Analysis of implicit HHT-α integration algorithm for real-time hybrid simulation

SUMMARY Real‐time hybrid simulation is a viable experiment technique to evaluate the performance of structures equipped with rate‐dependent seismic devices when subject to dynamic loading. The integration algorithm used to solve the equations of motion has to be stable and accurate to achieve a succ...

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Vydané v:Earthquake engineering & structural dynamics Ročník 41; číslo 5; s. 1021 - 1041
Hlavní autori: Chen, Cheng, Ricles, James M.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Chichester, UK John Wiley & Sons, Ltd 25.04.2012
Wiley
Predmet:
accuracy
discrete transfer function
Earth sciences
Earth, ocean, space
Earthquakes, seismology
Engineering and environment geology. Geothermics
Engineering geology
Exact sciences and technology
integration algorithm
Internal geophysics
real-time hybrid simulation
stability
experimental studies
real-time hybrid simulation
algorithms
integration algorithm
high frequency
simulation
testing
dynamic loading
accuracy
discrete transfer function
transfer functions
earthquake engineering
performances
stability
ISSN:0098-8847, 1096-9845
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Shrnutí:SUMMARY Real‐time hybrid simulation is a viable experiment technique to evaluate the performance of structures equipped with rate‐dependent seismic devices when subject to dynamic loading. The integration algorithm used to solve the equations of motion has to be stable and accurate to achieve a successful real‐time hybrid simulation. The implicit HHT α‐algorithm is a popular integration algorithm for conducting structural dynamic time history analysis because of its desirable properties of unconditional stability for linear elastic structures and controllable numerical damping for high frequencies. The implicit form of the algorithm, however, requires iterations for nonlinear structures, which is undesirable for real‐time hybrid simulation. Consequently, the HHT α‐algorithm has been implemented for real‐time hybrid simulation using a fixed number of substep iterations. The resulting HHT α‐algorithm with a fixed number of substep iterations is believed to be unconditionally stable for linear elastic structures, but research on its stability and accuracy for nonlinear structures is quite limited. In this paper, a discrete transfer function approach is utilized to analyze the HHT α‐algorithm with a fixed number of substep iterations. The algorithm is shown to be unconditionally stable for linear elastic structures, but only conditionally stable for nonlinear softening or hardening structures. The equivalent damping of the algorithm is shown to be almost the same as that of the original HHT α‐algorithm, while the period elongation varies depending on the structural nonlinearity and the size of the integration time‐step. A modified form of the algorithm is proposed to improve its stability for use in nonlinear structures. The stability of the modified algorithm is demonstrated to be enhanced and have an accuracy that is comparable to that of the existing HHT α‐algorithm with a fixed number of substep iterations. Both numerical and real‐time hybrid simulations are conducted to verify the modified algorithm. The experimental results demonstrate the effectiveness of the modified algorithm for real‐time testing. Copyright © 2011 John Wiley & Sons, Ltd.
Bibliografia:ArticleID:EQE1172
istex:870D170B2F8496AF9B86563FE38DA4BF74CF3B0F
ark:/67375/WNG-61RC88PS-0
ISSN:0098-8847
1096-9845
DOI:10.1002/eqe.1172