单阻尼与对称双阻尼弦系统减振特性对比

o explore the vibration reduction characteristics of a taut string with two dampers, derive the frequency equation, the frequency equation in which dampers are located at symmetric one third of the string length that can be analytically solved is algebraized. The analytical solution of its eigenvalues is obtained, which is further compared with the analytical solution of a taut string with a damper in one third length. Based on the complex domain characteristics of the analytical solutions of the two systems, the vibration reduction characteristics are discussed in two intervals: small damping and large damping. The results indicate that: 1) In different damping intervals, the eigenvalues of the two systems exhibit the same conjugate characteristics. 2) The damping effect of a taut string with two dampers located at symmetric one third of the string length is twice as strict as a taut string with one damper located at one third of the string length. 3) In the small damping interval, the same frequency will not occur no matter in which order of motion the two systems are, and the frequencies of the two systems form the entire real number domain, which can provide potential solutions for the frequency resonance problem of damping string systems.