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铁木辛柯纳米梁简谐强迫振动的格林函数解 预览

Green's Function for the Harmonic Forced Vibration of Timoshenko Nanobeam
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摘要 通过基于Gurtin-Murdoch模型的纳米梁的控制方程,研究了铁木辛柯纳米梁的简谐强迫振动问题。在理论分析过程中引入了格林函数法,并利用变量分离法和拉普拉斯变换得到了用简单函数表示的具有封闭形式的解析解,包括简谐强迫振动控制方程的通解,以及简支梁、固支梁和悬臂梁三种典型情况的特解。利用数值算例,检验了解的有效性,考察了表面效应对铁木辛柯纳米梁简谐强迫振动行为的影响规律。结果表明:(1)表面效应会增大或减小纳米梁的刚度,从而导致梁的固有频率发生变化;(2)表面效应对纳米梁的影响程度与梁的边界条件有关且随着梁的尺寸的增大而减小;(3)表面效应对简支梁和固支梁影响较小,而对悬臂梁影响较大;(4)表面效应可以分别从梁的挠度和截面转角两个方面进行衡量,且可以得到基本一致的结果。 On the basis of the governing equations of nanobeam, which are constructed with Gurtin-Murdoch model, the forced harmonic vibration of Timoshenko nanobeam is investigated. In the analysis, Green's function method is adopted, and the closed-form solutions are derived with separation of variables and Laplace transformation, including general solution and solutions for simply supported beam, clamped beam and cantilever beam. With numerical results, the validity of the solutions is checked, and the influence of surface effect on the forced harmonic vibration of Timoshenko nanobeam is studied. It is shown that surface effect may enlarge or reduce the stiffness of nanobeam, resulting in the change of natural frequency of nanobeam. The influence of surface effect is related with boundary conditions of beam, and decreases as the size of beam increases. Surface effect has much stronger influence on cantilever beam than on simply The influence of surface effect on nanobeam can be measured by transverse deflection or cross-sectional rotation of nanobeam, and the similar results can be obtained by the two ways.
作者 陈宵寒 吴太红 李翔宇 CHEN Xiaohan, WU Taihong, LI Xiangyu (Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China)
出处 《四川理工学院学报:自然科学版》 CAS 2018年第4期20-28,共9页 Journal of Sichuan University of Science & Engineering:Natural Science Editton
基金 国家自然科学基金项目(11672250)
关键词 纳米梁 表面效应 简谐强迫振动 铁木辛柯梁 格林函数 nanobeam surface effect harmonic forced vibration Timoshenko beam Green's function
作者简介 陈宵寒(1990-),女,广西南宁人,硕士生,主要从事纳米梁的振动力学方面的研究,(E-mail)blizzardisbig@163.com;;李翔宇(1979-),男,四川巴中人,教授,博士生导师,主要从事多场耦合力学、纳米力学等方面的研究,(E-mail)zjuparis6@hotmail.com
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