Impact analytical models for earthquake-induced pounding simulation

Abstract

Structural pounding under earthquake has been recently extensively investigated using various impact analytical models. In this paper, a brief review on the commonly used impact analytical models is conducted. Based on this review, the formula used to determine the damping constant related to the impact spring stiffness, coefficient of restitution, and relative approaching velocity in the Hertz model with nonlinear damping is found to be incorrect. To correct this error, a more accurate approximating formula for the damping constant is theoretically derived and numerically verified. At the same time, a modified Kelvin impact model, which can reasonably account for the physical nature of pounding and conveniently implemented in the earthquake-induced pounding simulation of structural engineering is proposed.

Keywords

structural pounding / Hertz model / Kelvin model / nonlinear damping / coefficient of restitution

References

[1] Anagnostopoulos S A, Spiliopoulos K V. An investigation of earthquake induced pounding between adjacent buildings. Earthquake Engineering & Structural Dynamics, 1992, 21(4): 289-302

[2] Davis R O. Pounding of buildings modelled by an impact oscillator. Earthquake Engineering & Structural Dynamics, 1992, 21(3): 253-274

[3] Papadrakakis M, Mouzakis H P, Alevridis A S. Three dimensional non-linear analysis of building pounding during earthquakes. In: Proceedings of the 1996 1st International Conference on Earthquake Resistant Engineering Structures, ERES 96, Oct 30-Nov 1 1996. Thessaloniki, Greece: Computational Mechanics Publ, Southampton, Engl, 1995, 253-267

[4] Kasai K, Maison B F. Building pounding damage during the 1989 Loma Prieta earthquake. Engineering Structures, 1997, 19(3): 195-207

[5] Penzien J. Evaluation of building separation distance required to prevent pounding during strong earthquakes. Earthquake Engineering & Structural Dynamics, 1997, 26(8): 849-858

[6] Pantelides C P, Ma X. Linear and nonlinear pounding of structural systems. Computers and Structures, 1998, 66(1): 79-92

[7] Goldsmith W. Impact: The Theory and Physical Behaviour of Colliding Solids. London: Edward Arnold, 1960

[8] Anagnostopoulos S A. Pounding of buildings in series during earthquakes. Earthquake Engineering and Structural Dynamics, 1988, 16(3): 443-456

[9] Komodromos P, Polycarpou P C, Papaloizou L, Marios P. Response of seismically isolated buildings considering poundings. Earthquake Engineering and Structural Dynamics, 2007, 36(12): 1605-1622

[10] Jankowski R. Non-linear viscoelastic modelling of earthquake-induced structural pounding. Earthquake Engineering and Structural Dynamics, 2005, 34(6): 595-611

[11] Muthukumar S, DesRoches R A. Hertz contact model with non-linear damping for pounding simulation. Earthquake Engineering and Structural Dynamics, 2006, 35(7): 811-828

[12] Lankarani H M, Nikravesh P E. Contact force model with hysteresis damping for impact analysis of multibody systems. Journal of Mechanisms, Transmissions, and Automation in Design, 1990, 112(3): 369-376

[13] Anagnostopoulos S A. Equivalent viscous damping for modeling inelastic impacts in earthquake pounding problems. Earthquake Engineering and Structural Dynamics, 2004, 33(8): 897-902

[14] Jankowski R. Analytical expression between the impact damping ratio and the coefficient of restitution in the non-linear viscoelastic model of structural pounding. Earthquake Engineering and Structural Dynamics, 2006, 35(4): 517-524

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Higher Education Press and Springer-Verlag Berlin Heidelberg