Nonlinear Error Propagation Analysis for Explicit Pseudodynamic Algorithm
Publication: Journal of Engineering Mechanics
Volume 129, Issue 8
Abstract
A technique to evaluate the error propagation of the pseudodynamic testing of a nonlinear system is proposed. This technique mainly relies upon the introduction of the degree of nonlinearity to describe the variation of stiffness for each time step. The commonly used Newmark explicit method is chosen for this study and it is analytically proved that the upper stability limit is enlarged for the case of stiffness softening and is reduced for the case of stiffness hardening. These theoretical results are thoroughly confirmed with numerical examples. It is also theoretically and numerically verified that for each time step stiffness softening encounters less error propagation while stiffness hardening experiences more severe error propagation than for the stiffness invariant case. This is because stiffness softening results in the decrease of the natural frequency and the value of the degree of softening nonlinearity while stiffness hardening leads to the increase of the natural frequency and the value of the degree of hardening nonlinearity.
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References
Chang, S. Y.(1997). “Improved numerical dissipation for explicit methods in pseudodynamic tests.” Earthquake Eng. Struct. Dyn., 26, 917–929.
Chang, S. Y.(2000). “The γ-function pseudodynamic algorithm.” J. Earthquake Eng., 4(3), 303–320.
Chang, S. Y.(2001). “Application of the momentum equations of motion to pseudodynamic testing.” Philos. Trans. R. Soc. London, Ser. A, 359(1786), 1801–1827.
Chang, S. Y.(2002). “Explicit pseudodynamic algorithm with unconditional stability.” J. Eng. Mech., 128(9), 935–947.
Chang, S. Y., Tsai, K. C., and Chen, K. C.(1998). “Improved time integration for pseudodynamic tests.” Earthquake Eng. Struct. Dyn., 27, 711–730.
Newmark, N. M. (1959). “A method of computation for structural dynamics.” J. Eng. Mech. Div., Am. Soc. Civ. Eng., 67–94.
Peek, R., and Yi, W. H.(1990a). “Error analysis for pseudodynamic test method. I: Analysis.” J. Eng. Mech., 116(7), 1618–1637.
Peek, R., and Yi, W. H.(1990b). “Error analysis for pseudodynamic test method. II: Application.” J. Eng. Mech., 116(7), 1638–1658.
Shing, P. B., and Mahin, S. A. (1983). “Experimental error propagation in pseudodynamic testing.” Rep. No. UCB/EERC-83/12, Earthquake Engineering Research Center, Univ. of California, Berkeley, Calif.
Shing, P. B., and Mahin, S. A. (1984). “Pseudodynamic method for seismic performance testing: Theory and implementation.” Rep. No. UCB/EERC-84/01, Earthquake Engineering Research Center, Univ. of California, Berkeley, Calif.
Shing, P. B., and Mahin, S. A.(1987a). “Cumulative experimental errors in pseudodynamic tests.” Earthquake Eng. Struct. Dyn., 15, 409–424.
Shing, P. B., and Mahin, S. A.(1987b). “Elimination of spurious higher-mode response in pseudodynamic tests.” Earthquake Eng. Struct. Dyn., 15, 425–445.
Shing, P. B., and Mahin, S. A.(1990). “Experimental error effects in pseudodynamic testing.” J. Eng. Mech., 116(4), 805–821.
Shing, P. B., and Manivannan, T.(1990). “On the accuracy of an implicit algorithm for pseudodynamic tests.” Earthquake Eng. Struct. Dyn., 19, 631–651.
Shing, P. B., Vannan, M. T., and Carter, E.(1991). “Implicit time integration for pseudodynamic tests.” Earthquake Eng. Struct. Dyn., 20, 551–576.
Strang, G. (1986). Linear algebra and its applications, Harcourt Brace Jovanovich, San Diego.
Takanashi, K., Udagawa, K., Seki, M., Okada, T., and Tanaka, H. (1975). “Nonlinear earthquake response analysis of structures by a computer-actuator on-line system.” Bull. of Earthquake Resistant Structure Research Center, 8, Institute of Industrial Science, Univ. of Tokyo, Tokyo.
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Copyright © 2003 American Society of Civil Engineers.
History
Received: Jun 13, 2001
Accepted: Dec 4, 2002
Published online: Jul 15, 2003
Published in print: Aug 2003
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