带有集中黏滞阻尼的张紧弦系统在力学模型上属于混杂动力学系统，为满足工程应用一般采用近似方法求解其本征问题。为进一步明确该系统振动特性，以两项集中阻尼对称布置于四等分跨的阻尼弦系统作为基础研究对象，并对其复本征值进行解析求解。推导系统的复频率方程和本征函数表达式，将超越函数形式的复频率方程换元处理为代数形式，利用代数方程给出系统复本征值的显式解。分析系统复本征值的结构和性质，讨论振动特性随阻尼系数的变化规律。结果表明：系统本征解可归为3个解支，在同一解支内本征值实部（相反数即为衰减率）不随系统运动阶次而改变，本征值虚部（即频率）则随运动阶次以4π为周期依次递增；各解支所对应的衰减率曲线均随阻尼系数呈先递增、后递减的趋势，且在衰减率曲线连续变化的阻尼区间内，系统各阶运动的频率相等。

The tension string system with concentrated viscous damping belongs to a hybrid dynamic system in mechanical models. Approximate methods are typically used to solve its inherent problems for engineering applications. In order to further clarify the vibration characteristics of the system, two centrally damped symmetrical damping string systems were taken as the basic research object, and their complex eigenvalues were solved analytically. The complex frequency equation and the eigenvalue expression of the system were derived, and the transformation of the complex frequency equation beyond the function form was treated as algebraic form, and the explicit solution of the complex eigenvalue of the system was given by the algebraic equation. The structure and properties of the complex eigenvalues of the system were analyzed, and the variation of vibration characteristics with damping coefficient was discussed. The results show that the eigenvalue solution of the system can be divided into three branches, in which the real part of the eigenvalue(the inverse is the decay rate) does not change with the order of the system motion, but the imaginary part of the eigenvalue(the frequency) increases with the order of the motion. The decay rate curves corresponding to each solution branch increase first and then decrease with the damping coefficient, and in the damping range of the decay rate curve, the frequencies of each order of the system are equal.