Vibration of Tensioned Beams with Intermediate Damper. II: Damper near a Support
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Volume 133, Issue 4
Abstract
Analytical solutions are used to investigate the free vibrations of tensioned beams with a viscous damper attached transversely near a support. This problem is of particular relevance for stay-cable vibration suppression, but no restrictions on the level of axial load are introduced, and the results are quite broadly applicable. Characteristic equations for both clamped and pinned supports are rearranged into forms suitable for numerical solution by fixed-point iteration, whereby the complex eigenfrequencies and corresponding damping ratios can be accurately computed within a few iterations. Explicit asymptotic approximations for the complex eigenfrequencies are also obtained, subject to restrictions on the closeness of the eigenfrequencies to their undamped values. These asymptotic approximations are expressed in the same “universal” form identified in previous studies. It is observed that the maximum attainable modal damping ratios and the corresponding optimal values of the damper coefficient can be significantly affected by bending stiffness and by the nature of the support conditions, and a nondimensional parameter grouping is identified that enables an assessment of when bending stiffness should be considered.
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References
Carne, T. G. (1981). “Guy cable design and damping for vertical axis wind turbines.” SAND80-2669, Sandia National Laboratories, Albuquerque, N.M.
Christenson, R. E. (2001). Semiactive control of civil structures for natural hazard mitigation: Analytical and experimental studies, Ph.D. dissertation, Dept. of Civil Engineering and Geological Sciences, Univ. of Notre Dame, Notre Dame, Ind.
Krenk, S. (2000). “Vibrations of a taut cable with an external damper.” J. Appl. Mech., 67, 772–776.
Krenk, S., and Nielsen, S. R. K. (2002). “Vibrations of a shallow cable with a viscous damper.” Proc. R. Soc. London, 458, 339–357.
Main, J. A., and Jones, N. P. (2001). “Evaluation of viscous dampers for stay-cable vibration mitigation.” J. Bridge Eng., 6(6), 385–397.
Main, J. A., and Jones, N. P. (2002). “Free vibrations of taut cable with attached damper. I: Linear viscous damper.” J. Eng. Mech., 128(10), 1062–1071.
Main, J. A., and Krenk, S. (2005). “Efficiency and tuning of viscous dampers on discrete systems.” J. Sound Vib., 286, 97–122.
Main, J. A., and Jones, N. P. (2005). “Vibration of tensioned beams with intermediate damper. I: Formulation, influence of damper location.” J. Eng. Mech., 133(4), 369–378.
Pacheco, B. M., Fujino, Y., and Sulekh, A. (1993). “Estimation curve for modal damping in stay cables with viscous damper.” J. Struct. Eng., 119(6), 1961–1979.
Tabatabai, H., and Mehrabi, A. B. (2000). “Design of mechanical viscous dampers for stay cables.” J. Bridge Eng., 5(2), 114–123.
Wittrick, W. H. (1986). “On the vibration of stretched strings with clamped ends and nonzero flexural rigidity.” J. Sound Vib., 110, 79–85.
Xu, Y. L., and Yu, Z. (1998). “Mitigation of three-dimensional vibration of inclined sag cable using discrete oil dampers. II: Application.” J. Sound Vib., 214, 675–693.
Yamaguchi, H., and Fujino, Y. (1998). “Stayed cable dynamics and its vibration control.” Proc., Int. Symp. on Advances in Bridge Aerodynamics, Balkema, Rotterdam, The Netherlands (1998), 235–253.
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© 2007 American Society of Civil Engineers.
History
Received: Oct 28, 2005
Accepted: Sep 12, 2006
Published online: Apr 1, 2007
Published in print: Apr 2007
Notes
Note. Associate Editor: Lambros S. Katafygiotis
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