New approach is presented for controlling the structural vibrations. The proposed active control method is based on structural dynamics theories in which multiactuators and sensors are utilized. Each actuator force is modeled as an equivalent viscous damper so that several lower vibration modes are damped critically. This subject is achieved by simple mathematical formulation. The proposed method does not depend on the type of dynamic load and it could be applied to control structures with multidegrees of freedom. For numerical verification of proposed method, several criterions such as maximum displacement, maximum kinetic energy, maximum drift, and time history of controlled force and displacement are evaluated in two- , five- , and seven-story shear buildings, subjected to the harmonic load, impact force, and the Elcentro base excitation. This study shows that the proposed method has suitable efficiency for reducing structural vibrations. Moreover, the uncertainty effect of different parameters is investigated here. 1. Introduction Smart structures are systems that can teach and protect themselves against the external excitation such as wind and earthquake. Analyzing and designing of smart structures is based on set of sciences including materials science, applied mechanics, electronics, biomechanics, and structural dynamics. In this procedure, maintaining the structural performance against the external hazards is a very important issue called control system. Many studies have been performed in the field of structural control. These methods can be categorized into three groups, that is, passive, semiactive, and active procedures [1]. Due to the simplicity, low cost of assembly and no need to the external power, the passive control systems are numerous. However, the constant control feature makes these systems fail during the earthquakes. In other words, these systems are designed to work only for a certain excitation and limited frequency bound. The passive control system tries to remove the kinetic energy from the structure. Because of the mentioned constraints in passive algorithms, active control is highly regarded systems to cope with the earthquake. These techniques have suitable efficiency in different excitation, so that they could exactly sense and adopt the structural vibrations. To achieve this goal, each active control method is constructed based on algorithm, which verifies its efficiency and accuracy. The application of such systems began in 1989. In these systems an external power source is required so that this applied force affects
References
[1]
S. Akutagawa, M. Otsuki, and Y. Kitagawa, “Hybrid control system with optimal fuzzy logic and genetic algorithm for high-rise buildings,” in Proceedings of the 13th World Conference on Earthquake Engineering, Vancouver, Canada, 2004.
[2]
R. Guclu and H. Yazici, “Vibration control of a structure with ATMD against earthquake using fuzzy logic controllers,” Journal of Sound and Vibration, vol. 318, no. 1-2, pp. 36–49, 2008.
[3]
G. Chen and J. Wu, “Optimal placement of multiple tune mass dampers for seismic structures,” Journal of Structural Engineering, vol. 127, no. 9, pp. 1054–1062, 2001.
[4]
F. Rüdinger, “Tuned mass damper with nonlinear viscous damping,” Journal of Sound and Vibration, vol. 300, no. 3–5, pp. 932–948, 2007.
[5]
N. Hoang, Y. Fujino, and P. Warnitchai, “Optimal tuned mass damper for seismic applications and practical design formulas,” Engineering Structures, vol. 30, no. 3, pp. 707–715, 2008.
[6]
D. S. Bayard, F. Y. Hadaegh, and D. R. Meldrum, “Optimal experiment design for identification of large space structures,” Automatica, vol. 24, no. 3, pp. 357–364, 1988.
[7]
T. F. Kamada, T. Fujita, T. Hatayama et al., “Active vibration control of flexural-shear type frame structures with smart structures using piezoelectric actuators,” Smart Materials and Structures, vol. 7, no. 4, pp. 479–488, 1998.
[8]
J.-H. Han and I. Lee, “Optimal placement of piezoelectric sensors and actuators for vibration control of a composite plate using genetic algorithms,” Smart Materials and Structures, vol. 8, no. 2, pp. 257–267, 1999.
[9]
A. M. Sadri, J. R. Wright, and R. J. Wynne, “Modelling and optimal placement of piezoelectric actuators in isotropic plates using genetic algorithms,” Smart Materials and Structures, vol. 8, no. 4, pp. 490–498, 1999.
[10]
F. Gao, Y. Shen, and L. Li, “Optimal design of piezoelectric actuators for plate vibroacoustic control using genetic algorithms with immune diversity,” Smart Materials and Structures, vol. 9, no. 4, pp. 485–491, 2000.
[11]
H. Zhang, B. Lennox, P. R. Goulding, and A. Y. T. Leung, “Float-encoded genetic algorithm technique for integrated optimization of piezoelectric actuator and sensor placement and feedback gains,” Smart Materials and Structures, vol. 9, no. 4, pp. 552–557, 2000.
[12]
Z.-J. Cao, B.-C. Wen, and G.-W. Meng, “Topological optimization of placements of the piezoelectric actuator of intelligent structures,” Journal of Northeastern University, vol. 21, no. 4, pp. 383–385, 2000.
[13]
M. K？gl and E. C. N. Silva, “Topology optimization of smart structures: design of piezoelectric plate and shell actuators,” Smart Materials and Structures, vol. 14, no. 2, pp. 387–399, 2005.
[14]
V. Sethi and G. Song, “Multimode vibration control of a smart model frame structure,” Smart Materials and Structures, vol. 15, no. 2, pp. 473–479, 2006.
[15]
J. V. Song, S. E. Johnson, and B. N. Agrawal, “Ambient active vibration control of a space truss using a lead zirconate stack actuator,” in Proceedings of the Institution of Mechanical Engineers, vol. 215, p. 355, 2001.
[16]
T. K. Datta, “A state of the art review on active control of structures,” 22nd ISET Annual Lecture, ISET Journal of Earthquake Technology, Paper no. 430, vol. 40, no. 1, pp. 1–17, 2003.
[17]
D. S. Michael and C. C. Michael, “Semi-active control systems for seismic protection of structures: a state-of-the-art review,” Engineering Structures, vol. 21, no. 6, pp. 469–487, 1999.
[18]
J.-N. Yang, “Application of optimal control theory to civil engineering structures,” Journal of Engineering Mechanics Division, vol. 101, no. 6, pp. 819–838, 1975.
[19]
M. Abdel-Rohman and H. H. Leipholz, “Active control of flexible structures,” Journal of Structural Division, vol. 104, no. 8, pp. 1251–1266, 1978.
[20]
L. Meirovitch and H. Oz, “Modal space control of distributed gyroscopic systems,” Journal of Guidance, Control, and Dynamics, vol. 6, pp. 20–25, 1980.
[21]
J. N. Yang, A. Akbarpour, and P. Ghaemmaghami, “New optimal control algorithms for structural control,” Journal of Engineering Mechanics, vol. 113, no. 9, pp. 1369–1386, 1987.
[22]
A. M. Reinhorn, G. D. Manolis, and C. Y. Wen, “Active control of inelastic structures,” Journal of Engineering Mechanics, vol. 113, no. 3, pp. 315–333, 1987.
[23]
Z. Wu, R. C. Lin, and T. T. Soong, “Non-linear feedback control for improved peak response reduction,” Smart Materials and Structures, vol. 4, no. 1, pp. A140–A148, 1995.
[24]
J. N. Yang, Z. Li, and S. C. Liu, “Instantaneous optimal control with acceleration and velocity feedback,” Probabilistic Engineering Mechanics, vol. 6, no. 3-4, pp. 204–211, 1991.
[25]
J. N. Yang, J. C. Wu, A. K. Agrawal, and Z. Li, “Sliding mode control for seismic-excited linear and non-linear civil engineering structures,” Technical Report NCEER 94-0017, 1994.
[26]
M. Abdel-Rohman, “Structural control considering time-delay effect,” Transactions of the Canadian Society for Mechanical Engineering, vol. 9, no. 4, pp. 224–227, 1985.
[27]
A. Tani, H. Kawamura, and S. Ryu, “Intelligent fuzzy optimal control of building structures,” Engineering Structures, vol. 20, no. 3, pp. 184–192, 1998.
[28]
M. H. Korayem and A. Alipour, “Dynamic analysis of moving cables with variable tension and variable speed,” International Journal of Engineering, Transactions B: Applications, vol. 23, no. 2, pp. 157–168, 2010.
[29]
J. Alamatian and J. Rezaeepazhand, “A simple approach for determination of actuator and sensor locations in smart structures subjected to the dynamic loads,” International Journal of Engineering, Transactions A, vol. 24, no. 4, pp. 341–349, 2011.
[30]
V. D. Rao, Matlab an Introduction and Applications, New Age Publishers, 2010.
[31]
R. W. Clough and J. Penzien, Dynamics of Structures, McGraw Hill, New York, NY, USA, 1993.
