-dependent continuum model for nanoscale circular plates[J]. IEEE Transactions on Nanotechnology, 2013, 12(1): 13-20. doi: 10.1109/TNANO.2012.2224880
    [15]
    MALEKZADEH P, FARAJPOUR A. Axisymmetric free and forced vibrations of initially stressed circular nanoplates embedded in an elastic medium[J]. Acta Mechanica, 2012, 223(11): 2311-2330. doi: 10.1007/s00707-012-0706-0
    [16]
    JANDAGHIAN A A, JAFARI A A, RAHMANI O. Vibrational response of functionally graded circular plate integrated with piezoelectric layers: an exact solution[J]. Engineering Solid Mechanics, 2014, 2(2): 119-130. doi: 10.5267/j.esm.2014.1.004
    [17]
    MAHINZARE M, ALIPOUR M J, SADATSAKKAK S A, et al. A nonlocal strain gradient theory for dynamic modeling of a rotary thermo piezo electrically actuated nano FG circular plate[J]. Mechanical Systems and Signal Processing, 2019, 115: 323-337. doi: 10.1016/j.ymssp.2018.05.043
    [18]
    ZAREI M, FAGHANI G R, GHALAMI M, et al. Buckling and vibration analysis of tapered circular nano plate[J]. Journal of Applied and Computational Mechanics, 2018, 4(1): 40-54.
    [19]
    王忠民, 王昭, 张荣, 等. 基于微分求积法分析旋转圆板的横向振动[J]. 振动与冲击, 2014, 33(1): 125-129. doi: 10.3969/j.issn.1000-3835.2014.01.021

    WANG Z M, WANG Z, ZHANG R, et al. Transverse vibration analysis of spinning circular plate based on differential quadrature method[J]. Journal of Vibration and Shock, 2014, 33(1): 125-129. (in Chinese) doi: 10.3969/j.issn.1000-3835.2014.01.021
    [20]
    YANG Y Q, WANG Z M, WANG Y Q. Thermoelastic coupling vibration and stability analysis of rotating circular plate in friction clutch[J]. Journal of Low Frequency Noise, Vibration and Active Control, 2019, 38(2): 558-573. doi: 10.1177/1461348418817465
    [21]
    倪振华. 振动力学[M]. 西安: 西安交通大学出版社, 1989.

    NI Z H. Vibration mechanics[M]. Xi'an: Xi'an Jiaotong University Press, 1989. (in Chinese)
    [22]
    SAHMANI S, BAHRAMI M, ANSARI R. Surface effects on the free vibration behavior of postbuckled circular higher-order shear deformable nanoplates including geometrical nonlinearity[J]. Acta Astronautica, 2014, 105(2): 417-427. doi: 10.1016/j.actaastro.2014.10.005
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