EI、Scopus 收录
中文核心期刊

黏性流体环境下V型悬臂梁结构流固耦合振动特性研究

胡璐, 闫寒, 张文明, 彭志科, 孟光

胡璐, 闫寒, 张文明, 彭志科, 孟光. 黏性流体环境下V型悬臂梁结构流固耦合振动特性研究[J]. 力学学报, 2018, 50(3): 643-653. DOI: 10.6052/0459-1879-18-028
引用本文: 胡璐, 闫寒, 张文明, 彭志科, 孟光. 黏性流体环境下V型悬臂梁结构流固耦合振动特性研究[J]. 力学学报, 2018, 50(3): 643-653. DOI: 10.6052/0459-1879-18-028
Hu Lu, Yan Han, Zhang Wenming, Peng Zhike, Meng Guang. ANALYSIS OF FLEXURAL VIBRATION OF V-SHAPED BEAMS IMMERSED IN VISCOUS FLUIDS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 643-653. DOI: 10.6052/0459-1879-18-028
Citation: Hu Lu, Yan Han, Zhang Wenming, Peng Zhike, Meng Guang. ANALYSIS OF FLEXURAL VIBRATION OF V-SHAPED BEAMS IMMERSED IN VISCOUS FLUIDS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 643-653. DOI: 10.6052/0459-1879-18-028
胡璐, 闫寒, 张文明, 彭志科, 孟光. 黏性流体环境下V型悬臂梁结构流固耦合振动特性研究[J]. 力学学报, 2018, 50(3): 643-653. CSTR: 32045.14.0459-1879-18-028
引用本文: 胡璐, 闫寒, 张文明, 彭志科, 孟光. 黏性流体环境下V型悬臂梁结构流固耦合振动特性研究[J]. 力学学报, 2018, 50(3): 643-653. CSTR: 32045.14.0459-1879-18-028
Hu Lu, Yan Han, Zhang Wenming, Peng Zhike, Meng Guang. ANALYSIS OF FLEXURAL VIBRATION OF V-SHAPED BEAMS IMMERSED IN VISCOUS FLUIDS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 643-653. CSTR: 32045.14.0459-1879-18-028
Citation: Hu Lu, Yan Han, Zhang Wenming, Peng Zhike, Meng Guang. ANALYSIS OF FLEXURAL VIBRATION OF V-SHAPED BEAMS IMMERSED IN VISCOUS FLUIDS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 643-653. CSTR: 32045.14.0459-1879-18-028

黏性流体环境下V型悬臂梁结构流固耦合振动特性研究

基金项目: 国家杰出青年科学基金(11625208)和国家自然科学基金(11572190)资助项目.
详细信息
    作者简介:

    通讯作者: 张文明, 教授, 主要研究方向: 动力学与振动控制.E-mail: wenmingz@sjtu.edu.cn

    通讯作者:

    张文明

  • 中图分类号: O327;

ANALYSIS OF FLEXURAL VIBRATION OF V-SHAPED BEAMS IMMERSED IN VISCOUS FLUIDS

  • 摘要: V型悬臂梁结构在原子力显微镜、微纳机械传感器件中得到了广泛应用, 该结构通常在黏性流体环境下实现精密检测、传感与性能表征,同时也会使得结构的流固耦合振动特性更为复杂, 直接影响器件的动态性能.本文针对V型结构变截面、变刚度等复杂几何特征, 建立了黏性流体环境下V型悬臂梁结构的流固耦合动力学模型, 导出了基于截面孔宽比参数的梁结构的修正水动力函数, 确定了截面孔宽比和频率参数影响下V型悬臂梁结构的水动力函数;理论分析得到了黏性流体中V型梁结构的频率响应特性.同时, 设计了多种不同几何尺寸的V型梁结构, 并在水环境中开展了实验验证, 结果表明, 实验所得频率响应与理论分析结果吻合较好, 验证了V型梁结构水动力函数修正表达式及流固耦合动力学模型.此外, 基于该流固耦合动力学模型, 详细分析了不同流体黏度、V 型梁角度及尺寸变化对耦合系统振动特性的影响.
    Abstract: V-shaped beams have been widely used in atomic force microscope (AFM) and micro-nano mechanical sensing applications.The structure is usually used for sophisticated detection, sensing and performance characterization in viscous fluids, thus making it complex to study the vibration characteristics of the structure by considering the fluid-structure interaction between the complicated geometry and viscous fluids.It is of fundamental importance to investigate the vibration characteristics of V-shaped beams submerged in viscous fluids owing to the fact that the vibration characteristics will directly affect the dynamic properties of the applications.In this paper, an underwater vibration model is developed to depict the dynamic characteristics of V-shaped beams immersed in viscous fluids by taking into account the fact that the cross-section and bending stiffness of the V-shaped beam are variable along the beam axis.A complex hydrodynamic function in terms of the gap to width ratio and the frequency parameter is developed to describe the hydrodynamic loading where the complex hydrodynamic function is derived from the modified hydrodynamic function based on the gap to width ratio in beam's cross-section.Besides, the frequency response of V-shaped beams vibrating in viscous fluids is obtained theoretically.Moreover, the experimental verifications on flexural vibrations of several V-shaped beams with different geometrical sizes are carried out.It demonstrates that the experimental data is in good agreement with the theoretical results, thus validating the modified expression of hydrodynamic function and the underwater dynamic model.Besides, the effect of different fluid viscosities, angles of V-shaped beams and the scale of the geometry on the vibration characteristics of the coupling system is analyzed based on the proposed fluid-structure interaction model.
  • [1] Stark RW, Drobek T, Heckl WM. Thermomechanical noise of a free v-shaped cantilever for atomic-force microscopy. Ultramicroscopy, 2001, 86(1): 207-215
    [2] Hu QQ, Chen LQ. Bifurcation and chaos in atomic force microscope. Chaos Solitons & Fractals, 2007, 33(2): 711-715
    [3] Chen LQ, Lim CW, Hu QQ, et al.Asymptotic analysis of a vibrating cantilever with a nonlinear boundary. Science in China, 2009, 52(9): 1414-1422
    [4] 徐金明, 白以龙.原子力显微镜形貌测量偏差的机理分析及修正方法.力学学报, 2011, 43(1): 112-21
    [4] (Xu Jinming, Bai Yilong. Analysis of topography measurement error in atomic force microscope (AFM) and its revision method. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(1): 112-121 (in Chinese))
    [5] Sader JE, Borgani R, Gibson CT, et al.A virtual instrument to standardise the calibration of atomic force microscope cantilevers. Review of Scientific Instruments, 2016, 87(9): 846-856
    [6] 魏征, 孙岩, 王再冉等.轻敲模式下原子力显微镜的能量耗散.力学学报, 2017, 49(6): 1301-1311
    [6] (Wei Zheng, Sun Yan, Wang Zairan, et al.Energy dissipation in tapping mode atomic force microscopy. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(6): 1301-1311 (in Chinese))
    [7] Hosseini R, Hamedi M. An investigation into resonant frequency of trapezoidal V-shaped cantilever piezoelectric energy harvester. Microsystem Technologies, 2016, 22(5): 1127-1134
    [8] Litak G, Abadal G, Rysak A, et al.Complex dynamics of a bistable electrically charged microcantilever: Transition from single well to cross well oscillations. Chaos Solitons & Fractals, 2017, 99: 85-90
    [9] Lee GB, Kuo TY, Wu WY. A novel micromachined flow sensor using periodic flapping motion of a planar jet impinging on a V-shaped plate. Experimental Thermal and Fluid Science, 2002, 26(5): 435-444
    [10] Steiner H, Keplinger F, Schalko J, et al.Highly efficient passive thermal micro-actuator. Journal of Microelectromechanical Systems, 2015, 24(6): 1981-1988
    [11] Wu S, Liu X, Zhou X, et al.Quantification of cell viability and rapid screening anti-cancer drug utilizing nanomechanical fluctuation. Biosensors & Bioelectronics, 2016, 77: 164-173
    [12] Enikov ET, Kedar SS, Lazarov KV. Analytical model for analysis and design of V-shaped thermal microactuators. Journal of Microelectromechanical Systems, 2005, 14(4): 788-798
    [13] Cleveland JP, Manne S, Bocek D, et al.A nondestructive method for determining the spring constant of cantilevers for scanning force microscopy. Review of Scientific Instruments, 1993, 64(2): 403-405
    [14] Sader JE, Larson I, Mulvaney P, et al.Method for the calibration of atomic force microscope cantilevers. Review of Scientific Instruments, 1995, 66(7): 3789-3798
    [15] Sader JE, Sanelli J A, Adamson BD, et al.Spring constant calibration of atomic force microscope cantilevers of arbitrary shape. Review of Scientific Instruments, 2012, 83(10): 103705
    [16] Lee HL, Chang WJ, Yang YC. Flexural sensitivity of a V-shaped cantilever of an atomic force microscope. Materials Chemistry and Physics, 2005, 92(2): 438-442
    [17] Lee HL, Chang WJ. Sensitivity of V-shaped atomic force microscope cantilevers based on a modified couple stress theory. Microelectronic Engineering, 2011, 88(11): 3214-3218
    [18] Lee HL, Chang WJ. Sensitivity analysis of rectangular atomic force microscope cantilevers immersed in liquids based on the modified couple stress theory. Micron, 2016, 80: 1-5
    [19] Korayem AH, Hoshiar AK, Badrlou S, et al.A comprehensive model for stiffness coefficients in V-shaped cantilevers. International Journal of Nanoscience and Nanotechnology, 2016, 12(1): 27-36
    [20] Korayem AH, Kianfar A, Korayem MH. Modeling and simulating of V-shaped piezoelectric micro-cantilevers using MCS theory considering the various surface geometries. Physica E : Low-dimensional Systems and Nanostructures, 2016, 84: 268-279
    [21] Korayem MH, Nahavandi A. Analyzing the effect of the forces exerted on cantilever probe tip of atomic force microscope with tapering-shaped geometry and double piezoelectric extended layers in the air and liquid environments. Journal of Sound & Vibration, 2016, 386: 251-264
    [22] Berthold T, Benstetter G, Frammelsberger W, et al.Numerical study of hydrodynamic forces for AFM operations in liquid. Scanning, 2017, 2017: 1-12
    [23] Dufrêne YF, Ando T, Garcia R, et al.Imaging modes of atomic force microscopy for application in molecular and cell biology. Nature Nanotechnology, 2017, 12(4): 295-307
    [24] Wu S, Liu H, Cheng T, et al.Highly sensitive nanomechanical assay for the stress transmission of carbon chain. Sensors & Actuators B Chemical, 2013, 186(9): 353-359
    [25] Wu S, Liu H, Liang XM, et al.Highly sensitive nanomechanical immunosensor using half antibody fragments. Analytical Chemistry, 2014, 86(9): 4271-4277
    [26] Phan CN, Aureli M, Porfiri M. Finite amplitude vibrations of cantilevers of rectangular cross sections in viscous fluids. Journal of Fluids and Structures, 2013, 40(7): 52-69
    [27] 吴应湘, 林黎明, 钟兴福.带有新型涡激振动抑制罩的圆柱体的水动力特性.力学学报, 2016, 48(2): 307-317
    [27] (Wu Yingxiang, Lin Liming, Zhong Xingfu. Investigation in hydrodynamics of a circular cylinder with the new suppressing shroud for vortex-induced vibration. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(2): 307-317 (in Chinese))
    [28] 牛文栋, 王延辉, 杨艳鹏等.混合驱动水下滑翔机水动力参数辨识.力学学报, 2016, 48(4): 813-822
    [28] (Niu Wendong, Wang Yanhui, Yang Yanpeng, et al.Hydrodynamic parameter identification of hybrid-driven underwater glider. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(4): 813-822 (in Chinese))
    [29] Maali A, Hurth C, Boisgard R, et al.Hydrodynamics of oscillating atomic force microscopy cantilevers in viscous fluids. Journal of Applied Physics, 2005, 97(7): 074907
    [30] 白玉川, 冀自青, 徐海珏.摆动河槽水动力稳定性特征分析.力学学报, 2017, 49(2): 274-288
    [30] (Bai Yuchuan, Ji Ziqing, Xu Haijue. Hydrodynamic instability characteristics of laminar flow in a meandering channel with moving boundary. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 274-288 (in Chinese))
    [31] Trivedi C. A review on fluid structure interaction in hydraulic turbines: A focus on hydrodynamic damping. Engineering Failure Analysis, 2017, 77: 1-22
    [32] Tuck E. Calculation of unsteady flows due to small motions of cylinders in a viscous fluid. Journal of Engineering Mathematics, 1969, 3(1): 29-44
    [33] Sader JE. Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope. Journal of Applied Physics, 1998, 84(1): 64-76
    [34] Aureli M, Porfiri M. Low frequency and large amplitude oscillations of cantilevers in viscous fluids. Applied Physics Letters, 2010, 96(16): 164102
    [35] Aureli M, Basaran M, Porfiri M. Nonlinear finite amplitude vibrations of sharp-edged beams in viscous fluids. Journal of Sound and Vibration, 2012, 331(7): 1624-1654
    [36] Falcucci G, Aureli M, Ubertini S, et al.Transverse harmonic oscillations of laminae in viscous fluids: a lattice Boltzmann study. Philosophical Transactions of the Royal Society of London A : Mathematical, Physical and Engineering Sciences, 2011, 369(1945): 2456-2466
  • 期刊类型引用(13)

    1. 杨浙栋,娄军强,陈特欢,崔玉国,魏燕定,李国平. 水下大振幅压电纤维致动柔性结构的非线性流体动力特性及实验. 振动工程学报. 2024(03): 365-373 . 百度学术
    2. 顾霆,娄军强,杨依领,陈特欢,陈海荣,魏燕定. 局部粘贴压电宏纤维致动器的水下弹性结构机-电-液耦合振动特性. 振动工程学报. 2022(02): 387-396 . 百度学术
    3. 谷森,宋亚勤,郑起. 光热激励下功能梯度梁在流体中的振动. 应用力学学报. 2021(02): 589-596 . 百度学术
    4. 黄珏皓,娄军强,杨依领,陈特欢,陈海荣,魏燕定. 黏性流体环境中压电宏纤维致动柔性结构的流固耦合振动特性及试验. 机械工程学报. 2021(22): 376-385 . 百度学术
    5. 刘星光,唐有绮,周远. 三种典型轴向运动结构的振动特性对比. 力学学报. 2020(02): 522-532 . 本站查看
    6. 魏征,郑骁挺,刘晶,魏瑞华. 轻敲模式下AFM动力学模型及能量耗散机理研究. 力学学报. 2020(04): 1106-1119 . 本站查看
    7. 张登博,陈立群. 计及非齐次边界条件的面内变速运动黏弹性板的稳态响应. 振动与冲击. 2020(13): 156-162 . 百度学术
    8. 易浩然,周坤,代胡亮,王琳,倪樵. 含集中质量悬臂输流管的稳定性与模态演化特性研究. 力学学报. 2020(06): 1800-1810 . 本站查看
    9. 张登博,唐有绮,陈立群. 非齐次边界条件下轴向运动梁的非线性振动. 力学学报. 2019(01): 218-227 . 本站查看
    10. 魏进,曹登庆,于涛. 复合柔性结构全局模态函数提取与状态空间模型构建. 力学学报. 2019(02): 341-353 . 本站查看
    11. 陈玲,唐有绮. 时变张力作用下轴向运动梁的分岔与混沌. 力学学报. 2019(04): 1180-1188 . 本站查看
    12. 陈倩,张汉哲,吴钦,傅晓英,张晶,王国玉. 复合材料水翼水动力与结构强度特性数值研究. 力学学报. 2019(05): 1350-1362 . 本站查看
    13. 周远,唐有绮,刘星光. 黏弹性阻尼作用下轴向运动Timoshenko梁振动特性的研究. 力学学报. 2019(06): 1897-1904 . 本站查看

    其他类型引用(3)

计量
  • 文章访问数:  2571
  • HTML全文浏览量:  234
  • PDF下载量:  311
  • 被引次数: 16
出版历程
  • 收稿日期:  2018-01-28
  • 刊出日期:  2018-05-17

目录

    /

    返回文章
    返回