01-01-2013, 04:30 PM
Hazardous Vibration Mitigation of Structures Using Magneto-Rheological Tuned Mass Dampers
[attachment=46059]
Abstract
This paper presents the results of a study to evaluate the performance of a magneto-rheological
tuned mass damper (MR-TMD) in reducing the vibrations of a structure subjected to hazardous
dynamic loads. Several vibration mitigation systems including the MR-TMD, tuned mass
damper (TMD), and magneto-rheological (MR) dampers are considered. The performance of
these vibration mitigation systems are compared through a numerical model example, and the
advantages of each vibration mitigation system are discussed. The numerical models of a singledegree-
of-freedom (SDOF) building in its uncontrolled state and with each vibration mitigation
system are simulated, excited by the Taft and Canoga Park earthquakes and a harmonic
excitation, using the Matlab Simulink Dynamic System Simulator. (MATLAB 2008) The
reduction in floor displacements and accelerations induced by each vibration mitigation system
are recorded and examined.
Introduction
Tuned mass dampers (TMDs) are currently being utilized to mitigate vibrations within structures
across the globe. The passive energy device consists of a mass, spring and damper and is tuned,
or designed, to one of the dominant frequencies of the structure, most commonly the resonance
frequency. By moving in opposition to the structure, the TMD reduces structural vibrations by
dissipating energy through the damper and transferring vibrational energy from the building to
the tuned mass.
In 1909 the concept of TMD was first introduced by Frahm (Housner et al. 1997) to reduce the
vertical vibration of ship hulls. Den Hartog (1956) authored a monograph pertaining to the
theory and principles of an un-damped SDOF structure subjected to harmonic forces. The
applicability of using TMDs for reducing wind induced structural vibrations was further explored
by McNamara (1977), and Tsai and Lin (1993) obtained the optimum parameters of TMDs for
steady state response reduction. These parameters are the current convention for TMD design
applied to wind induced vibrations, and have been shown to significantly reduce structural
dynamic response. However the TMD has been shown to have a varying effect on the vibrations
of a structure subjected to earthquake ground motions and in some cases TMDs can be
detrimental to the structure. (T. Haskett 2004)
Scope of Work
In order to evaluate and compare the performance of the MR-TMD system with other systems
described previously, computer models are formulated based on the equations of motion for the
dynamic systems. These equations of motion are written in state-space form which benefits this
simulation because the Matlab Simulink Dynamic System Simulator is capable of processing the
ordinary differential equations at real-time speeds. The five numerical models are presented in
this section. The Simulink system schematics and programming codes are presented in Appendix
A. First the model of the prototype SDOF structure is discussed.
Numerical Results
In this section the numerical simulation of the previously presented models is presented. The
earthquake ground motions recorded at Canoga Park during the 1994 Northridge earthquake and
Taft Lincoln School during the 1952 Kern County earthquake (PEER 1999), and a harmonic
excitation tuned to the natural frequency of the SDOF structure are selected.
The Kern County earthquake registered at 7.36 on the Richter scale, lasted over seventy seconds,
and the PGA was moderate at 0.178g. The Taft record is selected to display the behavior of the
MR damper when the stroke is minimal compared to its full capacity. Figures 3.0-3.3 present the
dynamic response of the numerical models subjected to the Taft ground motion. The dashed line
in each figure is the uncontrolled response of the SDOF structure.
Conclusions
The performance of the magneto-rheological tuned mass damper, for use in reducing the
dynamic response of a structure, has been investigated in comparison with an uncontrolled
building, a building with a conventional tuned mass damper, and a building with MR dampers. In
a numerical example, Matlab Simulink Dynamic Simulator was used to subject a SDOF structure
to moderate and severe ground motions as well as a harmonic excitation tuned to the natural
frequency of the building. The performance of the building with each vibration mitigation system
was evaluated throughout simulation.
In this study the MR-TMD was observed to have advanced performance in comparison with the
TMD. The semi-active behavior of the MR-TMD allows for the optimal adjustment of its applied
damper force in critical time, improving the conventional TMD system. The added reduction in
structural response that can be achieved by the semi-active behavior of the MR-TMD is
comparable with the use of MR dampers within a building. The MR-TMD was observed to
perform better across a broader range of loading when an equal number of MR dampers were
used for each application.
[attachment=46059]
Abstract
This paper presents the results of a study to evaluate the performance of a magneto-rheological
tuned mass damper (MR-TMD) in reducing the vibrations of a structure subjected to hazardous
dynamic loads. Several vibration mitigation systems including the MR-TMD, tuned mass
damper (TMD), and magneto-rheological (MR) dampers are considered. The performance of
these vibration mitigation systems are compared through a numerical model example, and the
advantages of each vibration mitigation system are discussed. The numerical models of a singledegree-
of-freedom (SDOF) building in its uncontrolled state and with each vibration mitigation
system are simulated, excited by the Taft and Canoga Park earthquakes and a harmonic
excitation, using the Matlab Simulink Dynamic System Simulator. (MATLAB 2008) The
reduction in floor displacements and accelerations induced by each vibration mitigation system
are recorded and examined.
Introduction
Tuned mass dampers (TMDs) are currently being utilized to mitigate vibrations within structures
across the globe. The passive energy device consists of a mass, spring and damper and is tuned,
or designed, to one of the dominant frequencies of the structure, most commonly the resonance
frequency. By moving in opposition to the structure, the TMD reduces structural vibrations by
dissipating energy through the damper and transferring vibrational energy from the building to
the tuned mass.
In 1909 the concept of TMD was first introduced by Frahm (Housner et al. 1997) to reduce the
vertical vibration of ship hulls. Den Hartog (1956) authored a monograph pertaining to the
theory and principles of an un-damped SDOF structure subjected to harmonic forces. The
applicability of using TMDs for reducing wind induced structural vibrations was further explored
by McNamara (1977), and Tsai and Lin (1993) obtained the optimum parameters of TMDs for
steady state response reduction. These parameters are the current convention for TMD design
applied to wind induced vibrations, and have been shown to significantly reduce structural
dynamic response. However the TMD has been shown to have a varying effect on the vibrations
of a structure subjected to earthquake ground motions and in some cases TMDs can be
detrimental to the structure. (T. Haskett 2004)
Scope of Work
In order to evaluate and compare the performance of the MR-TMD system with other systems
described previously, computer models are formulated based on the equations of motion for the
dynamic systems. These equations of motion are written in state-space form which benefits this
simulation because the Matlab Simulink Dynamic System Simulator is capable of processing the
ordinary differential equations at real-time speeds. The five numerical models are presented in
this section. The Simulink system schematics and programming codes are presented in Appendix
A. First the model of the prototype SDOF structure is discussed.
Numerical Results
In this section the numerical simulation of the previously presented models is presented. The
earthquake ground motions recorded at Canoga Park during the 1994 Northridge earthquake and
Taft Lincoln School during the 1952 Kern County earthquake (PEER 1999), and a harmonic
excitation tuned to the natural frequency of the SDOF structure are selected.
The Kern County earthquake registered at 7.36 on the Richter scale, lasted over seventy seconds,
and the PGA was moderate at 0.178g. The Taft record is selected to display the behavior of the
MR damper when the stroke is minimal compared to its full capacity. Figures 3.0-3.3 present the
dynamic response of the numerical models subjected to the Taft ground motion. The dashed line
in each figure is the uncontrolled response of the SDOF structure.
Conclusions
The performance of the magneto-rheological tuned mass damper, for use in reducing the
dynamic response of a structure, has been investigated in comparison with an uncontrolled
building, a building with a conventional tuned mass damper, and a building with MR dampers. In
a numerical example, Matlab Simulink Dynamic Simulator was used to subject a SDOF structure
to moderate and severe ground motions as well as a harmonic excitation tuned to the natural
frequency of the building. The performance of the building with each vibration mitigation system
was evaluated throughout simulation.
In this study the MR-TMD was observed to have advanced performance in comparison with the
TMD. The semi-active behavior of the MR-TMD allows for the optimal adjustment of its applied
damper force in critical time, improving the conventional TMD system. The added reduction in
structural response that can be achieved by the semi-active behavior of the MR-TMD is
comparable with the use of MR dampers within a building. The MR-TMD was observed to
perform better across a broader range of loading when an equal number of MR dampers were
used for each application.