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Keywords: bell, inertia forces, Spanish system, double pendulum, yoke, clapper.

Summary

To know the inertial forces acting by the swinging of a bell is a main subject when bell towers are designed. These forces have been extensively studied for the Central European system [1,2] and English [3,4], although the Spanish case has been only considered in a few analytical models [5] starting from the basis stated by the authors that studied the English and Central European systems.

This document presents the evaluation of the inertial forces originated during the swinging of a bell by the Spanish system. The numerical model is made with ANSYS [6] code and it includes the brass, the wooden bell cage and the clapper modeled by means of solid elements with elasto-plastic behaviour under large displacements. This model considers the double pendulum formed by the bell and clapper. Traditional analytical models ignore the effect of the clapper. A particular characteristic of this model is that the axis bell swing does not coincide with the axis clapper swing, being the latter jointed to the bell by means of a kneecap. The movement of the clapper is conditioned by the movement and the geometry of the brass, since it pivots in its interior. The analysis carried out was dynamic, considering an asymmetric contact between the brass and the clapper. Two analyses have been carried out: one after the location of the bell face up and the liberation of it under the exclusive action of the gravity considering the damping ratio obtained experimentally. The second analysis consists of introducing a forced angular velocity in the axis of bell swing; this second analysis includes the gravitational load and the corresponding damping ratio. Results of inertial forces with and without clapper are presented for this system of swinging bells and compared with the Central European system of swinging bells.

The assumption made in [2,4], not considering the weight of the clapper to obtain the analytical equations of the inertial forces produced by the swinging of the bells, is validated in the Central European system, not in the Spanish system.

Both vertical and horizontal forces in the bearings are much higher in the Central European system. Fatigue stresses appear on the shaft of the clapper much higher in the Spanish system. It is an important factor in the design.

References

1: DIN 4178: "Glockentürme: Berechnung und Ausführung", 1978.
2: Müller, F.P., "Statische und dynamische Probleme beim Bau von Glockentürmen", Deutsche Bauzeitung, Heft 12, 1-4, 1963.
3: Heyman, J., Therelfall B.D., "Inertia Forces due to bell-Ringing", International Journal of Mechanical Science, Pergamon Press, 18, 161-164, 1976. doi:10.1016/0020-7403(76)90020-5
4: Selby, A.R. and Wilson J.M., "Dynamic behaviour of masonry church bell towers", Worldwide Advances in Structural Concrete and Masonry. In: Proceedings of the CCMS Symposium, Chicago, ASCE, New York, 188-199, 1997.
5: Ivorra, S., Palomo, M.J., Verdú G., Zasso, A., "Dynamic forces produced by swinging bells", Meccanica, 41, 47-62, 2006. doi:10.1007/s11012-005-7973-y
6: ANSYS theory reference 9.0. ANSYS Inc., 2004.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 85 PROCEEDINGS OF THE FIFTEENTH UK CONFERENCE OF THE ASSOCIATION OF COMPUTATIONAL MECHANICS IN ENGINEERING Edited by: B.H.V. Topping Paper 36 Numerical Simulation of Spanish Bell Ringing S. Ivorra¹, E. Segovia¹, R. Irles¹ and F. Pallarés² ¹Department of Construction Engineering, OO. PP. e I.U., University of Alicante, Spain ²Department of Applied Physics, Technical University of Valencia, Spain doi:10.4203/ccp.85.36 purchase the full-text of this paper Full Bibliographic Reference for this paper , "Numerical Simulation of Spanish Bell Ringing", in B.H.V. Topping, (Editor), "Proceedings of the Fifteenth UK Conference of the Association of Computational Mechanics in Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 36, 2007. doi:10.4203/ccp.85.36 Keywords: bell, inertia forces, Spanish system, double pendulum, yoke, clapper. Summary To know the inertial forces acting by the swinging of a bell is a main subject when bell towers are designed. These forces have been extensively studied for the Central European system [1,2] and English [3,4], although the Spanish case has been only considered in a few analytical models [5] starting from the basis stated by the authors that studied the English and Central European systems. This document presents the evaluation of the inertial forces originated during the swinging of a bell by the Spanish system. The numerical model is made with ANSYS [6] code and it includes the brass, the wooden bell cage and the clapper modeled by means of solid elements with elasto-plastic behaviour under large displacements. This model considers the double pendulum formed by the bell and clapper. Traditional analytical models ignore the effect of the clapper. A particular characteristic of this model is that the axis bell swing does not coincide with the axis clapper swing, being the latter jointed to the bell by means of a kneecap. The movement of the clapper is conditioned by the movement and the geometry of the brass, since it pivots in its interior. The analysis carried out was dynamic, considering an asymmetric contact between the brass and the clapper. Two analyses have been carried out: one after the location of the bell face up and the liberation of it under the exclusive action of the gravity considering the damping ratio obtained experimentally. The second analysis consists of introducing a forced angular velocity in the axis of bell swing; this second analysis includes the gravitational load and the corresponding damping ratio. Results of inertial forces with and without clapper are presented for this system of swinging bells and compared with the Central European system of swinging bells. The assumption made in [2,4], not considering the weight of the clapper to obtain the analytical equations of the inertial forces produced by the swinging of the bells, is validated in the Central European system, not in the Spanish system. Both vertical and horizontal forces in the bearings are much higher in the Central European system. Fatigue stresses appear on the shaft of the clapper much higher in the Spanish system. It is an important factor in the design. References 1 DIN 4178: "Glockentürme: Berechnung und Ausführung", 1978. 2 Müller, F.P., "Statische und dynamische Probleme beim Bau von Glockentürmen", Deutsche Bauzeitung, Heft 12, 1-4, 1963. 3 Heyman, J., Therelfall B.D., "Inertia Forces due to bell-Ringing", International Journal of Mechanical Science, Pergamon Press, 18, 161-164, 1976. doi:10.1016/0020-7403(76)90020-5 4 Selby, A.R. and Wilson J.M., "Dynamic behaviour of masonry church bell towers", Worldwide Advances in Structural Concrete and Masonry. In: Proceedings of the CCMS Symposium, Chicago, ASCE, New York, 188-199, 1997. 5 Ivorra, S., Palomo, M.J., Verdú G., Zasso, A., "Dynamic forces produced by swinging bells", Meccanica, 41, 47-62, 2006. doi:10.1007/s11012-005-7973-y 6 ANSYS theory reference 9.0. ANSYS Inc., 2004. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £75 +P&P)
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