Optimization criteria of TMD to reduce vibrations generated by the wind in a slender structure

Abstract

This paper deals with the reduction of vibrations caused by wind load in slender structures. The structure is modeled as a Single-Degree-of-Freedom system and the wind load is estimated through the pre-filter technique: the aerodynamic force is a function of White Noise filtered by a simple oscillator. Two optimization criteria to calculate the best values of the frequency and the damping ratio of the Tuned Mass Damper (TMD) are compared here. The aim of the first criterion is the reduction of the displacement of the top end of the structure, while the aim of the second criterion is the reduction of the inertial acceleration of the top end of the structure. The comparison of the two criteria is carried out through sensitivity analyses for different environmental conditions and system configurations. The comparison shows that the acceleration criterion is more attractive only for some conditions. Moreover, it is plain that the different efficiencies of the TMD optimized through each of two criteria are related to the mass ratio. Finally, the optimization criteria are applied to estimate the TMD design parameters to reduce the vibrations due to wind load in a lighting tower.

Keywords

Tuned mass damper optimal design wind excitation covariance analysis slender structure

Get full access to this article

View all access options for this article.

References

Benfratello

Falsone

Muscolino

(1996) Influence of the quadratic term in the along-wind stochastic response of SDoF Structures. Engineering Structures 18: 685–706.

Bishop RED and Welbourn DB (1952) The problem of the dynamic vibration absorber Engineering London.

Brock

(1946) A note on the damped vibration absorber. ASME Journal of Applied Mechanics 13: A–284.

Chang

(1999) Mass dampers and their optimal designs for building vibration control. Engineering Structures 21: 454–463.

Colwell

Basu

(2009) Tuned liquid column dampers in offshore wind turbines for structural control. Engineering Structures 31: 358–368.

Den Hartog

(1956) Mechanical Vibrations, 4th ed, New York: McGraw-Hill.

Hoang

Warnitchai

(2005) Design of multiple tuned mass dampers by using a numerical optimizer. Earthquake Engineering & Structural Dynamics 34: 125–144.

Housner

Bergman

Caughey

(1987) Elastic seismic response of buildings with supplemental damping, Report No. UMCE 87-1, University of Michigan: Ann Arbor, MI.

Lutes

Sarkani

(2004) Random vibrations: Analysis of structural and mechanical systems, 1st ed, Oxford: Butterworth-Heinemann.

10.

Marano

Greco

(2010) Optimization criteria for tuned mass dampers for structural vibration control under stochastic excitation. Journal of Vibration and Control 17: 679–688.

11.

Marano

Greco

Trentadue

(2007) Constrained reliability-based optimization of linear tuned mass dampers for seismic control. International Journal of Solids and Structures 44: 7370–7388.

12.

Nigam

(1972) Structural optimization in random vibration environments. AIAA Journal 10: 551–553.

13.

Rana

Soong

(1998) Parametric study and simplified design of tuned mass dampers. Engineering Structures 20: 193–204.

14.

Ricciardelli

Occhiuzzi

Clemente

(2000) Semi-active tuned mass damper control strategy for wind-excited structures. Journal of Wind Engineering and Industrial Aerodynamics 88: 57–74.

15.

Rundinger

(2006) Optimal vibration absorber with nonlinear viscous power law damping and white noise excitation. ASCE Journal of Engineering Mechanics 132: 46–53.

16.

Simiu

Scanlan

(1978) Wind Effects on Structures, New York: John Wiley & Sons.

17.

Soong

Dargush

(1997) Passive Energy Dissipation Systems in Structural Engineering, Chichester: John Wiley & Sons.