XU Jian, YANG Qian-biao. Flow-Induced Internal Resonances and Mode Exchange in Horizontal Cantilevered Pipe Conveying Fluid(Ⅰ)[J]. Applied Mathematics and Mechanics, 2006, 27(7): 819-824.
 Citation: XU Jian, YANG Qian-biao. Flow-Induced Internal Resonances and Mode Exchange in Horizontal Cantilevered Pipe Conveying Fluid(Ⅰ)[J]. Applied Mathematics and Mechanics, 2006, 27(7): 819-824.

# Flow-Induced Internal Resonances and Mode Exchange in Horizontal Cantilevered Pipe Conveying Fluid(Ⅰ)

• Rev Recd Date: 2006-03-01
• Publish Date: 2006-07-15
• The Newtonian method is employed to obtain nonlinear mathematical model of motion of a horizontally cantilevered and inflexible pipe conveying fluid. The order magnitudes of relevant physical parameters are analyzed qualitatively to establish a foundation on the further study of the model. The method of multiple scales is used to obtain eigenfunctions of the linear free-vibration modes of the pipe. The boundary conditions yield the characteristic equations from which eigenvalues can be derived. It is found that flow velocity in the pipe may induced the 3:1, 2:1 and 1:1 internal resonances between the first and second modes such that the mechanism of flow-induced internal resonances in the pipe under consideration is explained theoretically. The 3:1 internal resonance first occurs in the system and is, thus, the most important since it corresponds to the minimum critical velocity.
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