Discussion of Paper 'Improved Explicit Integration Algorithms for Structural Dynamic Analysis with Unconditional Stability and Controllable Numerical Dissipation' by Chinmoy Kolay & James M. Ricles, Journal of Earthquake Engineering 2017, http://www.tandfonline.com/loi/ueqe20

Although it was claimed that the MKR-α method can improve the overshoot and nonlinear stability characteristics of the KR-α method, it seems that it still has a high frequency overshoot in steady-state responses and a weak instability. Three examples are applied to numerically illustrate the two adv...

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Bibliographic Details
Published in:Journal of earthquake engineering : JEE Vol. 25; no. 14; pp. 2993 - 3000
Main Authors: Chang, Shuenn-Yih, Veerarajan, S., Wu, Tsui-Huang
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 06.12.2021
Taylor & Francis Ltd
Subjects:
Algorithms
Control stability
Damping
Difference equations
Dynamic analysis
Dynamic stability
Earthquake engineering
Earthquakes
High frequencies
High frequency
Instability
Integration
Numerical dissipation
overshoot
Seismic activity
Seismic engineering
Stability analysis
Steady state
steady-state response
transient response
Weak instability
ISSN:1363-2469, 1559-808X
Online Access:Get full text
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Summary:Although it was claimed that the MKR-α method can improve the overshoot and nonlinear stability characteristics of the KR-α method, it seems that it still has a high frequency overshoot in steady-state responses and a weak instability. Three examples are applied to numerically illustrate the two adverse properties. A loading-correction term is introduced into the displacement difference equation to remove the adverse overshoot in high frequency steady-state responses. Besides, it is analytically verified that the MKR-α method has an adverse weak instability. Although the problem of high frequency overshoot in steady-state responses can be overcome, there is no way to eliminate the adverse weak instability for both the KR-α method and MKR-α method. Thus, the applications of the two families of integration methods are very limited. It is demonstrated that a high frequency numerical damping is incapable of mitigating the overshoot caused by a weak instability.
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ISSN:1363-2469
1559-808X
DOI:10.1080/13632469.2019.1662345