Scale effect on the natural frequency and vibration mode of a cantilever micro beam

被引：0
|
作者：
Xie X. [1 ]
Liu Z. [1 ,2 ,3 ]
Du Q. [2 ]
机构：
[1] College of Aerospace Engineering, Chongqing University, Chongqing
[2] State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chonqing University, Chongqing
[3] Chongqing Key Laboratory of Heterogeneous Material Mechanics, Chongqing University, Chongqing
来源：
Zhendong yu Chongji/Journal of Vibration and Shock | 2018年 / 37卷 / 12期
关键词：
Cantilever micro-beam; Generalized elasticity; Natural frequency; Scale effect; Vibration mode;
D O I：
10.13465/j.cnki.jvs.2018.12.028
中图分类号：
学科分类号：
摘要：
The first frequency of a cantilever micro-beam predicted by classical elasticity is far lower than measured by experiments. Generalized elasticity is especially applicable to structure dynamics analysis with scale effect, where both the rotational deformation and couple stress is taken into account. The measurement of deformation was improved. Finite element dynamic equations of generalized elasticity were established through the principle of virtue work, and a numerical analysis method was used to study the natural frequency and vibration mode of the cantilever micro-beam. The results show that the existent of scale effect of its natural frequency is related to its corresponding mode. The corresponding natural frequencies of bending and torsional modes have significant increment compared to classical elasticity. The torsional mode is taken into consideration. However, little change of natural frequency of tensile mode can be observed because deformation is not involved. © 2018, Editorial Office of Journal of Vibration and Shock. All right reserved.
引用
收藏
页码：187 / 192
页数：5
相关论文
共 23 条
  • [11] Mindlin R.D., Tiersten H.F., Effects of couple-stresses in linear elasticity, Archive for Rational Mechanics and Analysis, 11, 1, pp. 415-448, (1962)
  • [12] Fleek N.A., Hutehinson J.W., A phenomenological theory for strain gradient effects in plasticity, Journal of the Mechanics and Physics of Solids, 41, 12, pp. 1825-1857, (1993)
  • [13] Fleek N.A., Hutehinson J.W., Strain gradient plasticity, Advances in Applied Mechanics, 33, pp. 295-361, (1997)
  • [14] Huang K., Qiu X., Jiang H., Recent advances in strain gradient plasticity-I-couple stress theory and SG theory, Journal of Mechanical Strength, 21, 2, pp. 81-87, (1999)
  • [15] Chen S., Wang Z., Advances in strain gradient theory, Advances in Mechanics, 33, 2, pp. 207-216, (2003)
  • [16] Yang F., Chong A.C.M., Lam D.C.C., Et al., Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39, 10, pp. 2731-2743, (2002)
  • [17] Liu Z.F., Fu Z., Scale effects of the stress symmetry in generalized elasticity, International Journal of Aerospace and Lightweight Structures, 2, 4, pp. 509-521, (2012)
  • [18] Yan S., Liu Z., A modified couple stress linear elasticity and finite element method for generalized elastic bodies, Chinese Journal of Solid Mechanics, 33, 3, pp. 279-287, (2012)
  • [19] Liu Z., Yan S., Feng X., Dynamic analysis of elastic body with rotation gradient effects in centrifugal field, Journal of Vibration and Shock, 31, 16, pp. 164-168, (2012)
  • [20] Liu Z.F., Sun X.Y., Guo Y., Et al., On elastic stress waves in an impacted plate, International Journal of Applied Mechanics, 6, 4, (2014)
123