Selection of Rayleigh Damping Coefficients for Seismic Response Analysis of Soil Layers

Authors: Huai-Feng Wang, Meng-Lin Lou, Ru-Lin Zhang

Abstract:

One good analysis method in seismic response analysis is direct time integration, which widely adopts Rayleigh damping. An approach is presented for selection of Rayleigh damping coefficients to be used in seismic analyses to produce a response that is consistent with Modal damping response. In the presented approach, the expression of the error of peak response, acquired through complete quadratic combination method, and Rayleigh damping coefficients was set up and then the coefficients were produced by minimizing the error. Two finite element modes of soil layers, excited by 28 seismic waves, were used to demonstrate the feasibility and validity.

Keywords: Rayleigh damping, modal damping, damping coefficients, seismic response analysis.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1128809

References:

[1] Chopra, A. K. (2001). Dynamics of Structures: Theory and Applications to Earthquake Engineering, 2nd edition. New Jersey, Upper Saddle River, Prentice-Hall.
[2] Nielsen, A. H. (2009). "On the use of Rayleigh damping for seismic analysis." Proceedings of the Institution of Civil Engineers: Engineering and Computational Mechanics 162 (4): 215-220.
[3] Kausel, E. (2014). "Damping Matrices Revisited." Journal of Engineering Mechanics 140 (8): 04014055.
[4] Clough, R. W. and J. Penzien (2003). Dynamics of Structures. Berkeley, USA, Computers & Structures.
[5] Luco, J. E. (2008). "A note on classical damping matrices." Earthquake Engineering and Structural Dynamics 37 (15): 1801-1804.
[6] Hall, J. F. (2006). "Problems encountered from the use (or misuse) of Rayleigh damping." Earthquake Engineering and Structural Dynamics 35 (5): 525-545.
[7] Charney, F. A. (2006). Unintended consequences of modeling damping in structures: Rayleigh damping. 17th analysis and computation specialty conference, St. Louis, M0, United states, American Society of Civil Engineers.
[8] Ryan, K. L. and J. Polanco (2008). "Problems with Rayleigh damping in base-isolated buildings." Journal of Structural Engineering 134 (11): 1780-1784.
[9] Zou, D. and B. Xu, et al. (2011). "Study of influence of different methods for calculating Rayleigh damping coefficient on high earth-rock dam seismic response." Rock and Soil Mechanics 32 (3): 797-803.
[10] Erduran, E. (2012). "Evaluation of Rayleigh damping and its influence on engineering demand parameter estimates." Earthquake Engineering and Structural Dynamics 41 (14): 1905-1919.
[11] Lou, M. and X. Shao (2013). "Discussion on modeling issues of Rayleigh damping matrix in soil layers with deep deposit." Chinese Journal of Geotechnical Engineering 35 (07): 1272-1279.
[12] Ju, S. and S. Ni (2007). "Determining Rayleigh damping parameters of soils for finite element analysis." International Journal for Numerical and Analytical Methods in Geomechanics 31 (10): 1239-1255.
[13] Yang, D. B. and Y. G. Zhang, et al. (2010). "Computation of Rayleigh damping coefficients inseismic time-history analysis of spatial structures." Journal of the International Association for Shell and Spatial Structures 51 (2): 125-135.
[14] Spears, R. E. and S. R. Jensen (2012). "Approach for selection of Rayleigh damping parameters used for time history analysis." Journal of Pressure Vessel Technology 134 (6): 061801 (7 pp.).
[15] Pan, D (2013). "An Optimization Solution for Rayleigh Damping Coefficients in Seismic Response Analysis." Engineering Mechanics 30 (11): 15-20+27.
[16] Booth, A. D. (1957). Numerical methods, 2nd edition. London, Butterworths Scientific Publications.