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Free vibration of a taut cable with a damper and a concentrated mass
Recent numerical studies showed the combined effects of mass and viscous damper would behave like that of semiactive damper with “negative stiffness properties.” This paper analytically studied the characteristic equation of the cable‐mass‐damper system derived with help of the transfer matrix method. After the expansion of the complex frequency equation in terms of real and imaginary parts, the special limiting solutions are obtained, together with three different classified mode behaviors. Asymptotic approximate formulations for damper and concentrated mass close to the cable end are developed provided that both the nondimensional mass coefficient and the frequency shift between the free and damped cable system are small. The influences of the nondimensional mass coefficient and its location on the maximum cable vibration damping and the corresponding optimal damper constant are also studied as the damper is installed near the cable anchorage and the mass is moved along the cable axis. When the damper and concentrated mass are located at the same position, the mode behaviors are investigated in three regimes by means of varying the nondimensional mass coefficient. The general solutions for the arbitrary location of damper and concentrated mass along the cable axis are further discussed. It is found that the concentrated mass will significantly affect the system damping, especially when the concentrated mass and the damper are located at the same half wave of the mode shape.
Free vibration of a taut cable with a damper and a concentrated mass
Recent numerical studies showed the combined effects of mass and viscous damper would behave like that of semiactive damper with “negative stiffness properties.” This paper analytically studied the characteristic equation of the cable‐mass‐damper system derived with help of the transfer matrix method. After the expansion of the complex frequency equation in terms of real and imaginary parts, the special limiting solutions are obtained, together with three different classified mode behaviors. Asymptotic approximate formulations for damper and concentrated mass close to the cable end are developed provided that both the nondimensional mass coefficient and the frequency shift between the free and damped cable system are small. The influences of the nondimensional mass coefficient and its location on the maximum cable vibration damping and the corresponding optimal damper constant are also studied as the damper is installed near the cable anchorage and the mass is moved along the cable axis. When the damper and concentrated mass are located at the same position, the mode behaviors are investigated in three regimes by means of varying the nondimensional mass coefficient. The general solutions for the arbitrary location of damper and concentrated mass along the cable axis are further discussed. It is found that the concentrated mass will significantly affect the system damping, especially when the concentrated mass and the damper are located at the same half wave of the mode shape.
Free vibration of a taut cable with a damper and a concentrated mass
Zhou, Haijun (author) / Huang, Xigui (author) / Xiang, Ning (author) / He, Jiawei (author) / Sun, Limin (author) / Xing, Feng (author)
2018-11-01
21 pages
Article (Journal)
Electronic Resource
English
damper , stay cable , frequency , mass , damping
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