New Kelvin-Voigt Model to simulate the collision of rigid bodies

Document Type : Research Article

Authors

Department of Civil Engineering, Razi University, Kermanshah, Iran

Abstract

The effective simulation of collision between two adjacent structures has always been of interest in structural engineering. Several analytical models have been proposed by different scholars to simulate this phenomenon. The Kelvin-Voigt Model is one of the popular ones due to its linearity, and ease of application. In this study, a parameter (coefficient α) is introduced in the original Kelvin-Voigt Model to calculate the energy dissipation both in the compression and restitution (separation) phases of the contact. Besides, the accuracy of the modified model has been improved by presenting a new equation for the estimation of damped energy. Furthermore, the tensile force is eliminated in the restitution phase. The effectiveness of the proposed modified model in the simulation of the collision was examined by comparing the results with those of the original model, as well as previous experimental studies. The mean relative error between the selected coefficient of restitution before the collision and the coefficient of restitution after the collision that was evaluated by different models were compared. The modified model proposed in this study showed the least error values among all of the other models. This indicated the ability of the model to estimate the damped energy with better accuracy.  The results of this research study indicate that the proposed modified Kelvin-Voigt Model is effective in the simulation of collision between two structures.

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References

[1] A. Banerjee, A. Chanda, R. Das, Historical origin and recent development on normal directional impact models for rigid body contact simulation: a critical review, Archives of Computational Methods in Engineering, 24(2) (2017) 397-422.
[2] E. Rosenblueth, R.J.C.i. Meli, The 1985 Mexico earthquake, 8(5) (1986) 23-34.
[3] H. Otsuka, S. Unjoh, T. Terayama, J. Hoshikuma, K. Kosa, Damage to highway bridges by the 1995 Hyogoken Nanbu earthquake and the retrofit of highway bridges in Japan, in: Proceedings of the 3rd US Japan Workshop on Seismic Retrofit of Bridge, 1996.
[4] M. Saatcioglu, D. Mitchell, R. Tinawi, N.J. Gardner, A.G. Gillies, A. Ghobarah, D.L. Anderson, D.J.C.J.o.C.E. Lau, The August 17, 1999, Kocaeli (Turkey) earthquake damage to structures, 28(4) (2001) 715-737..
[5] R.J.E.s. Jankowski, Earthquake-induced pounding between equal height buildings with substantially different dynamic properties, 30(10) (2008) 2818-2829.
[6] S.A.J.E.e. Anagnostopoulos, s. dynamics, Pounding of buildings in series during earthquakes, 16(3) (1988) 443-456.
[7] C.G. Karayannis, M.J.J.E.E. Favvata, S. Dynamics, Earthquake‐induced interaction between adjacent reinforced concrete structures with non‐equal heights, 34(1) (2005) 1-20.
[8] R. Jankowski, Assessment of damage due to earthquake-induced pounding between the main building and the stairway tower, in: Key Engineering Materials, Trans Tech Publ, 2007, pp. 339-344.
[9] B. Madani, F. Behnamfar, H.T.J.S.D. Riahi, E. Engineering, Dynamic response of structures subjected to pounding and structure–soil–structure interaction, 78 (2015) 46-60.
[10] M. Ghandil, F. Behnamfar, M.J.S.D. Vafaeian, E. Engineering, Dynamic responses of structure–soil–structure systems with an extension of the equivalent linear soil modeling, 80 (2016) 149-162.
[11] B.D.J.E.e. Westermo, s. dynamics, The dynamics of interstructural connection to prevent pounding, 18(5) (1989) 687-699.
[12] K. Kasai, J.A. Munshi, B.F. Maison, Viscoelastic dampers for seismic pounding mitigation, in: Structural Engineering in Natural Hazards Mitigation, ASCE, 1993, pp. 730-735.
[13] J.E. Luco, F.C.J.E.E. De Barros, S. Dynamics, Optimal damping between two adjacent elastic structures, 27(7) (1998) 649-659.
[14] W. Zhang, Y.J.J.o.S. Xu, Vibration, Vibration analysis of two buildings linked by Maxwell model-defined fluid dampers, 233(5) (2000) 775-796.
[15] P.C. Polycarpou, P. Komodromos, A.C.J.E.E. Polycarpou, S. Dynamics, A nonlinear impact model for simulating the use of rubber shock absorbers for mitigating the effects of structural pounding during earthquakes, 42(1) (2013) 81-100.
[16] A. Malhotra, T. Roy, V. Matsagar, Effectiveness of friction dampers in seismic and wind response control of connected adjacent steel buildings, Shock and Vibration, 2020 (2020).
[17] M. Papi, H. Toopchi-Nezhad, “A Literature Review on Modeling and Mitigating the Pounding Effects in Buildings”,Amirkabir J. Civil Eng., ,” vol. 50, no. 6, pp. 1113-1126, 2019( in Persian).
[18] M. Miari, K.K. Choong, R. Jankowski, Seismic pounding between bridge segments: a state-of-the-art review, Archives of Computational Methods in Engineering, 28(2) (2021) 495-504.
[19] T. Brown, A. Elshaer, Pounding of structures at proximity: A state-of-the-art review, Journal of Building Engineering, (2022) 103991.
[20] H.J.M.p. Hertz, On the contact of solids—on the contact of rigid elastic solids and on hardness, (1896) 146-183.
[21] S.A.J.E.E. Anagnostopoulos, S. Dynamics, Equivalent viscous damping for modeling inelastic impacts in earthquake pounding problems, 33(8) (2004) 897-902.
[22] S. Mahmoud, R.J.I.J.o.S. Jankowski, T.T.o.C. Engineering, Modified linear viscoelastic model of earthquake-induced structural pounding, 35(C1) (2011) 51.
[23] K. Ye, L.J.F.o.A. Li, C.E.i. China, Impact analytical models for earthquake-induced pounding simulation, 3(2) (2009) 142-147.
[24] K. Ye, L. Li, H.J.E.E. Zhu, S. Dynamics, A note on the Hertz contact model with nonlinear damping for pounding simulation, 38(9) (2009) 1135-1142.
[25] MATLAB 2021a., Natick, Massachusetts, USA: MathWorks, Inc., 2021.
[26] R. Jankowski, S. Mahmoud, Earthquake-induced structural pounding, Springer, 2015.
Amirkabir Journal of Civil Engineering
Volume 54, Issue 9
December 2022
Pages 3497-3508

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