Sensitivity and Hessian Matrix Analysis of Evolutionary PSD Functions for Nonstationary Random Seismic Responses
Publication: Journal of Engineering Mechanics
Volume 138, Issue 6
Abstract
This paper describes a numerical method for calculation of the sensitivity and Hessian matrix of the response evolutionary power spectral density (PSD) functions of structures subjected to uniformly modulated evolutionary random seismic excitation. The method is formulated based on the pseudoexcitation method and the Gauss precise time step integration method. The evolutionary nonstationary random response analysis is converted into step-by-step integration computations using the pseudoexcitation method. The formulas of the pseudoresponses and their first and second derivatives with respect to the structural design variables are derived based on the Gauss precise time step integration method. The evolutionary PSD functions, their sensitivity, and the Hessian matrix are calculated using the pseudoresponses and their first and second derivatives, respectively. Finally, the evolutionary PSD functions’ sensitivity and Hessian matrix analysis of a three-story, two-bay planar frame subjected to uniformly modulated evolutionary random earthquake ground motion has been studied to elucidate the proposed method.
Get full access to this article
View all available purchase options and get full access to this article.
References
Benfratello, S., Caddemi, S., and Muscolino, G. (2000). “Gaussian and non-gaussian stochastic sensitivity analysis of discrete structural system.” Comput. Struct., 78(1–3), 425–434.CMSTCJ
Bogomolni, M., Kirsch, U, and Sheinman, I. (2006). “Efficient design sensitivities of structures subjected to dynamic loading.” Int. J. Solids Struct., 43(18–19), 5485–5500.IJSOAD
Cacciola, P., Colajanni, P., and Muscolino, G. (2005). “A modal approach for the evaluation of the response sensitivity of structural systems subjected to non-stationary random processes.” Comput. Methods Appl. Mech. Eng.CMMECC, 194(42–44), 4344–4361.
Chaudhuri, A., and Chakraborty, S. (2004). “Sensitivity evaluation in seismic reliability analysis of structures.” Comput. Methods Appl. Mech. Eng., 193(1–2), 59–68.CMMECC
Chopra, A. K. (2001). Dynamics of structures: Theory and applications to earthquake engineering, 2nd Ed., Prentice-Hall, Englewood Cliffs, NJ.
Kanai, K. (1961). “An empirical formula for the spectrum of strong earthquake motions.” Bull. Earthquake Res. Inst., Univ. Tokyo, 39(1), 85–95.TDJKAZ
Lin, J., and Zhang, Y. (2004). Pseudo-excitation method of random vibration, Science Press, Beijing (in Chinese).
Lin, J., Zhao, Y., and Zhang, Y. (2001). “Accurate and highly efficient algorithms for structural stationary/non-stationary random responses.” Comput. Methods Appl. Mech. Eng., 191(1–2), 103–111.CMMECC
Lin, Y. K., and Cai, G. O. (1995). Probabilistic structural dynamics: Advanced theory and application, McGraw-Hill, New York.
Liu, Q., Zhang, J., and Yan, L. (2009). “Response sensitivity and Hessian matrix analysis of planar frames subjected to earthquake excitation.” Finite Elem. Anal. Des.FEADEU, 45(10), 695–709.
Liu, Q., Zhang, J., and Yan, L. (2010a). “A numerical method of calculating first and second derivatives of dynamic response based on Gauss precise time step integration method.” Eur. J. Mech. A. SolidsEJASEV, 29(3), 370–377.
Liu, Q., Zhang, J., and Yan, L. (2010b). “An optimal method for seismic drift design of concrete buildings using gradient and Hessian matrix calculations.” Arch. Appl. Mech., 80(11), 1225–1242.AAMEEA
Szopa, J. (1984). “Sensitivity of stochastic dynamic systems to initial conditions.” J. Sound Vib., 97(4), 645–649.JSVIAG
Zhang, Y., and Kiureghian, A. D. (1993). “Dynamic response sensitivity of inelastic structures.” Comput. Methods Appl. Mech. Eng., 108(1–2), 23–36.CMMECC
Zhong, W. X., and Williams, F. W. (1994). “A precise time step integration method.” Proc. Inst. Mech. Eng., Part C: Mech. Eng. Sci.PMCSED, 208(6), 427–430.
Information & Authors
Information
Published In
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Jan 24, 2011
Accepted: Dec 12, 2011
Published online: Dec 14, 2011
Published in print: Jun 1, 2012
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.