Generalized Den Hartog Tuned Mass Damper
System For Control Of Vibrations In Structures
Author(s)
I. M. Abubakar & B. J. M. Farid
Abstract
The Den Hartog method is one of old, but efficient methods for the design of
tuned mass damper (TMD) systems for passive control vibrations in buildings
subjected to earthquake excitations. However, Den Hartog, in his model, did not
include the main mass (structure) damping in deriving the equations for
computing the optimum design parameters for the TMD system (damping and
frequency ratios). In this work an attempt is made to generalize the Den Hartog
method to include the effect of the structure damping in the derived equations.
The dynamic equations for a TMD system attached to SDOF structure with
damping are derived. Then, using the complex numbers technique, the equation
for maximum displacement of the structure when subjected to harmonic
excitation is derived. The numerical optimization technique is used to compute
the optimum values of TMD parameters that will minimize the maximum
displacement of the structure. Finally, the curve fitting procedure with trial
functions is used to obtain equations for computing the optimum frequency ratio
and optimum damping ratio for a TMD system.
Keywords: tuned mass damper, Den Hartog model, structural damping,
earthquake engineering, harmonic excitation.
1 Introduction
The tuned mass damper (TMD) system is a passive energy absorbing device
consisting of a translational mass, translational spring and translational viscous
damper attached to a vibrating structure to reduce undesirable vibrations. There
has been a considerable amount of research done on how best to design the mass
dampers for use in the passive control of structures under excitation forces such
Keywords
tuned mass damper, Den Hartog model, structural damping,
earthquake engineering, harmonic excitation.
Related Book
Other papers in this volume
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