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.
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