semi-active seismic control of mid-rise structures...
TRANSCRIPT
IJST, Transactions of Civil Engineering, Vol. 38, No. C1, pp 21-36 Printed in The Islamic Republic of Iran, 2014 © Shiraz University
SEMI-ACTIVE SEISMIC CONTROL OF MID-RISE STRUCTURES USING MAGNETO-RHEOLOGICAL DAMPERS AND TWO
PROPOSED IMPROVING MECHANISMS*
S. M. ZAHRAI** AND H. SALEHI Center of Excellence for Eng. and Management of Civil Infrastructures, School of Civil Eng., University of Tehran,
Tehran, I. R. of Iran Email: [email protected]
Sahid Sattari Aeronautical University of Science and Technology, Tehran, I. R. of Iran
Abstract– This research examines performance of semi-active control of structures using Magneto-Rheological (MR) dampers. Mechanical specifications of this smart fluid damper change by falling into the magnetic field, so by increasing intensity of magnetic field the resulting damper power consequently increases. In this paper, two models of 9 and 20-story buildings were first selected as case studies and respective specifications of these structures (mass, stiffness and damping matrices) were calculated using valid sources as well as analysis of structures ignoring axial deformations against imposed loads. Then, sample structures were simulated in a Simulink environment. Consequently, optimum force determination processor, control system and MR damper were modeled in Simulink environment and were installed on a structural system. Finally, the obtained results from damper equipped structure were compared with non-controlled structure. In semi-active control case, clipped optimal algorithm was considered as control algorithm and optimal classic linear control method was used to determine control power. Based on the obtained results, it is observed that using this control method will significantly decrease structure response, such that MR damper can be about 12% to 36% effective in reducing maximum lateral drift and up to 21% in reducing maximum acceleration. Two mechanisms are eventually offered to improve the function of dampers and their performance. The proposed mechanism is shown to be effective in reducing the capacity and number of dampers required.
Keywords– Smart fluid dampers, magneto-rheological (MR) dampers, clipped optimal algorithm, linear optimal control algorithm, simulink modeling, mid–rise structures
1. INTRODUCTION
Seismic sources in most parts of the world cause earthquakes to occur and consequently leave severe damage behind. Accurate calculation of gravity loads is possible because of their simple behavioral nature, but obtaining the same result in earthquake induced loads is far beyond our reach as mid-rise buildings might be more affected by earthquake due to their special structural specifications. On the other hand, there are a large number of people in such residential or office buildings, making it more crucial that they be useable during and after earthquakes as any damage will jeopardize the lives of many people. Some research studies have already been carried out on MR dampers. Dyke et al. studied modeling and reduction of vibrating response of a 3-story building by using an MR damper and obtained suitable results to control the model. The semi-active control performance of MR damper to reduce the maximum drift, while requiring less energy, was better than active control performance [1, 2].
Qu and Xu in 2001 conducted research on using ER/MR damper for semi-active control of vibration response of high rise structure connected to the podium structure. This smart material damper was used to Received by the editors June 12, 2012; Accepted December 28, 2013. Corresponding author
S. M. Zahrai and H. Salehi
IJST, Transactions of Civil Engineering, Volume 38, Number C1 February 2014
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connect tower structure to podium structure to reduce the impact effect of tower structure when exposed to vibration excitations [3].
Iwata et al. in 2002 have described the applicability of the MR damper to base-isolated building structures. They proposed a simple semi-active control algorithm, which aims at controlling the hysteresis shape. In order to verify the effectiveness of the proposed method, shaking table tests were carried out using a newly-developed MR fluid damper. It was shown that the MR damper significantly improves the performance of base-isolated structures [4].
Jung et al. proposed a semi-active control strategy using MR dampers by investigating the ASCE first generation benchmark control problem for seismic responses of cable-stayed bridges. The modified Bouc-Wen model was considered as a dynamic model of the MR damper. The numerical results demonstrated that the performance of the proposed control design is nearly the same as that of the active control system. In addition, semi-active control strategy has many attractive features, such as the bounded-input, bounded-output stability and small energy requirements. The results of this preliminary investigation, therefore, indicated that MR dampers can be effectively used to control seismically excited cable-stayed bridges [5].
Amini and Karagah studied optimal placement of semi-active dampers by pole assignment method and showed that the optimal control analysis results in less control force and a small number of controllers in comparison with the non-optimal case. In most cases, the number of controllers does not have a great effect on the desired control performance and controlling can be done with fewer optimal controllers [6].
Chooi and Oyadiji conducted research on designing, modeling and testing of MR dampers using analytical flow solutions [7]. Ahmadian and Norris by making an experimental model in 2008 analyzed the performance of MR damper against the impact loads. Their model included a 55-pound load which dropped from 12, 24, 48, 72 and 96 inch heights and made impact velocities of 86, 127, 224, and 260 inch per second [8].
Zahrai and Shafieezadeh studied the application of semi-active variable dampers for wind response control of tall buildings and demonstrated that the fuzzy controller is more effective than the passive controller in retuning the damping of the semi-active device and reducing the structural response due to wind excitations[9].
In 2009, Zasso and Resta investigated using MR damper in high rise building to reduce structure response against vibrations due to wind. Dampers were connected to the structure in two forms of internal and external braces. To improve that performance, a lever mechanism was used with MR damper. Their proposed mechanism had a noticeable effect on reduction of capacity and number of needed dampers [10].
Since research projects on seismic control of high and mid-rise structures by using magnetic smart fluid dampers still suffer from some deficiencies, there is a lack of information in this regard and presenting control algorithms as well as desirable creative strategies can significantly improve performance of this kind of damper. In this paper, using magnetic smart fluid dampers for seismic control of mid-rise structures is discussed.
For successful function of MR dampers, they should connect two points that might have noticeable displacement. Therefore two mechanisms for improving the function of these kinds of dampers are offered and a combination of them is eventually used and comparison between the results of using new methods and using dampers in normal condition is made. Since the displacement across the damper is shown to be small, a lever mechanism is also proposed for motion magnification. Control algorithm of clipped optimal showed that MR dampers with the proposed lever mechanism are effective in reducing responses under earthquake excitations in all three models.
2. DAMPER WITH MAGNETIC SMART FLUID
Damping system with smart fluid is considered a kind of semi-active control instrument. This group of instruments includes dampers in which fluid viscosity is changeable. This change in viscosity changes stiffness of dampers and consequently increases or decreases their desire to absorb energy.
Semi-active seismic control of mid-rise structures using…
February 2014 IJST, Transactions of Civil Engineering, Volume 38, Number C1
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These dampers include magnetic polarized particles floating in oil and have the ability to change from fluid state to semi-solid matter with controllable obedience resistance in a few milliseconds or vice versa. This change is done by increasing or decreasing the intensity of magnetic field and as a result makes them helpful to controllable dampers.
The main benefit of these dampers, compared to other semi-active vibration absorbers, is that they have no moveable parts except pistons and thus are very simple and reliable. Two practical examples of dampers application in structures are: i) two dampers containing 30-ton magnetic fluid were used in Tokyo in 2001, to improve response of national science and innovation museum between floors 3 and 4, regarded as the first application of damper (containing magnetic fluid) in an actual scale building; ii) the first application of magnetic fluid dampers in bridges was implemented in a cable-stayed bridge on Dongting Lake in Hunan, China). a) Dynamic analysis by semi-active control
In the case where initial structures are controlled by dampers, system movement equation due to imposing control forces on linear structure is written as follows [11]:
M X C X K X Λf t M 1 X t (1)
f (t): control forces vector : Matrix 0, 1 (n×1) shows the location of active dampers at freedom degrees of structure (if damper
is installed on a stated freedom degree, corresponding element will be 1, otherwise, it is 0). In the case that backward–forward system is used to control structure, in which linear function
control force is in terms of location change vector, velocity (measured responses of the structure) and input stimulation, we have :
)2 ( f t C X t K X t M 1 X t
Where C , K , M are the matrices of corresponding control. By substituting corresponding control force to equation 1, we have:
)3 ( M X C ΛC X K ΛK X M M 1 X t
Comparing equations 1 and 3 shows the influence of forward control is modification of mechanical
specifications of the structure (stiffness and damping) in order to improve its seismic performance. In addition, choosing control matricesC ,K , M depends on the type of selected control algorithm. b) Modified Bouc–wen dynamic model
This model consists of a viscous damper tied with original Bouc-wen model in series and a spring which works in parallel with the whole system [12].
Produced force by damper in modified Bouc-wen model is described as follows:
)4( F αz C x y K x y K x x C y K x x
Where z is an evolutionary variable that accounts for the history dependence of the response. The evolutionary variables z and y are governed by:
z γ|x y|z|z| β x y |z| A x y (5)
Y
αz C x k x y (6)
In which K =accumulator stiffness; C =viscous damping at large velocities; C =viscous damping for force roll off at low velocities; K =stiffness at large velocities; x =relative displacement of one end of the
S. M. Zahrai and H. Salehi
IJST, Transactions of Civil Engineering, Volume 38, Number C1 February 2014
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MR damper; x=the piston velocity, y=internal displacement of the MR damper, and x =initial displacement of springK1.
To determine a model which is valid under fluctuating input voltage, the functional dependence of
the parameters on the input voltage must be determined. Since the fluid yield stress is dependent on input
voltage, α can be assumed as a function of the input voltage v. Moreover, as determined from the
experiment results, C , and c1 are also functions of the input voltage.
γ, β , and A are the parameters that control the shape of the hysteresis loops in Bouc-Wen yielding
element. Finally, α and n are other parameters that refer to the internal state z and determine its coupling
with the force f and its evolution.
To specify a model dependent on volatile magnetic field, relation of damper parameters with exerted
voltage should be determined. Since MR fluid yielding resistance changes directly with intensity of
magnetic field, parameter α in Eqs. (7) to (9) is regarded as a function of an exerted voltage.
Changes in obedience tension depend on linear input voltage and have initial value of non-zero at
voltage 0. This non-zero value is related with additive matter to MR fluid in order to sustain its
sedimentary endurance. In addition, fixed damping coefficients change with exerted voltages in a linear
manner. Therefore parameters,C0, C should be considered as functions of input current into the damper.
The relationship between MR dampers input current and input voltage using these coefficients is defined
as follows [13]:
)7 ( α α u α α u
)8 ( C C u C C u
)9( C C u C C
In these equations, value of u is calculated from the following differential equation, where V is input voltage to MR damper:
)10 (u η u V
The above Eq is necessary to model the dynamics involved in reaching rheological equilibrium and in
driving the electromagnet in the MR damper.
Other parameters (η, n ، A ، y ،β ، α ، αα ، x ، k ، k ، C ، C α ، C ، C α) are fixed coefficients that are
calculated by adjusting the behavior of MR damper obtained from the laboratory data.
Table 1 provides the optimized parameters for the dynamic model that were determined to best fit the
data based on the experimental results of a 20-ton MR damper [5]. In order to obtain the parameters for
the 100-ton (i.e., 1000kN) damper considered in this study, the experimental data of the 20-ton damper
have been linearly scaled up 5 times in the damper force.
Table 1. Parameters of the dynamic model for MR damper [5]
Value Parameter Value Parameter
46.2 kN/m α 110 kN.sec/m C
41.2 kN/m/V α 114.3 kN.sec/m/V C
164 m γ 0.01 kN/m k
164 m β 8359 kN.sec/m C
1107.2 A 7482.9 kN.sec/m/V C
2 n 0.485 kN/m k
100 sec η 0 m x
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Semi-active seismic control of mid-rise structures using…
February 2014 IJST, Transactions of Civil Engineering, Volume 38, Number C1
35
Table 4. The response reduction for the controlled models with lever mechanism subjected to the Kobe and Northridge earthquakes
Northridge Kobe
Absolute acceleration Drift Absolute acceleration Drift
23% 24% 6% 15% 9 (With 2 Dampers)
22% 26% 12% 19% 20 (With 3 Dampers)
6. CONCLUSION
In this paper, two models of 9 and 20-story buildings were first selected as case studies and then sample structures, optimum force determination process, control system and MR damper were simulated in a Simulink environment. In semi-active control case, clipped optimal algorithm was considered as control algorithm and optimal classic linear control method was used to determine control power.
1. With respect to the results obtained in this study, it is found that using MR damper is extremely effective in structural seismic response control. In maximum drift reduction perspective, the damper can be effective to reduce peak lateral drift about 12% to 36 %. For the above amounts the maximum reduction is for the Northridge earthquake with 36% and the least amount is related to the Kobe earthquake with 12% in the 20-story structure.
2. In maximum absolute acceleration reduction perspective, the damper can be effective in reducing structural peak acceleration 1- 21%. The maximum reduction is related to the 9-story structure with 21% and the least amount is related to the 20-story structure subjected to the Kobe, earthquakes while the peak accelerations in controlled and uncontrolled state are equal.
3. RMS displacement and absolute acceleration were reduced 33-71 % and 7-58%, respectively. 4. When moving MR dampers to the upper floors, they have better contribution to relative
displacement reduction. It is due to the fact that displacement and velocity are assumed as main input values and by increasing these amounts, better performance for damper would appear.
5. In structures with high number of floors, drift can be desirably decreased by increasing the number of dampers.
Two mechanisms are eventually offered to improve the function of dampers and their performance. Lever mechanism improved MR damper function 15-26% and 6-23%, respectively in maximum drift and absolute acceleration reduction perspectives, compared to normal condition.
The results of this limited investigation, therefore, indicate that the two proposed mechanisms for MR dampers can not only be effectively used to seismically control mid-rise structures, but also to reduce the required number of dampers.
Acknowledgments: The authors wish to acknowledge the support provided by college of engineering at the University of Tehran.
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