臺灣博碩士論文加值系統

隔震器與調諧質量阻尼器被廣泛用來防護結構，是現今常見的被動控制裝置。基底隔震器裝設於結構物底層，而該基底隔震器可視為一可運動桿件，其藉由運動的特性以改變建築物基本頻率，延長週期並使建築物頻率遠離地震的主要頻率範圍，以防護主要建築的結構安全。然而，此隔震裝置可運動的特性亦會使結構物的位移增加，因此在大多數地震設計規範中皆建議基底隔震器應安裝額外的黏性阻尼器裝置。調諧質量阻尼器是一種具有單一頻率的動力系統，大多裝設於高樓建築物中，幫助高樓抵抗強風和地震等外力。調諧質量阻尼器是透過與主結構物的共振效應，將輸入的能量轉移至調諧質量阻尼器上，進而減緩結構物在受到外力時的反應，以達到防護主結構的功能。綜合以上觀點，本篇的研究目的是利用反饋控制（Feedback control）與線性二次調節控制（Linear quadratic regulator, LQR）的演算法來設計基底隔震器和調諧質量阻尼器的設計程序。此新的設計方法的優勢為能同時設計被動控制裝置的勁度與阻尼係數，並且設計出符合需求的最佳基底隔震器與調諧質量阻尼器參數。
在基底隔震器設計程序中，上部結構物的質量、阻尼與勁度皆已知，且上部結構物與基底隔震層的質量比亦已事先給定。首先先利用線性二次調節控制演算法求得基底隔震器的勁度與阻尼係數，但此時的係數中還包括一未確定的權重值，此權重值為線性二次調節控制演算法公式中的權重參數。為了要確定最合適的勁度和阻尼係數，故需推算出性能曲線，利用此性能曲線來找取曲線中的最佳權重值，進而得到相對應的最佳勁度與阻尼係數，在此阻尼係數值由兩部分實現，一部分由鉛芯橡膠支承隔震器達成，而剩餘的阻尼係數部分則由附加的黏性阻尼器完成。除此之外，性能曲線可由H∞ 標準最小化得到，或是藉由模擬簡化為二自由度後的隔震結構物在地表運動下的反應所得到。最後，由設計出的最佳勁度與阻尼係數，配合前後降伏勁度比和設計位移的假設，即可設計鉛芯橡膠支承隔震器的雙線性模型，完成整體基底隔震器的設計。
在調諧質量阻尼器設計程序中，相似於同基底隔震器設計。主結構物的質量、阻尼與勁度皆已知，且主結構物與調諧質量阻尼器的質量比亦已事先給定。先利用動態輸出反饋控制演算法求得含有一未知權重值的調諧質量阻尼器的勁度與阻尼係數，此未知權重值為反饋控制中的參數。接著再選取最合適的權重值以得到最佳勁度與阻尼係數，而選取最合適的權重值方法是則利用傳遞函數找出其最大極點值(Pole)，並在不同權重值下的反應量值最小化，即可尋找出最合適的權重值，進而得到調諧質量阻尼器的最佳勁度與阻尼係數，完成調諧質量阻尼器的設計。
這項研究中，進行了數個數值實例來分別演示所提出的兩種設計程序，包括基底隔震器與調諧質量阻尼器的設計。除此之外，本篇內容還包含了在不同情況下的最佳參數變化情形和在不同外力與結構物下的數值模擬，且由模擬結果所顯示，所提出的基底隔震器設計與調諧質量阻尼器設計，皆有效地設計了相對應的被動控制裝置，並防護結構物免於強烈外力的破壞。

Seismic isolation and tuned mass damper (TMD) have been widely accepted as a passive control strategy for protection of structures. A base-isolated building employs a flexible element underneath the structure that shifts the fundamental frequency of the building away from the dominant frequencies of earthquakes. Due to the fact that the flexible element can introduce excessive displacements at base during severe earthquakes, additional viscous damping devices are recommended to be installed along with the isolation layer in most seismic design codes. On the other hand, a TMD system consists of a mass, spring, and damping device with a tuned frequency, thus the response of the structure can be regulated by the effect of resonance. In tall buildings, TMD is usually employed to reduce structural responses against strong winds and earthquakes. Therefore, the objective of this study is to develop new design procedures for base-isolated buildings and buildings with a tuned mass damper. In these design procedures, both stiffness and damping are concurrently determined using the feedback control algorithm, e.g., the linear quadratic regulator (LQR) control algorithm or linear quadratic Gaussian control algorithm.
In the seismic isolation design procedure, the mass, damping, and stiffness of a superstructure is assumed to be known, and a mass ratio between the superstructure and isolation layer is predetermined. The stiffness and damping coefficient of the base isolation can be obtained by the LQR control algorithm, while these two terms vary with the weighting selected in LQR. To determine the most appropriate stiffness and damping, a performance curve is generated in terms of maximum time- or frequency-domain responses. Note that the time-domain responses are obtained when the isolated building is subjected to spectrum-compatible ground motions. Subsequently, the stiffness and partial damping coefficient are achieved by lead-rubber bearings, while the remaining damping coefficient is realized by additional viscous dampers. Moreover, the detailed design of lead-rubber bearings is parameterized by a bi-linear model, consisting of the designed stiffness, damping coefficient, pre-to-post yielding stiffness ratio, and a target displacement.
In the TMD design procedure, the mass, damping, and stiffness of a primary structure is assumed to be known, and a mass ratio between the primary structure and TMD is predetermined. The stiffness and damping coefficient of the TMD can be obtained by the feedback control algorithm in accordance with different control objectives, and these two terms can be realized by varying the weightings selected in the control algorithm. Then, the maximum poles in transfer functions are employed to determine the most appropriate parameters, which result in the minimum poles among a number of transfer functions. Consequently, the optimal natural frequency and damping ratio of TMD system are achieved.
In this study, several numerical examples are carried out to demonstrate the proposed design procedures. Moreover, the numerical study also examines various sets of optimum parameters in different scenarios. As shown in the simulation results, the seismic isolation and TMD design procedures are quite effective for buildings against earthquakes.

ACKNOWLEDGEMENT i
摘要 ii
ABSTRACT iv
CONTENTS vi
LIST OF FIGURES ix
LIST OF TABLES xiii
Chapter 1 Introduction 1
1.1 Background 1
1.2 Literature review 2
1.3 Research motivation 5
1.4 Overview of thesis 7
Chapter 2 Design of Passive Control Systems Using Active Control Algorithms 9
2.1 Modeling of buildings with passive control systems 9
2.1.1 Base isolation 10
2.1.2 Tuned mass damper 10
2.2 Derivation of base isolation design 11
2.2.1 Structure with an output feedback system 11
2.2.2 Design using active control algorithm 12
2.3 Derivation of tuned mass damper design 13
2.3.1 Structure with an output feedback system 13
2.3.2 Design using active control algorithm 14
2.4 Summary 16
Chapter 3 Optimal Passive Control Systems 17
3.1 LQR-based design criteria 17
3.2 Optimal parameters of base isolation 18
3.2.1 Method 1: peak response performance 19
3.2.2 Method 2: H∞ norm minimization 21
3.2.3 Damping adjustment 22
3.2.4 Lead-rubber bearing parameters 23
3.3 Optimal parameters of tuned mass damper 25
3.3.1 Damped primary system 25
3.3.2 Method: pole minimization 27
3.4 Stability check 30
3.4.1 Base isolation 30
3.4.2 Tuned mass damper 32
3.5 Summary 34
Chapter 4 Optimal Passive Controller Parameters in Terms of Various Structures 43
4.1 Base isolation 43
4.2 Tuned mass damper 44
4.3 The suggested scope of optimal weighting q/r 46
4.4 Summary 47
Chapter 5 Design Examples 56
5.1 Main structure parameters 56
5.2 Base isolation 57
5.2.1 Method 1: Peak response performance 57
5.2.2 Method 2: H∞ norm minimization 60
5.2.3 Damping adjustment 61
5.2.4 Lead-rubber bearing parameters 62
5.3 Tuned mass damper 63
5.3.1 Method: response quantity minimization 63
5.4 Summary 66
Chapter 6 Performance Evaluation 67
6.1 Base isolation simulations under seismic excitation 67
6.1.1 Base isolated building subjected to seismic excitation 67
6.1.2 Floor responses of MDOF building 73
6.1.3 Comparison between two design methods 76
6.1.4 Comparison with the active control design results 79
6.2 TMD simulations under impulse and seismic excitations 86
6.2.1 TMD simulations under impulse excitation 86
6.2.2 TMD simulations under seismic excitation 89
6.3 Summary 90
Chapter 7 Conclusions and Recommendations 91
7.1 Conclusions 91
7.2 Future Studies 93
REFERENCE 94
APPENDIX 98
Linear–quadratic regulator (LQR) 98
RESUME 99
RESUME(IN CHINESE) 100

[1]Abe, M. (1996) "Semi‐active tuned mass dampers for seismic protection of civil structures." Earthquake Engineering and Structural Dynamics, 25,743-749.
[2]Bakre, S. V. and Jangid, R. S. (2007). "Optimum parameters of tuned mass damper for damped main system." Structural Control and Health Monitoring, 14, 448–470.
[3]Bekdaş, G. and Nigdeli, S. M. (2011) "Estimating optimum parameters of tuned mass dampers using harmony search" Engineering Structures, 33, 2716–2723.
[4]Buckle, I., Nagarajaiah, S., and Ferrell, K. (2002). "Stability of elastomeric isolation bearings: Experimental study." ASCE Journal of Structural Engineering, 128(1), 3-11.
[5]Chang, C. C. and Yang, T. Y.(1995) "Control of buildings using active tuned mass dampers." ASCE Journal of Engineering Mechanics, 121(3), 355-366.
[6]Chang, C.M. and Spencer, B.F., Jr. (2010). "Active base isolation of buildings subjected to seismic excitations." Earthquake Engineering and Structural Dynamics, 39(13), 1493-1512.
[7]Chang, C.M., Spencer, B.F., Jr., and Shi, P. (2014). "Multiaxial active isolation for seismic protection of buildings." Structural Control and Health Monitoring, 21(4), 484-502.
[8]Chen, G. and Wu, J. (2001) "Optimal placement of multiple tune mass dampers for seismic structures." ASCE Journal of Structural Engineering, 127(9), 1054-1062.
[9]Chung, L.L., Reinhorn, A.M., and Soong, T.T. (1988). "Experiments on active control of seismic structures." ASCE Journal of Engineering Mechanics, 114(2), 241-256.
[10]Den Hartog JP. (1956). Mechanical Vibrations (4th edn). McGraw-Hill: New York.
[11]Dyke, S.J., Spencer, B.F., Jr., Quast, P., Kaspari, D.C., and Sain, M.K. (1994a). "Implementation of an active mass driver using acceleration feedback control." Microcomputers in Civil Engineering: Special Issue on Active and Hybrid Structural Control, 11, 305-323.
[12]Dyke, S.J., Spencer, B.F., Jr., Quast, P., Sain, M.K., Kaspari, D.C., and Soong, T.T. (1994b). "Experimental verification of acceleration feedback control strategies for an active tendon system." NCEER Rep. 94-0024, State Univ. of New York at Buffalo, New York.
[13]Fenz, D.M. and Constantinou, M.C. (2006). "Behaviour of the double concave friction pendulum bearing." Earthquake Engineering and Structural Dynamics, 35(11), 1403–1424. D
[14]Fenz, D.M. and Constantinou, M.C. (2008). "Spherical sliding isolation bearings with adaptive behavior: experimental verification." Earthquake Engineering and Structural Dynamics, 37(2), 185–205.
[15]Hrovat, D., Barak, F., and Rabins, M. (1983) "Semi‐active versus passive or active tuned mass dampers for structural control." ASCE Journal of Engineering Mechanics, 109(3), 691-705.
[16]Inaudi, J. A., Kelly, J. M. (1990). "Active isolation." U.S. National Workshop on Structural Control Research, Los Angeles, 125-130.
[17]International Conference of Building Officials. (1997). "Uniform building code." Earthquake regulation for seismic-isolated structures, 2, Appendix, Chap. 16, Whittier, CA.
[18]Kelly, J.M. (1997). Earthquake resistant design with rubber. 2nd ed., Springer, New York.
[19]Kelly, J.M. (1999). "The role of damping in seismic isolation." Earthquake Engineering and Structural Dynamics, 28, 3-20.
[20]Kelly, J.M., Leitmann, G., and Soldatos, A.G. (1987). "Robust control of base-isolated structures under earthquake excitation." Journal of Optimization Theory and Applications, 53, 159-180.
[21]Kwok, K. C. S. and Samali, B. (1995) "Performance of tuned mass dampers under wind loads." Engineering Structures, 17(9), 655-67.
[22]Mohamed, A. R. (1984). "Optimal design of active TMD for buildings control." Building and Environment, 19(3), 191-195.
[23]Nagarajaiah, S. and Ferrell, K. (1999). "Stability of elastomeric seismic isolation bearings." ASCE Journal of Structural Engineering, 125(9), 946-954.
[24]Narasimhan, S., Nagarajaiah, S., Johnson, E.A., and Gavin, H.P. (2006). "Smart base-isolated benchmark building. Part I: Problem definition." Structural Control and Health Monitoring, 13(2-3), 573-588.
[25]Nishimura, I., Kobori, T., Sakamoto, M., Koshika, N., Sasaki, K., and Ohrui, S. (1992) "Active tuned mass damper." Smart Materials and Structures, 1, 306-311.
[26]Samali, B. and Al-Dawod, M. (2003) "Performance of a five-storey benchmark model using an active tuned mass damper and a fuzzy controller." Engineering Structures, 25, 1597–1610.
[27]Sladek, J. R. and Klingner, R. E. (1983) "Effect of tuned-mass dampers on seismic response." ASCE Journal of Structural Engineering, 109(8), 2004-2009.
[28]Soong, T.T. (1988). "Active structural control in civil engineering." Engineering Structures, 10, 74-84.
[29]Soong, T.T. and Constantinou, M.C. (1994). "Passive and active structural vibration control in civil engineering." Springer-Verlag New York, Inc, New York.
[30]Soong, T.T. and Manolis, G.D. (1987). "Active structures." ASCE Journal of Structural Engineering, 113, 2290-2301.
[31]Spencer, B.F., Jr., Suhardjo, J., and Sain, M.K. (1994). "Frequency domain optimal control strategies for aseismic protection." ASCE Journal of Engineering Mechanics, 120(1), 135-158.
[32]Tsai, H. C. and Lin, G. C. (1993). "Optimum tuned-mass dampers for minimizing steady -state response of support-excited and damped systems. " Earthquake Engineering and Structural Dynamics, 22, 957-973.
[33]Varadarajan, N. and Nagarajaiah, S. (2004) "Wind response control of building with variable stiffness tuned mass damper using empirical mode decomposition/Hilbert transform." ASCE Journal of Engineering Mechanics, 130(4), 451-458.
[34]Warn, G.P, and Ryan, K.L. (2012). "A review of seismic isolation for buildings: Historical development and research needs." Building, 2(3), 300-325.
[35]Yang, J.N., Li, Z., Liu, S.C. (1992). "Stable controllers for instantaneous optimal control." ASCE Journal of Engineering Mechanics, 118(8), 1612-1630.
[36]Yoshioka, H., Ramallo, J. C., Spencer, B. F., Jr. (2002). ""Smart" base isolation strategies employing magnetorheological damper." ASCE Journal of Structural Engineering, 128(5), 540-551.