Scale Effects on Natural Frequencies and Vibration Modes of Micro Cantilever Beams Based on Generalized Elasticity

SHEN Anming; CHEN Rui; DU Qiumei

doi:10.21656/1000-0887.380301

Volume 39 Issue 9

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SHEN Anming, CHEN Rui, DU Qiumei. Scale Effects on Natural Frequencies and Vibration Modes of Micro Cantilever Beams Based on Generalized Elasticity[J]. Applied Mathematics and Mechanics, 2018, 39(9): 999-1008. doi: 10.21656/1000-0887.380301

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Scale Effects on Natural Frequencies and Vibration Modes of Micro Cantilever Beams Based on Generalized Elasticity

doi: 10.21656/1000-0887.380301

¹College of Aerospace Engineering, Chongqing University, Chongqing 400044, P.R.China;²State Key Laboratory of Mechanical Transmissions(Chongqing University), Chongqing 400044, P.R.China

Funds: The National Natural Science Foundation of China(51505044)

Received Date: 2017-12-05
Rev Recd Date: 2018-01-09
Publish Date: 2018-09-15

Abstract

Abstract

Classical elasticity has been widely applied in engineering technologies. But the length scale parameter is not included in the classical elasticity, which leads to the scale effects on mechanical characteristics and no longer satisfies the micro scale. Generalized elasticity is especially applicable to microstructures with scale effects, where both the rotational deformation and the couple stress are taken into account, and the measurement of deformation is improved. By means of Hamilton’s variation principle and generalized elasticity, the vibration differential equations for the micro cantilever beam in different motion states were derived. Then natural frequencies and vibration modes of the micro cantilever beam were analyzed. The results show that, with the decreasing of the micro beam height, the scale effect on the natural frequency is closely related to the mode. The corresponding natural frequencies of torsional and bending modes have significant increment and scale effect compared with those according to the classical elasticity, for the rotational deformation is considered. However, little variation of the natural frequency of the tensile mode is found because there is no rotational deformation involved.
- scale effect,
- generalized elasticity,
- Hamilton’s principle,
- natural frequency,
- mode,
- micro cantilever beam

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References(23)

References

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