Elastic Velocity Damping Model for Inelastic Structures
Publication: Journal of Structural Engineering
Volume 144, Issue 6
Abstract
An alternative inherent damping model for inelastic vibrations is presented in which the damping matrix is represented by , where is the initial stiffness matrix, is the tangent stiffness matrix, and is the initial damping matrix. The model is based on consideration of a dissipation function that depends only on the elastic components of velocity as opposed to the total velocity, which includes elastic and plastic components. For elastic loading and unloading, the model reduces to the standard viscous model as the matrix becomes equal to . The damping matrix can be represented by Rayleigh, modal, or Caughey damping matrices based on initial structural properties. The model allows for appropriate representation of the modal damping ratios as a function of frequency in the limiting linear case and complies with the recommendations from some prominent researchers that inherent damping should be included mostly during loading and unloading phases. The approach can be formulated at a total system level as well as at an element-by-element level.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The need to discuss the possibility of applying the proposed approach at an element-by-element basis was suggested by a reviewer of an initial version of the paper.
References
Bernal, D. (1994). “Viscous damping in inelastic structural response.” J. Struct. Eng., 1240–1254.
Carr, A. J. (1997). “Damping models for inelastic structures.” Proc., Asia-Pacific Vibration Conf., Vol. 1, Kyongju, Korea, 42–48.
Carr, A. J. (2005). “Damping models for time-history structural analyses.” Proc., Asia-Pacific Vibration Conf., Langkawi, Malaysia, 287–293.
Carr, A. J. (2007). Ruaumoko manual. Vol 1: Theory and user’s guide to associated programs, Univ. of Canterbury, Christchurch, New Zealand.
Caughey, T. K. (1960a). “Classical normal modes in damped linear dynamic systems.” J. Appl. Mech., 27(2), 269–271.
Caughey, T. K. (1960b). “Sinusoidal excitation of a system with bilinear hysteresis.” J. Appl. Mech., 27(4), 640–643.
Caughey, T. K., and O’Kelly, M. E. J. (1965). “Classical normal modes in damped linear dynamic systems.” J. Appl. Mech., 32(3), 583–588.
Charney, F. A. (2008). “Unintended consequences of modeling damping in structures.” J. Struct. Eng., 581–592.
Chopra, A. K., and McKenna, F. (2016a). “Modeling viscous damping in nonlinear response history analysis of buildings for earthquake excitation.” Earthquake Eng. Struct. Dyn., 45(2), 193–211.
Chopra, A. K., and McKenna, F. (2016b). “Response to John Hall’s discussion (EQE-16-0008) to Chopra and McKenna’s paper ‘Modeling viscous damping in nonlinear response history analysis of buildings for earthquake excitation’.” Earthquake Eng. Struct. Dyn., 45(13), 2235–2238.
Chrisp, D. J. (1980). “Damping models for inelastic structures.” M.S. thesis, Univ. of Canterbury, Christchurch, New Zealand.
Hall, J. F. (1998). “Seismic response of steel frame buildings to near-source ground motions.” Earthquake Eng. Struct. Dyn., 27(12), 1445–1464.
Hall, J. F. (2006). “Problems encountered from the use (or misuse) of Rayleigh damping.” Earthquake Eng. Struct. Dyn., 35(5), 525–545.
Hall, J. F. (2016a). “Discussion of ‘Modelling viscous damping in nonlinear response history analysis of buildings for earthquake excitation’ by Anil K. Chopra and Frank McKenna.” Earthquake Eng. Struct. Dyn., 45(13), 2229–2233.
Hall, J. F. (2016b). “Discussion on ‘An investigation into the effects of damping and nonlinear geometry models in earthquake analysis’ by Andrew Hardyniec and Finley Charney.” Earthquake Eng. Struct. Dyn., 46(2), 341–342.
Hardyniec, A., and Charney, F. (2015). “An investigation into the effects of damping and nonlinear geometry models in earthquake analysis.” Earthquake Eng. Struct. Dyn., 44(15), 2695–2715.
Hardyniec, A., and Charney, F. (2016). “Response to Professor John Hall’s discussion of Hardyniec and Charney’s paper, ‘An investigation into the effects of damping and nonlinear geometry models in earthquake analysis’.” Earthquake Eng. Struct. Dyn., 46(2), 343–346.
Jehel, P., Leger, P., and Ibrahimbegovic, A. (2014). “Initial versus tangent-stiffness based Rayleigh damping in inelastic time history analysis.” Earthquake Eng. Struct. Dyn., 43(3), 476–484.
Lanzi, A., and Luco, J. E. (2017). “Caughey damping series in terms of products of the flexibility matrix.” J. Eng. Mech., 04017089.
Leger, P., and Dussault, S. (1992). “Seismic-energy dissipation in MDOF structures.” J. Struct. Eng., 1251–1269.
Luco, J. E. (2008). “Author’s reply: A note on classical damping matrices.” Earthquake Eng. Struct. Dyn., 37(15), 1805–1809.
Luco, J. E. (2014). “Effects of soil–structure interaction on seismic base isolation.” Soil Dyn. Earthquake Eng., 66, 167–177.
Luco, J. E., and Lanzi, A. (2017a). “A new inherent damping model for inelastic time-history analyses.” Earthquake Eng. Struct. Dyn., 46(12), 1919–1939.
Luco, J. E., and Lanzi, A. (2017b). “Optimal Caughey series representation of classical damping matrices.” Soil Dyn. Earthquake Eng., 92, 253–265.
McKenna, F. (2011). “OpenSees: A framework for earthquake engineering simulation.” Comput. Sci. Eng., 13(4), 58–66.
Paulay, T., and Priestley, M. J. N. (1992). Seismic design of reinforced concrete and masonry buildings, Wiley, New York.
Priestley, M. J. N., and Grant, D. N. (2005). “Viscous damping in seismic design and analysis.” J. Earthquake Eng., 9(S2), 229–255.
Ryan, K. L., and Polanco, J. (2008). “Problems with rayleigh damping in base-isolated buildings.” J. Struct. Eng., 1780–1784.
Shing, P. B., and Mahin, S. A. (1987). “Elimination of spurious higher-mode response in pseudodynamic tests.” Earthquake Eng. Struct. Dyn., 15(4), 425–445.
Smyrou, E., Priestley, M. J. N., and Carr, A. J. (2011). “Modelling of elastic damping in nonlinear time-history analyses of cantilever RC walls.” Bull. Earthquake Eng., 9(5), 1559–1578.
Wilson, E. L., and Penzien, J. (1972). “Evaluation of orthogonal damping matrices.” Int. J. Numer. Methods Eng., 4(1), 5–10.
Zareian, F., and Medina, R. A. (2010). “A practical method for proper modeling of structural damping in inelastic plane structural systems.” Comput. Struct., 88(1–2), 45–53.
Information & Authors
Information
Published In
Copyright
©2018 American Society of Civil Engineers.
History
Received: Feb 28, 2017
Accepted: Dec 2, 2017
Published online: Apr 12, 2018
Published in print: Jun 1, 2018
Discussion open until: Sep 12, 2018
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.