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中文摘要：
陀螺系统的特征值问题是一个重要课题.通过构造Green函数,解决了轴向行进弦附带单质量-弹簧振子耦合系统的特征值问题.根据Green函数构造定理,给出了耦合模型Green函数的显式形式,从而得到了精确的特征方程.讨论了当振子的特征频率接近于弦线的基频时,行进弦低阶模态与振子间的耦合作用,采用特征频率的最大变化定量地表征了这种耦合强度.数值结果表明：耦合系统的特征频率随着弹簧刚度的增大而增大,随着行进速度的增大而减小.最后,给出了系统可能出现重根的条件.
英文摘要：
There have been considerable efforts to analyze the eigenvalue problem for gyroscopic systems in practice.The eigenvalue problem of an axially moving string with an attached mass-spring oscillator is solved by means of Green′s function method.The explicit Green′s function is obtained by the Construction Theorem of Green′s Function and thus the closed form transcendental equations of the natural frequencies are presented.The maximum variance rate is adopted to express the dynamical interaction between the subsystems.It is found out that the dynamical interaction between subsystems mainly acts on the first two modes of the moving string when the eigenfrequency of the oscillator is close to the first eigenfrequency of the moving string.Numerical results demonstrate that the eigenfrequencies of the coupled system increase with the spring stiffness and decrease with the transport speed.The possible existence condition for the duplicate eigenvalues is also proposed.
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