力学与实践 ›› 2018, Vol. 40 ›› Issue (4): 380-386.DOI: 10.6052/1000-0879-18-022

• 应用研究 • 上一篇    下一篇

纳米板振动特性的两类尺度效应研究1)

钱晨飞, 沈火明2), 张波, 刘娟, 张英蓉   

  1. 西南交通大学力学与工程学院,应用力学与结构安全四川省重点实验室,成都 610031
  • 收稿日期:2018-01-11 出版日期:2018-08-08 发布日期:2018-09-11
  • 作者简介:2) 沈火明,教授。 E-mail: hmshen@126.com
  • 基金资助:
    1) 国家自然科学青年基金资助项目(11602204)

TWO KINDS OF SCALE EFFECTS OF VIBRATION CHARACTERISTICS OF NANO-PLATE1)

QIAN Chenfei, SHEN Huoming2), ZHANG Bo, LIU Juan, ZHANG Yingrong   

  1. College of Mechanics and Engineering,Southwest Jiaotong University,Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province,Chengdu 610036,China
  • Received:2018-01-11 Online:2018-08-08 Published:2018-09-11

摘要: 利用非局部应变梯度理论研究了纳米板横向自由振动特性。通过迭代法获得非局部应力的渐近表达式,利用哈密顿变分原理推导了纳米板的振动控制方程。针对四边简支边界条件,运用双重三角级数法给出了板固有频率的表达式,然后研究了非局部参数、材料特征参数、几何尺寸对纳米板自振频率的影响。数值结果表明:非局部效应会弱化纳米板的等效刚度,因而使板的固有频率降低,应变梯度效应则与之相反,两类效应仅在纳米尺度下对自振频率有显著影响;板几何尺寸的改变也会对其振动频率产生重要影响。

关键词: 非局部应变梯度理论|纳米板|自振频率|小尺度参数

Abstract: In this paper, the lateral free vibration of nano plates is studied based on the nonlocal strain gradient theory. The expression of the nonlocal stress is obtained via the iterative method and the vibration governing equation of the nano-plate is derived based on the Hamilton variational principle. Under the simply supported boundary conditions, the expression of the natural frequency of the plate is obtained by using the double triangle series method. The influences of the nonlocal parameters, the material characteristic parameters and the geometrical dimensions on the natural frequencies of the nano plate are studied. Numerical results show that the nonlocal effect weakens the equivalent stiffness of the nano-plate and thus the natural frequency of the plate is reduced. The effect on the material characteristic parameter is just the opposite. The two kinds of effects have a significant bearing on the frequency of the vibration only in the nanoscale. The change of the geometrical size also has an important effect on the vibration frequency.

Key words: nonlocal strain gradient theory|nano-plate|natural frequency of vibration|small scale parameters

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