FLOW-INDUCED INTERNAL RESONANCES AND MODE EXCHANGE IN HORIZONTAL CANTILEVERED PIPE CONVEYING FLUID (Ⅱ)  

作　　者：徐鉴 杨前彪 

机构地区：[1]School of Aerospace Engineering and Applied Mechanics Tongji University, Shanghai 200092, P. R. China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2006年第7期935-941,共7页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (No.10472083) and the National Natural Science Key Foundation of China (No.10532050)

摘　　要：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.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.

关 键 词：pipe conveying fluid internal resonance STABILITY BIFURCATION 

分 类 号：U173[交通运输工程]