The eigen solution and properties of a taut string with concentrated damping at one-third-span
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Abstract:
A frequency equation of the damping string is simplified in which the damping is located at one third of the string length, and its analytical solution is obtained. The properties of the solution are discussed in three cases: large damping, moderate damping and small damping. The results show that, compared with the taut strings with damping which is located at half of the string length, the taut strings with damping which is located at one third of the string length has three new characteristics: 1) In the functional relationship between the eigenvalues and damping, the former has and only has one mutation point, while the latter has two; 2) In the damping - frequency relationship, the frequency of the former is not affected by the damping value in each damping interval, while the frequency of the latter is related to the damping; 3) For any given damping, the former eigen solution has only one attenuation rate in each damping interval, and the latter has two attenuation rates except for small damping. The above properties show that the dynamic characteristics of the two are different in essence (not only in quantity). Considering that they differ only in damping position, this should be paid special attention to.
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Supported by National Natural Science Foundation of China （51978112，51878106）.
