【摘要】 运用牛顿法导出水平悬臂刚性输液管的非线性动力学数学模型.为了对该模型进行理论分析,通过对各个相关实际物理量的量级定性分析,给出了模型中各个物理参数的量级.在此基础上,应用多尺度法首先得到输液管自由振动模态的特征函数,利用悬臂管的边界条件给出了特征值满足的特征方程,发现管内流体速度可以诱发第一阶模态和第二阶模态3种形式的内共振分别是3∶12、∶1和1∶1内共振,从理论上解释了流速诱发水平悬臂输液管系统内共振的机理.由于3∶1内共振所对应的流速最小,因此这种形式的内共振是最先出现的,也是最重要的.更多还原

【Abstract】 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.更多还原