# Horizontal and Vertical Vibration Control of The Power Transmission Tower Cable Using Optimal TMDs

Document Type : Research Article

Authors

1 Earthquake Engineering Department, University of Tehran, Tehran, Iran

2 international institute of earthquake engineering and seismology

3 School Civil Engineering, University of Tehran, Tehran, Iran

Abstract

Using Tuned Mass Dampers (TMDs) is among the most typical methods for passive control of structures subjected to earthquake excitations. TMDs often reduce the displacement response of structures by influencing their first mode of vibration. The structure of these dampers consists of three main parameters: mass, damping, and stiffness. Since the parameters of TMDs are constant during the vibrations, optimal tuning of these parameters is very important. Finding the optimal values of the key parameters for a TMD in nonlinear structures using numerical methods involves numerous nonlinear dynamic analyses; therefore, the computations would be time-consuming. Recent studies, carried out on the application of the TMDs in the building structures, have mainly focused on reducing the lateral displacements of the building structures. However, in this research, the application of TMDs and their effectiveness were investigated for cables of the power transmission tower in both the lateral and vertical directions simultaneously. In order to numerically study the behavior of the power transmission tower, the structure of the telescopic steel tower was modeled in the OpenSEES software and to reduce the volume of computation, a numerical search method was used to find the optimal values for the parameters of the TMDs to minimize the lateral displacement in the middle of the cable span. The mass ratio of the TMDs was equal to 0.5% of the total mass of the structure. Using this mass ratio, numerical analyses of the system indicated that the maximum reduction of the lateral displacement in the middle of the cable mitigated due to implementing the TMDs is about 50% under the applied earthquakes with 0.5g maximum acceleration.

Keywords

Main Subjects

#### References

[1]  S. Ozono, J. Maeda, M. Makino, Characteristics of in-plane free vibration of transmission line systems, Engineering Structures, 10(4) (1988) 272-280.
[2]  L. Tian, X. Gai, Nonlinear seismic behavior of different boundary conditions of transmission line systems under earthquake loading, Shock and Vibration, (2016).
[3]  A. Simpson, Determination of the inplane natural frequencies of multispan transmission lines by a transfermatrix method, in:  Proceedings of the Institution of Electrical Engineers, IET, 1966, pp. 870-878.
[4]  W.M. Henghold, J.J. Russell, J. Morgan III, Free vibrations of cable in three dimensions, Journal of the Structural Division, 103(ASCE 12954 Proceeding) (1977).
[5]  F. Daneshjoo, Nonlinear Static Analysis of Cable Structures by Minimization of Total Potential Energy Including Instability Effects, scientia Iranica, 6(3)  0-0.
[6]  M. Gambhir, B.d. Batchelor, Parametric study of free vibration of sagged cables, Computers & Structures, 8(5) (1978) 641-648.
[7]  H. Jayaraman, W. Knudson, A curved element for the analysis of cable structures, Computers & Structures, 14(3-4) (1981) 325-333.
[8]  G.V. Rao, R. Iyengar, Seismic response of a long span cable, Earthquake engineering & structural dynamics, 20(3) (1991) 243-258.
[9]  T. Suzuki, K. Tamamatsu, T. Fukasawa, Seismic response characteristics of transmissions towers, in:  Proceedings of the 10th World Conference on Earthquake Engineering, 1992, pp. 4961-4967.
[10] R.S. Harichandran, Spatial variation of earthquake ground motion, what is it, how do we model it, and what are its engineering implications, Dept. of Civil and Environmental Engineering, Michigan State Univ., East Lansing, Mich,  (1999).
[11] A. Zerva, On the spatial variation of seismic ground motions and its effects on lifelines, Engineering Structures,16(7)(1994)534-546.
[12]  L. Tian, H. Li, G. Liu, Seismic response of power transmission tower-line system subjected to spatially varying ground motions, Mathematical Problems in Engineering, 2010 (2010).
[13]  T. Aziz, A. Ghobarah, M. El-Attar, Non-linear dynamics of transmission lines, in:  11th World Conference on Earthquake Engineering, 1996, pp. 1616-1620.
[14]  M.M. El-Attar, Nonlinear dynamics and seismic response of power transmission lines, 1997.
[15]  H.-N. Li, W.-L. Shi, G.-X. Wang, L.-G. Jia, Simplified models and experimental verification for coupled transmission tower–line system to seismic excitations, Journal of Sound and Vibration, 286(3) (2005) 569-585.
[16] G. Addala, D.N. Satyam, R.P. Kumar, Dynamic analysis of transmission towers under strong ground motion, in: 3rd International Earthquake Symposium, Bangladesh, Dhaka, 2010.
[17] Y. Liu, A.P. Tang, The present research situation and earthquake damage defensive measures of the transmission lines, in:  Proceedings of the 15th World Conference of Earthquake Engineering, 2012, pp. 24-28.
[18] L. Tian, W. Wang, R. Ma, L. Wang, Progressive Collapse Analysis of Power Transmission Tower Under Earthquake Excitation, The Open Civil Engineering Journal, 7(1) (2013).
[19]  S.M. Zahrai, S. Amirzadeh, Numerical Study of Using Diamond Metalic Damper for Seismic Retrofit of Mediumrise Steel Frames, Journal of Modeling in Engineering, 1(15) (2007).
[20] M. Mohebbi, H. Shabani, Optimal Design of Active Multiple Tuned Mass Dampers (AMTMDs) For Nonlinear Hysteretic Structures, Journal of Modeling in Engineering, 15(48) (2017) 151-163.
[21] F. Kordi, J. Alamatian, The TMD design based on complex stiffness theory, Journal of Modeling in Engineering, 15(51) (2017) 10-10.
[22] H. Valizade, Determination of Effective Geometric Parameters in Seismic Analysis of Steel Tapered Hollow Transmission Poles, Master of Science Thesis, Tarbiat Modares University,  (2016).
[23] S. Mazzoni, F. McKenna, M.H. Scott, G.L. Fenves, OpenSees command language manual, Pacific Earthquake Engineering Research (PEER) Center, 264 (2006).
[24] M. Markiewicz, Optimum dynamic characteristics of stockbridge dampers for dead-end spans, Journal of sound and vibration, 188(2) (1995) 243-256.