Accurate Representation of External Force in Time History Analysis
Publication: Journal of Engineering Mechanics
Volume 132, Issue 1
Abstract
It is usually thought that the integration time step should be small enough to represent properly the variation of the dynamic loading with respect to time. However, there is no evaluation criterion that can be used to determine whether the external force is accurately represented. In this paper, criteria for accurate representation of external force are proposed based on analytical results. It is found that amplitude distortion both in the transient response and the steady-state response for each time step is closely related to the step discretization error of external force. In fact, for a negligible period distortion, an amplitude distortion will be less than 5% if the relative step discretization error is constrained to be less than 5% at each time step for the Newmark explicit method, Fox–Goodwin method, and linear acceleration method while for the constant average acceleration method it must be less than 2.5%. This criterion leads to the need of using of eight or more integration time steps to accurately represent a complete cycle of a harmonic loading for the Newmark explicit method, Fox–Goodwin method, and linear acceleration method while for the constant average acceleration method 12 or more integration time steps are required.
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Acknowledgment
The writer gratefully acknowledges financial support for this study provided by the National Science Council, Taiwan, Republic of China, under Grant No. NSCTNSC-91-2218-E-027-010.
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History
Received: Dec 4, 2002
Accepted: Jul 14, 2005
Published online: Jan 1, 2006
Published in print: Jan 2006
Notes
Note. Associate Editor: Henryk Stolarski
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