An experimental determination of joint connection type influence to damping in frame towers.

Prodanovic, Novak ; Isic, Safet ; Voloder, Avdo 等

1. INTRODUCTION

Damping is material or system property that is characterized by energy dissipation in a vibration. Analysis of mechanical vibrations without damping is a mathematical fiction, which takes place in the introductory considerations in the theory of vibrations (Beards, 1996). Any realistic analysis of system vibrations requires consideration of the damping effect. However, the damping is the effect that is still less researched and which modeling is the difficult. Practically, experimental determination of a damping is the most used method (Fanti et al., 2006), (Dolecek et al., 2008). In many constructions exploited to a dynamical load it is also desirable to have possibility of damping increasing. This is very important in the case of towers, exploited to a wind load, which may cause effect of galloping vibrations. In this paper is presented experimental determination of damping factor and its dependence on considered type joint in the case of tower construction model.

2. PRELIMINARY VIBRATION MODE ANALYSIS

In order to produce the simplest vibration form of the tower model, its vibration modes are determined. Vibration modes are extracted from the finite element equation

[M]{[??]}+[K]{D} = 0 (1)

where [M] is mass matrix, [K] is stiffness matrix and {D} is displacement vector of the tower. It should be noted that mass and stiffness matrix could be calculated from geometry and material properties of the tower. First bending and torsional modes are shown in the Fig. 1.

[FIGURE 1 OMITTED]

These vibration modes are used as the template for tower initial deformation in order to produce vibration for damping measurement. Initial deformation in the form of selected vibration modes is possible to obtain by simple force acting on the top of the tower. Axerting of two forces in the same direction produce the bending mode and two forces of the opposite direction produce the torsional mode.

3. EXPERIMENT SETUP

Experimental setup for damping research is presented in the Fig. 2. The model of the tower is mounted on the heavy concrete foundation. "L" shaped members of the tower are connected by using joints with screws and rivets. For all used joint types, tower is excited to vibrate in the form of bending and torsional eigenmodes, shown in the Fig. 1. Acceleration of produced vibrations are measured in the two perpendicular directions by two acceleration sensors KD 37V (Metra Mess Technick--Germany) mounted on the tower (Fig. 3). Measuring signal is recorded on the computer by using CATMAN software (Hottinger Baldwin Messtechnik--Germany).

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

The recorded accelerograms of vibrations are shown in the Fig. 4. It could be seen that resulting vibration have the form of free damped vibration, which amplitude exponentially decrease.

[FIGURE 4 OMITTED]

For statistical analysis of the results, for all joint type and form of vibration ten repetition of the measurement are made.

4. DAMPING FACTOR CALCULATION

In the case of damped vibrations, amplitude decreases exponentially as shown in the Fig. 5, and amplitude decreasing could be expressed as

x(t)[[varies][e.sup.-ct] (2)

where x is amplitude of vibration, c is damping factor and t is time.

[FIGURE 5 OMITTED]

In order to calculate damping factor from recorded accelerograms, maximum values of accelerations are extracted and interpolated by exponential function of the form Aexp(-ct), from which damping factor c is determined. Obtained results for all performed measurement by using screwed and riveted joints and vibration in the form of bending (B) and torsional (T) eigenmode are given in the Table 1.

5. RESULTS ANALYSIS

Statistical analysis of experimental results is presented in the Fig. 6. It could be seen that damping factor is less about 30% in the case of riveted joints. Statistical analysis of the results obtained from different vibration modes for one joint type show that there is no significant difference between them.

[FIGURE 6 OMITTED]

6. CONCLUSION

Influence of used joint type to the damping in frame towers is analysed experimentally. Experimental results of damping factor in the case of joints with screws and rivets are presented. Presented results of experimental damping factor determination show that screw joints produce about 30% higher damping factor than joints with rivets. The reason for it is in the fact that screws enable better tightening of members in the joints what produces higher stiffness of the used tower.

7. REFERENCES

Beards, C.F. (1996). Structural Vibration--Analysis and Damping, Arnold, ISBN 0-340-64580-6, London

Dolecek V., Isic S. & Voloder A. (2008). An Experimental Damping Determination In Beam Bifurcation Process, Proceedings of 19th International DAAAM Symposium "Intelligent Manufacturing & Automation: Focus on Next Generation of Intelligent Systems and Solutions", Trnava, Slovakia, 22-25th October 2008, Katalinic, B. (Ed.), pp 205-206, ISBN 978-3-901509-68-1, Published by DAAAM International, Vienna

Fanti, G., Basso, R. & Montauti, V. (2006).Damping Measurement of Bending Vibration in Alpine Skis: An Improvement of Standard ISO 6267, Applied Mechanics and Materials, Vols. 5-6, 2006, pp 199-206, ISSN 1662-7482

Geradin, M. & Rixon, D. (1998). Mechanical Vibrations, Second Edition, John Willey & Sons, ISBN 047197546X, New York

Isic, S., Dolecek, V. & Karabegovic, I. (2007). The Simulation and Vizualization of Plane Truss Eigenvibration, Proceedings of 18th International DAAAM Symposium "Intelligent Manufacturing & Automation: Focus on Creativity, Responsibility and Ethics of Engineers", Katalinic, B. (Ed.), Zadar, 24-27th October, 2007, pp 347-348, ISBN 3-901509-58-5, Published by DAAAM International, Vienna

Virgin, L.N. (2000). Introduction to Experimental Nonlinear Dynamics: A Case Study in Mechanical Vibration, Cambridge University Press, ISBN 0-521-66286-9

Tab. 1. Experimental values of damping factor c

Screw joints

T 0.0232 0.0234 0.02883 0.02693 0.02960
 0.03265 0.03407 0.03072 0.02904 0.02632
B 0.02323 0.03231 0.02936 0.02870 0.02960
 0.03079 0.02724 0.03916 0.03417 0.02531

Riveted joints

T 0,03039 0,01059 0,01851 0,02439 0,02232
 0,02313 0,02211 0,02057 0,02136 0,01895
B 0,02139 0,01023 0,02558 0,02345 0,02407
 0,01229 0,01600 0,01730 0,01964 0,02043