Passive Vibration Control Synthesis of Power Transmission Tower Using ANSYS: Part I - Control of Free Vibration

Transcription

1 Passive Vibration Control Synthesis of Power Transmission Tower Using ANSYS: Part I - Control of Free Vibration Huang Li-Jeng 1, Lin Yi-Jun 1 Associate Professor, Department of Civil Engineering, National Kaohsiung University of Applied Science, 80778, Taiwan, Republic of China Master Student, Institute of Civil Engineering, National Kaohsiung University of Applied Science, 80778, Taiwan, Republic of China Abstract This paper is aimed at passive vibration control synthesis of power transmission tower due to initial displacement using ANSYS. Finite element formulation of passively controlled dynamic system of power transmission tower is built-up. The Tower frame is modelled with BEAM-4 elements of ANSYS. Three passive control strategies are attempted for vibration suppression: (1) added mass: four concentrated masses installed on the four corners of top level of the transmission tower (modeled with MASS-1 elements); () added damping: a pair of diagonal dashpots embedded on the both sides of tower frame from bottom to top (modeled using COMBIN-14 elements); (3) added stiffness: a pair of diagonal steel tendons embedded on the both sides of tower frame from bottom to top (modeled using LINK-10 elements). APDL programming commands are coded for passive vibration control tests. A typical 345 KV self-supporting transmission tower structure modeled by totally 1179 BEAM- 4 elements along with 495 nodes is taken as numerical example. A Results show that additional damping is the most effective scheme for passive vibration control for typical power transmission tower in free vibration due to initial displacement Keywords ANSYS, APDL, Free Vibration, Passive Vibration, Control, Power Transmission Tower I. INTRODUCTION Electric power transmission towers are usually built in modern cities and towns for energy supply, industrial manufacture and economic development. There are many design types of electric power transmission tower conveying 110 to 750 kv, e.g. self-gravity supported and cable-stayed; among the self-gravity supported types there are a lot of types of shapes. A typical electric power transmission tower employed by Taiwan Power Company are designed with the following data: 345 KV, Type-B tower with height 36. m and base width 11.8m, built with structural members: JIS GB 101 SS55 H, JIS G3101 SS41 H, gusset plate of JIS G3101 5S41, and bolts of ASTM A394,O 11/16,O 13/16. The features of electric power transmission towers are light weight, flexible, low natural frequencies and damping ratios and therefore sensitive to horizontal loads, e.g. wind and earthquake excitations. Understanding the dynamic characteristics of electric power transmission towers is very important task for the structural engineers when design a power supply system. Basically power transmission towers are designed in a form of space truss structures or space frame structures if members are connected with gusset plates. The total structure is a highly statically indeterminated construction which is stable under self-weight and in general, using L-shape structural steel members and connected by the use of high tension bolts can leads to a strong horizontal drift resisting structure when subjected to wind or earthquake loads. However, a wind loads with Beaufort Number greater than 8 (wind speed ranges 17.~0.7 m/sec) or seismic excitation with magnitude over 6 might induce instantaneous collapse or long-term fatigue failure. ASCE Committee (198, 1991) had reported manual for loadings for electrical transmission structures [1, ]. Freitas and Ribeiro (199) conducted elasto-plastic analysis of space truss [3] while Yan et al. (1996) considered geometric nonlinearity [4]. 3

2 Albermani (003) studied structural behavior of transmission towers [5]. Li et al. (004) investigated effect of lines on tower system [6] while Lei and Chien (005) conducted seismic analysis of transmission towers considering both geometric and material nonlinearities [7], Shi et al. (006) conducted shaking table tests of Coupled System of Transmission Lines and Tower [8]. On the application of numerical analysis to transmission tower systems, Chao and Kin (004) investigated the effects of three different structural models including space truss, space frame and beam-rod structure, on the dynamic behavior of tower frame structures [9]; Zhu et al. (006) employed SAP000 and FEM to study the dynamic responses of power transmission tower under different seismic ground accelerations considering the randomness of earthquakes [10]; Luo et al. (010) employed ANSYS to study the dynamic properties of drum-shape power transmission tower using 3D FEM model and obtain natural frequencies, natural modes as well as acceleration responses due to seismic excitation [11]. Recently, Huang and Lin (014) reported a paper on the free vibration and seismic responses of power transmission tower using ANSYS and SAP000 [1]. However, when the structure produces excessive displacement, velocity or acceleration due to dynamic loads, passive or active control strategies can be designed for vibration suppression. These techniques employed for vibration control of bridges and buildings have been introduced in textbook [13]. On the application of active control schemes to power transmission-line system, Chen et al. (007) studied the use of magneto-rheological dampers [14], visco-elastic damper [15]. Xu and Chen (008), Chen et al. (010) proposed the use of friction dampers [16-18]. Zhang et al. (013) considered the use of pounding TMD [19]. Recently, Chen et al. (014) presented a state-of-the-art review on the dynamic response and vibration control of the transmission tower-line system [0]. It is well know that though active control techniques possess advantages of high efficiency responses and feedback responses the high cost and sluggish servomechanism usually makes these techniques less applicable in practice. On the other hand, passive control strategies are conservative, confident and usually more inexpensive. This makes passive control strategies seem to be more appropriate employed for vibration control of power transmission towers. This paper presents numerical modeling and structural vibration control analysis of a power transmission tower. Finite element method is adopted for numerical modelling and ANSYS was employed for analysis. A typical numerical example of 345KV self-supporting transmission tower was considered, totally 1179 three-dimensional beam elements (BEAM-4 element) along with 495 nodes are employed for modelling the transmission tower structure. Three passive vibration control schemes, added-mass, added-damping and added-stiffness, are modelled by the use of MASS-1, COMBIN-14, and LINK-10 elements, respectively. Vibration control synthesis of power transmission tower due to initial displacement is conducted. Time history of dynamic response and maximal displacements, velocities and accelerations are reported and discussed. II. DYNAMICS MODEL OF A POWER TRANSMISSION TOWER FRAME A. Problem Description A typical 345 KV self-supporting transmission tower structure is shown in Fig. 1 along with Cartesian coordinate system (x is positive in the right hand direction, y is positive upwards, and z is positive pointed out of plane). The vertical tower frame is with 50 m height and rectangular base with width 10. m. For convenience of analysis we isolated the tower structure from the connected power conveying cables. B. Basic Assumptions For the structural analysis of the transmission tower frame we employed the following hypotheses: 1) all the members are considered to be threedimensional thin beams and only flexural and stretching behaviors are included, Euler-Bernoulli assumptions are employed; ) shear deformation and rotary inertia of members are neglected; 3) damping of system is neglected; 4) all the members are perfectly connected; 5) effect of power conveying cables if isolated; 6) stress-strain relationship of structural members is linearly elastic; 7) tower frame is rigidly connected on the ground. 33

3 C. Finite Element Models In this research we employ ANSYS to build up the finite element model of the transmission tower structure using BEAM-4 element and the results are compared with those obtained from SAP000. The shape functions for displacements in a typical BEAM4 element and the associated element inertia matrix, element stiffness matrix, element loading vector can be referred to [1]. D. Dynamic Equations of Transmission Tower System After assemblage of the element mass and stiffness matrices and loading vectors, we obtain the global systematic matrices and vectors and then enforce the prescribed boundary conditions (e.g. the fixed ends at the bottom of the vertical supporting frames) we can express the equations of motion of the finite element model of the transmission tower as [ Ms ]{ x [ K s ]{ x( { f (1) Where [ M s ] and [ Ks ] denotes the global inertia and stiffness matrix of the transmission tower, respectively; { x and { x denotes the acceleration vector and displacement vector, respectively, and { f denotes the external loading vector. E. Passive Controlled Dynamic Equations of Transmission Tower System If we add additional inertia, damping or stiffness elements onto the overall power transmission tower, the dynamic system equations can be described as ([ M s ] [ Ma ]){ x( [ C a ]{ x ([ K s ] [ K a ]){ x( {0} Where [ M a ], [ C a ], [ Ka ] denotes mass, damping and stiffness matrices corresponding to additional masses, additional damping and additional tendons for passively vibration control, respectively. If the initial displacements {x(0)} or initial velocities {x (0)} are prescribed, the dynamic responses can be evaluated via direct integration in time domain such as Newmark- method, Wilson- method, state-space method or method of normal mode superposition, etc. When ANSYS is employed, the analysis method can be decided and the time increment can be adjusted. () 34 These control strategies can be designed separately as follows: (a) Effect of Additional Mass: ([ Ms ] [ M a ]){ x [ K s ]{ x( {0} (3a) from which we can see the effect of added masses might reduce the acceleration responses if all another dynamic properties kept fixed. In this investigation we design the additional masses to be four concentrated masses installed on the four corners of top level of the transmission tower. In the analysis using ANSYS, the dashpots are modeled using MASS-1 elements. The mass ratio m a / ms is considered to be 0.1, 0.5, 0.5, respectively. (b) Effect of Additional Damping: [ Ms ]{ x [ C a ]{ x [ K s ]{ x( {0} (3b) from which we can see the effect of added damping makes the dynamic system from undamped one to damped one and the amplitude of dynamic system will decay with time. In this research we design the additional damping to be a pair of diagonal dashpots embedded on the both sides of tower frame from bottom to top. In the analysis using ANSYS, the dashpots are modeled using COMBIN-14 elements. The damping coefficient of the dashpots are varied from 10000, to N s / m, respectively. (c) Effect of Additional Stiffness: [ Ms]{ x ([ K s ] [ K a ]){ x( {0)} (3c) from which we can see the effect of added stiffness is to shorten the periods (or increase the frequencies) of the dynamic system. For static problems the displacement will be reduced, but for dynamic cases the responses depends on the additional weight due to additional members. In this study we design the additional stiffness to be a pair of diagonal steel tendons embedded on the both sides of tower frame from bottom to top. In the analysis using ANSYS, the dashpots are modeled using LINK-10 elements. Three different sizes of steel rods with effective area of m, m, m are taken into account.

4 III. NUMERICAL EXAMPLE AND RESULTS A. Case Description We consider a typical transmission tower frame with totally height 50 m and base width 10. m, made of the Q345 L-shape structural steel members with the sizes 0.17m 0.17m m and properties: A 6 4 s m, I x m, I m 4 y, E s 06 GPa, 7850kg / m 3 s. Totally 1184 BEAM4 elements with 495 degrees of freedom (each member has 6 degrees of freedom) are employed in the ANSYS modelling of transmission tower frame. Overall space frame is fixed onto rigid ground. B. Free Vibration Analysis The natural frequencies and corresponding vibration modes of the finite element model of typical power transmission tower can be obtained using ANSYS and verified by the use of SAP000. The first leading 6 natural frequencies (f = ω/π) and natural periods (T=1/f) are summarized in Table 1. The corresponding first leading 6 various vibration modes obtained from ANSYS and compared with those obtained from SAP000 are shown in [1]. C. Passively Control of Free Vibration Excited from Initial Displacements The analysis is conducted using ANSYS along with the APDL coded by the authors as shown in Appendix. Numerical results are discussed as follows: (1) Additional Masses: Typical results of effect of added-mass on the acceleration responses of free vibration of power transmission tower can be observed in Fig.. The results of maximal dynamic responses due to additional masses are summarized in Table II. It can be noticed that maximal acceleration (and maximal velocity) is reduced by the additive masses along with smaller vibrating frequency. () Additional Damping: Typical results of effect of additional damping on the velocity responses of free vibration of power transmission tower can be observed in Fig. 3. The results of maximal dynamic responses due to additional dashpot are summarized in Table III. It can be noticed that maximal velocity (and maximal acceleration) is reduced by the additive damping along with smaller decaying vibrating amplitudes. (3) Additional Stiffness: Typical results of effect of additional steel tendon on the displacement responses of free vibration of power transmission tower can be observed in Fig. 4. The results of maximal dynamic responses due to additional tendon are summarized in Table IV. Because we didn t consider the additional tendon be pre-stressed, the effect of restoring displaced tower frame is not obvious. The steel tendons or cables for vibration control maybe more effective if they are installed from tower to the fixed ground on both sides of tower. IV. CONCLUSION Finite element modelling using ANSYS and structural vibration control analysis of a typical power transmission tower due to initial displacement has been conducted. A typical numerical example of 345KV self-supporting transmission tower was modelled using totally 1179 threedimensional beam elements (BEAM-4 element) along with 495 nodes are employed for modelling the transmission tower structure. Three passive vibration control schemes, added-mass, added-damping and added-stiffness, are modelled by the use of MASS-1, COMBIN-14, and LINK-10 elements, respectively. Time history of dynamic response and maximal displacements, velocities and accelerations are reported and discussed. The results indicated that among three passive control strategies technique of added damping is the most effective for seismic responses of power transmission tower. REFERENCES [1] ASCE Committee on Electrical Transmission Structures, 198. Loadings for Electrical Transmission Structures, ASCE, J. Struct. Div., 108(5), [] ASCE, Guidelines for Electrical Transmission Line Structural Loading, ASCE, Manuals and Reports on Engng Practice, No. 74. [3] J. A. T. De Freitas, and A.C.B.S. Ribeiro, 199. Large Displacement Elasto-plastic Analysis of Space Trusses, Int. J. Computers and Structures, 5, [4] H. Yan, Y. J. Liu, and D. S. Zhao, Geometric Nonlinear Analysis of Transmission Tower with Continous Legs, J. Advances in Steel Struct., 5,

5 [5] F. G. Albermani, A, Kitipornchai and S.Numerical, 003. Simulation of Structural Behavior of Transmission Towers, J. Thin-Walled Struct. 41, [6] H. N. Li, W. L. Shi and L. G. Jia, 004. The Effect of Lines on Transmission Tower System and Simplified Calculation Method, J. Vib and Shock, 3(), 1-7. [7] Y. H. Lei and Y. L. Chien, 005. Seismic Analysis of Transmission Towers Considering Both Geometric and Material Nonlinearities, Tamkang J. of Sci. and Engng., 8(1), 9-4. [8] W. L. Shi, H. N. Li, and L. G. Jia, 006. Shaking Table Test of Coupled System of Transmission Lines and Tower, J. Engng Mech., 3(5), [9] D. S. Chao and S. A. Kin, 004. Effection of Finite Element Models for Dynamic Characteristics Analysis of Transmission Tower Structure, J. Spec. Struct., 1(3). [10] B. L. Zhu, W. T. Hu, and C. X. Li, 006. Estimating seismic responses of transmission towers by finite element method, J. Earth. Engng. and Engng. Vib, 6(5). [11] L. Luo, B. Y. Liu, and Z. H. Niu, 010. Research on the Dynamic Properties of Drum-Type Transmission Tower, J. Indus. Archi., S1. [1] L. J. Huang and Y. J. Lin, 014. Free Vibration and Seismic Responses of Power Transmission Tower Using ANSYS and SAP000, Int.. J. Emerg. Tech. and Advan. Engng, 4(8), [13] H. H. E. Leipholz and M. Abdel-Rohman, Control of Structures, Martinus Nijhoff Publishers. [14] B. Chen, J. Zeng and W. L. Qu, 007. Wind-Induced Vibration Control of Transmission Tower Using Magneto-rheological Dampers, Proc. Int. Con. Heal. Monit. Struct. Mat. and Env, 1, 33-37, Nanjing, China. [15] B.Chen, J. Zheng and W. L. Qu, 007. Practical Method for Wind- Resistant Design of Transmission Tower-Line System y Using Visco-elastic Dampers, Proc. nd Int. Con. Struct. Cond. Assess., Monit. and Impr, , Changsha, China. [16] Y. L. Xu and B. Chen, 008. Integrated Vibration Control and Health Monitoring of Building Structures Using Semi-Active Friction Dampers: Part I-Methodology, Engng. Struct., 30(7), [17] B. Chen and Y. L. Xu, 008. Integrated Vibration Control and Health Monitoring of Building Structures Using Semi-Active Friction Dampers: Part II-Numerical Investigation, Engng. Struct., 30(3), [18] B. Chen J. Zeng and W. L. Qu, 010. Vibration Control and Damage Detection of Transmisssion Tower-Line System Under Earthquake by Using Friction Dampers, Proc. 11 th Int. Symp. Struct. Engng., , Guangzhou, China. [19] P. Zhang, G. B. Song, H. N. Li and Y. X. Lin, 013. Seismic Control of Power Transmission Tower Using Pounding TMD, J. Engng. Mech., 139(10), [0] B. Chen, W. H. Guo, P. Y. Li and W. P. Xie, 014. Dynamic Response and Vibration Control of the Transmission Tower-Line System: A State-of-the-Art Review, The Sci. World J., Article ID [1] E. Hinton and D. R. J. Owen, An Introduction to Finite Element Computations, Pineridge Press, U.K. [] G.. C. Hart and K. Wong, 000. Structural Dynamics for Structural Engineers, John-Wiley & Sons, Inc. 36 Appendix: APDL for dynamic response /SOLU ANTYPE, 4, NEW TRNOPT, FULL OUTRES, ALL, ALL D, 467, ALL,,,,,, D, 47, ALL,,,,,, D, 480, ALL,,,,,, D, 488, ALL,,,,,, TIMINT, OFF D, 40, UZ, 0.1 TIME, NSUBST, KBC, 1 LSWRITE TIMINT,ON DDELE, 40, UZ DELTIM, 0.0 TIME, LSWRITE LSSOLVE, 1, FINISH /POST6 NSOL,,40,U,Z,UZ DERIV,3,,1,,VZ40,,, DERIV,4,3,1,,ACCZ40,,, /GRID, 1 /AXLAB, X, TIME (s) /AXLAB, Y, DISPLACEMENT (m) PLVAR, /AXLAB, Y, VELOCITY (m/s) PLVAR, 3 /AXLAB, Y, ACCELERATION (m/s^) PLVAR, 4 PRVAR,, 3, 4 FINISH

6 TABLE I Natural frequencies and periods for a typical TRANSMISSION tower FRAME Frequencies (Hz) ANSYS Frequencies(Hz) SAP000 Periods (sec) ANSYS Periods (sec) SAP000 Discrepancies (%) ( ( SAP- ANSYS)/ANSYS *100% Mode Mode Mode Mode Mode Mode TABLE II MAXIMAL DYNAMIC RESPONSES OF POWER TRANSMISSION TOWER FRAME WITHOUT AND WITH ADDED-MASSES Ma (kg) u max ( m) u max ( m/ s) u max 0 (uncontrolled) ( m / s ) TABLE III MAXIMAL DYNAMIC RESPONSES OF POWER TRANSMISSION TOWER FRAME WITHOUT AND WITH ADDED-DAMPINGS Ca ( N s / m) u max ( m) u max ( m/ s) u max 0 (uncontrolled) ( m / s ) TABLE IV MAXIMAL DYNAMIC RESPONSES OF POWER TRANSMISSION TOWER FRAME WITHOUT AND WITH ADDED- (m ) u max ( m) u max ( m/ s) A sa u max 0 (uncontrolled) ( m / s ) TENDON 37

7 8 m 6 m 8 m 8 m 4.45 m International Journal of Emerging Technology and Advanced Engineering 10.4 m 6.38 m 6.88 m 7.45 m z y x a g (t) 10. m Figure 1 Schematic of a typical transmission tower frame using ANSYS and SAP000 38

8 (a) Uncontrolled (Ma = 0 kg) (b) Added-mass Ma = 375 kg (c) Added-mass Ma = 936 kg (d) Added-mass Ma = 187 kg Figure Effect of added-mass on the acceleration responses of free vibration of power transmission tower 39

9 (a) Uncontrolled (Ca = 0 N s / m ) (b) Added-damping (Ca = N s / m ) (c) Added-damping (Ca = N s / m ) (d) Added-damping (Ca = N s / m ) Figure 3 Effect of added-damping on the velocity responses of free vibration of power transmission tower 40

10 (a) Uncontrolled (Asa = 0 m ) (b) Added-tendon (Asa = m ) (c) Added-tendon (Asa = m ) (d) Added-tendon (Asa = m ) Figure 4 Effect of added-tendon on the displacement responses of free vibration of power transmission tower 41