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双功能梯度纳米梁系统振动分析的辛方法

周震寰 李月杰 范俊海 隋国浩 张俊霖 徐新生

周震寰, 李月杰, 范俊海, 隋国浩, 张俊霖, 徐新生. 双功能梯度纳米梁系统振动分析的辛方法[J]. 应用数学和力学, 2018, 39(10): 1159-1171. doi: 10.21656/1000-0887.390130
引用本文: 周震寰, 李月杰, 范俊海, 隋国浩, 张俊霖, 徐新生. 双功能梯度纳米梁系统振动分析的辛方法[J]. 应用数学和力学, 2018, 39(10): 1159-1171. doi: 10.21656/1000-0887.390130
ZHOU Zhenhuan, LI Yuejie, FAN Junhai, SUI Guohao, ZHANG Junlin, XU Xinsheng. A Symplectic Approach for Free Vibration of Functionally Graded Double-Nanobeam Systems Embedded in Viscoelastic Medium[J]. Applied Mathematics and Mechanics, 2018, 39(10): 1159-1171. doi: 10.21656/1000-0887.390130
Citation: ZHOU Zhenhuan, LI Yuejie, FAN Junhai, SUI Guohao, ZHANG Junlin, XU Xinsheng. A Symplectic Approach for Free Vibration of Functionally Graded Double-Nanobeam Systems Embedded in Viscoelastic Medium[J]. Applied Mathematics and Mechanics, 2018, 39(10): 1159-1171. doi: 10.21656/1000-0887.390130

双功能梯度纳米梁系统振动分析的辛方法

doi: 10.21656/1000-0887.390130
基金项目: 国家自然科学基金(11672054);国家重点基础研究发展计划(973计划)(2014CB046803);国家重点研发计划(2016YFB0201600);辽宁省自然科学基金(20470540186);中央高校基本科研业务费(DUT17LK57)
详细信息
    作者简介:

    周震寰(1983—),男,副教授,博士(通讯作者. E-mail: zhouzh@dlut.edu.cn).

  • 中图分类号: O326

A Symplectic Approach for Free Vibration of Functionally Graded Double-Nanobeam Systems Embedded in Viscoelastic Medium

Funds: The National Natural Science Foundation of China(11672054); The National Basic Research Program of China(973 Program)(2014CB046803); The National Key R&D Program of China(2016YFB0201600)
  • 摘要: 在辛力学与非局部Timoshenko(铁木辛柯)梁理论的基础上,针对黏弹性介质中的双功能梯度纳米梁系统的自由振动问题,提出了一种全新的解析求解方法.在Hamilton(哈密顿)体系下,位移与广义剪力、转角与广义弯矩互为对偶变量。以对偶变量为基本未知量,Lagrange(拉格朗日)体系下的高阶偏微分控制方程简化为一系列常微分方程。该纳米梁系统的振动问题归结为辛空间下的本征问题,解析频率方程和振动模态可以通过辛本征解和边界条件直接获得.数值结果验证了该方法的正确性与有效性,并针对纳米梁系统的小尺度效应、纳米梁间的相互作用以及黏弹性地基的影响进行了系统的参数分析.
  • [1] EICHENFIELD M, CAMACHO R, CHAN J, et al. A picogram and nanometre-scale photonic-crystal optomechanical cavity[J]. Nature,2009,459(7246): 550-555.
    [2] LIN Q, ROSENBERG J, CHANG D, et al. Coherent mixing of mechanical excitations in nano-optomechanical structures[J]. Nature Photonics,2010,4(4): 236-242
    [3] FU Y, DU H, HUANG W, et al. TiNi-based thin films in MEMS applications: a review[J]. Sensors and Actuators A: Physical,2004,112(2): 395-408.
    [4] KAHROBAIYAN M H, ASGHARI M, RAHAEIFARD M, et al. Investigation of the size-dependent dynamic characteristics of atomic force microscope microcantilevers based on the modified couple stress theory[J]. International Journal of Engineering Science,2010,48(12): 1985-1994.
    [5] ERINGEN A C. On differential-equations of nonlocal elasticity and solutions of screw dislocation and surface-waves[J]. Journal of Applied Physics,1983,54(9): 4703-4710.
    [6] ERINGEN A C. Nonlocal Continuum Field Theories [M]. New York: Springer, 2002.
    [7] RAFII-TABAR H, GHAVANLOO E, FAZELZADEH S A. Nonlocal continuum-based modeling of mechanical characteristics of nanoscopic structures[J]. Physics Reports,2016,638: 1-97.
    [8] 林 C W. 基于非局部弹性应力场理论的纳米尺度效应研究: 纳米梁的平衡条件、控制方程以及静态挠度[J]. 应用数学和力学,2010,31(1): 35-50.(LIM C W. On the truth of nanoscale for nanobeams based on nonlocal elastic stress field theory: equilibrium, governing equation and static deflection[J]. Applied Mathematics and Mechanics,2010,31(1): 35-50. (in Chinese))
    [9] 尹春松, 杨洋. 考虑非局部剪切效应的碳纳米管弯曲特性研究[J]. 应用数学和力学, 2015,36(6): 600-606.(YIN Chunsong, YANG Yang. Shear deformable bending of carbon nanotubes based on a new analytical nonlocal Timoshenko beam model[J]. Applied Mathematics and Mechanics,2015,36(6): 600-606.(in Chinese))
    [10] ELTAHER M A, EMAM S A, MAHMOUD F F. Free vibration analysis of functionally graded size-dependent nanobeams[J]. Applied Mathematics and Computation,2012,218(14): 7406-7420.
    [11] LI L, LI X, HU Y. Free vibration analysis of nonlocal strain gradient beams made of functionally graded material[J]. International Journal of Engineering Science,2016,102: 77-92.
    [12] RAHMANI O, PEDRAM O. Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory[J]. International Journal of Engineering Science,2014,77(7): 55-70.
    [13] ELTAHER M A, ALSHORBAGY A E, MAHMOUD F F. Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams[J]. Composite Structures,2013,99(5): 193-201.
    [14] NIKNAM H, AGHDAM M M. A semi analytical approach for large amplitude free vibration and buckling of nonlocal FG beams resting on elastic foundation[J]. Composite Structures,2015,119: 452-462.
    [15] EL-BORGI S, FERNANDES R, REDDY J N. Non-local free and forced vibrations of graded nanobeams resting on a non-linear elastic foundation[J]. International Journal of Non-Linear Mechanics,2015,77: 348-363.
    [16] NAZEMNEZHAD R, HOSSEINI-HASHEMI S. Nonlocal nonlinear free vibration of functionally graded nanobeams[J]. Composite Structures,2014,110: 192-199.
    [17] ELTAHER M A, KHAIRY A, SADOUN A M, et al. Static and buckling analysis of functionally graded Timoshenko nanobeams[J]. Applied Mathematics and Computation,2014,229: 283-295.
    [18] LI L, HU Y. Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material[J]. International Journal of Engineering Science,2016,107: 77-97.
    [19] KE L L, WANG Y S, YANG J, et al. Nonlinear free vibration of size-dependent functionally graded microbeams[J]. International Journal of Engineering Science,2012,50(1): 256-267.
    [20] 杨晓东, 林志华. 利用多尺度方法分析基于非局部效应纳米梁的非线性振动[J]. 中国科学: 技术科学, 2010,40(2): 152-156.(YANG Xiaodong, LIN Zhihua. The nonlinear vibration of nanoscale beam based on nonlocal effect by multiscale method[J]. Chinese Science: Technical Science,2010,40(2): 152-156. (in Chinese))
    [21] YAO W A, ZHONG W X, LIM C W. Symplectic Elasticity [M]. Hackensack: World Scientific Pubinshing Company, 2009.
    [22] LIM C W, XU X S. Symplectic elasticity: theory and applications[J]. Applied Mechanics Reviews,2011,63(5): 050802.
    [23] ZHOU Z, RONG D, YANG C, et al. Rigorous vibration analysis of double-layered orthotropic nanoplate system[J]. International Journal of Mechanical Sciences,2017,123: 84-93.
    [24] AYDOGDU M. A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration[J].Physica E: Low-Dimensional Systems and Nanostructures,2009,41(9): 1651-1655.
    [25] ARASH B, WANG Q. A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes[J]. Computational Materials Science,2012,51(1): 303-313.
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出版历程
  • 收稿日期:  2018-04-23
  • 修回日期:  2018-05-18
  • 刊出日期:  2018-10-01

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