ZHENG Gang, LI Zhangyu, GUO Zengwei, ZHANG Xiaodong. Properties of the Eigen Solution of Taut Strings With Concentrated Damping[J]. Applied Mathematics and Mechanics, 2019, 40(9): 980-990. doi: 10.21656/1000-0887.400023
 Citation: ZHENG Gang, LI Zhangyu, GUO Zengwei, ZHANG Xiaodong. Properties of the Eigen Solution of Taut Strings With Concentrated Damping[J]. Applied Mathematics and Mechanics, 2019, 40(9): 980-990.

# Properties of the Eigen Solution of Taut Strings With Concentrated Damping

##### doi: 10.21656/1000-0887.400023
Funds:  The National Natural Science Foundation of China（51478072；51878106）
• Rev Recd Date: 2019-01-24
• Publish Date: 2019-09-01
• By means of the Dirac delta function, the free-vibration equation of motion for taut strings with concentrated damping, namely the damping hybrid string system, was established and solved. The analytic solution to the eigen problem was obtained for the system with only one single damping dashpot at the midspan, and the properties of the eigen value and the eigen function were analyzed. The dynamic behaviors of the damping hybrid string system, including the frequency-damping relationship, the decay ratio and the full suppression of the motion at the optimal damping, which distinctly differentiate the hybrid system from a continuous system or a discrete system, were identified: 1) The frequency of the hybrid string system is independent of its damping ratio; 2) The decay ratios keep the same for different orders of eigen functions; 3) The decay ratios approach infinity when the damping ratio equals 2, which indicates any damped vibration of the system will be fully suppressed.
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