微尺度悬臂管的空间弯曲振动—非线性运动方程及尺度效应

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Abstract Flexural vibration of a micro-scale cantilever fluid-conveying pipe with annulus cross section can occur in each direction in three-dimensional space. According to the Euler-Bernoulli beam theory, the displace components of the pipe and the relevant geometrical relations can be analyzed. The geometric nonlinearity, arising from the Lagrange strain tensor, is taken into account. Based on a modified couple stress theory, the strain energy in the pipe is calculated. The nonlinear dynamical equations of three-dimensional flexural vibration for a micro-scale cantilever fluid-conveying pipe are derived by using the Hamilton principle. The effect of the dimensionless material length scale parameter on the dynamics of the system is investigated. It is found that the scale effect increase the critical flow velocity of the pipe and that the larger the dimensionless material length scale parameter is, the wider (narrower) the region of stable planar (spatial) periodic motion is.

Key words： Micro-scale cantilever pipe Three-dimensional flexural vibration Couple stress theory Lagrange strain tensor Periodic motion

Received: 18 October 2016 Published: 15 November 2017

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	Articles by authors
	Guo Yong1
	Xie Jian-hua1

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Guo Yong1,Xie Jian-hua1. Three-dimensional flexural vibration of a micro-scale cantilever pipe—Nonlinear equations of motion and scale effect[J]. JOURNAL OF VIBRATION AND SHOCK, 2017, 36(22): 65-72.

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http://jvs.sjtu.edu.cn/EN/ OR http://jvs.sjtu.edu.cn/EN/Y2017/V36/I22/65

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