Abstract
ABSTRACT 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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