Optimal Vibration Absorber with Nonlinear Viscous Power Law Damping and White Noise Excitation
Publication: Journal of Engineering Mechanics
Volume 132, Issue 1
Abstract
A tuned mass damper with a nonlinear power law viscous damper excited by white noise is considered. The system is analyzed by statistical linearization and stochastic simulation with the objective of minimizing the standard deviation of the response. It is shown that the optimal parameters for the tuned mass damper are unaffected by the magnitude of the structural damping in the linear case. However, in the nonlinear case the structural damping influences the equivalent parameters obtained by statistical linearization and thereby indirectly the optimal values for the damper parameters. Results from stochastic simulation show good agreement with results from statistical linearization in terms of the standard deviation of the response. It is shown that the optimal damping, which can be obtained by the passive device, is the same for the linear and nonlinear damper. However, for the nonlinear tuned mass damper the optimal parameters will depend on both structural damping and excitation intensity (or vibration amplitude). The results are presented in such a way that they can be used directly for the design of a tuned mass damper with damping governed by a nonlinear viscous power law.
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Acknowledgment
The present project has been supported by the Danish Technical Research Council. The support is gratefully acknowledged.
References
Ankireddi, S., and Yang, T. Y. (1996). “Simple ATMD control methodology for tall buildings subject to wind loads.” J. Struct. Eng., 122(1), 83–91.
Ayorinde, E. O., and Warburton, G. B. (1980). “Minimizing structural vibrations with absorbers.” Earthquake Eng. Struct. Dyn., 8, 219–236.
Clough, R. W., and Penzien, J. (1975). Dynamics of structures, McGraw–Hill, New York.
Den Hartog, J. P. (1956). Mechanical vibrations, McGraw–Hill, New York.
Gaul, L., and Nitsche, R. (2000). “Friction control for vibration suppression.” Mech. Syst. Signal Process., 14, 139–150.
Gradshteyn, I. S., and Ryzhik, I. M. (1965). Table of integrals, series, and products, 4th Ed., Academic, London.
Inaudi, J. A., and Kelly, J. M. (1995). “Mass damper using friction-dissipating devices.” J. Eng. Mech., 121(1), 142–149.
Lin, W. H., and Chopra, A. K. (2003). “Earthquake response of elastic single-degree-of-freedom systems with nonlinear viscoelastic dampers.” J. Eng. Mech., 129(6), 597–606.
Ricciardelli, F., Pizzimenti, A. D., and Mattei, M. (2003). “Passive and active mass damper control of the response of tall buildings to wind gustiness.” Eng. Struct., 25, 1199–1209.
Ricciardelli, F., and Vickery, B. J. (1999). “Tuned vibration absorbers with dry friction damping.” Earthquake Eng. Struct. Dyn., 28, 707–724.
Roberts, J. B., and Spanos, P. D. (1990). Random vibration and statistical linearization, Wiley, Chichester, Unided Kingdom.
Rüdinger, F., and Krenk, S. (2003). “Spectral density of an oscillator with power law damping excited by white noise.” J. Sound Vib., 261, 365–371.
Snowdon, J. C. (1959). “Steady-state behaviour of the dynamic absorber.” J. Acoust. Soc. Am., 31, 1096–1103.
Terenzi, G. (1999). “Dynamics of SDOF systems with nonlinear viscous damping.” J. Eng. Mech., 125(8), 956–963.
Warburton, G. B. (1981). “Optimum absorber parameters for minimizing vibration response.” Earthquake Eng. Struct. Dyn., 9, 251–262.
Warburton, G. B. (1982). “Optimum absorber parameters for various combinations of response and excitation parameters.” Earthquake Eng. Struct. Dyn., 10, 381–401.
Warburton, G. B., and Ayorinde, E. O. (1980). “Optimum absorber parameters for simple systems.” Earthquake Eng. Struct. Dyn., 8, 197–217.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 132 • Issue 1 • January 2006
Pages: 46 - 53
Copyright
© 2006 ASCE.
History
Received: Oct 20, 2003
Accepted: May 5, 2005
Published online: Jan 1, 2006
Published in print: Jan 2006
Notes
Note. Associate Editor: Gerhart I. Schueller
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