Free vibration of a taut cable with a damper and a concentrated mass

Abstract

Summary 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 two taut cables interconnected by a damper

“…Further studies shows this phenomenon is due to the effect of the fifth mode, the modal crossover for the fourth mode and the fifth mode occurred when l 2,1 / L 2 is between 0.414 and 0.415. Similar modal crossover phenomena was also reported in other reference . The system shows underdamped modes in this regime.…”

“…Similar modal crossover phenomena was also reported in other reference. 31,38,45 The system shows underdamped modes in this regime. Figure 12b shows the typical mode shape, which is also a mixed vibration of different wavelengths for the upper and the lower cable.…”

“…Lazar et al and Lu et al studied the damping of cable with inerter damper. The coauthors then further studied the general results of cable–damper–mass system …”

“…The coauthors then further studied the general results of cable-damper-mass system. 31 Researchers and engineers also developed cross-ties to mitigate cable vibrations. 32 Caracoglia and Jones 9 studied the linear dynamics of a basic two-cable network connected by rigid rods or linear elastic springs.…”

Motion-Based Design of Passive Damping Devices to Mitigate Wind-Induced Vibrations in Stay Cables

“…There are several examples in the literature of the use of semi-active systems to control the response of stay cables under dynamic actions. Thus, Zhou and Sun checked the effectiveness of magnetorheological dampers to increase the damping of stay cables [7]; subsequently, Yeganeh Fallah et al proposed the use of magnetorheological dampers to mitigate seismic-induced vibrations in these structural elements under uncertainty conditions [8], and more recently, Zhou et al have shown the high performance of semi-active control devices based on the modification of a conventional passive damper via the implementation of concentrated masses [9]. Finally, passive control systems, in which a device is installed in the structure in order to increase its damping, have been widely used to tackle the problem of wind-induced vibrations in stay cables of bridges.…”