隐式中点法对于非线性阻尼结构的稳定性

潘天林 吴 斌

振动与冲击 ›› 2013, Vol. 32 ›› Issue (23) : 38-42.

PDF(1278 KB)
PDF(1278 KB)
振动与冲击 ›› 2013, Vol. 32 ›› Issue (23) : 38-42.
论文

隐式中点法对于非线性阻尼结构的稳定性

  • 潘天林 吴 斌
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Stability of implicit midpoint algorithm applied to nonlinear damping structure

  • Tianlin Pan, Bin Wu
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文章历史 +

摘要

用能量守恒的方法证明了隐式中点法对于非线性指数阻尼的结构动力方程为数值稳定。工程中常用的双线性本构模型作为这种指数模型的特殊情况,同样满足数值稳定性条件。为了验证证明过程的可靠性,对一个单自由度体系和两个多自由度结构进行动力非线性计算分析,对比不同时间增量步的计算结果。从而给出了针对这种非线性动力方程计算的稳定的数值积分方法,为动力计算数值稳定性提供理论基础。

Abstract

Stability of midpoint algorithm applied on solving the equation of motion with nonlinear damping is analyzed by using conservation of energy in this paper. Bilinear model, a special case of the nonlinear damping, is also discussed in stability analysis of this algorithm. nonlinear computation of one SDOF model and two MDOF models are finished to check the reliability of the proof progress. From the studying property of the nonlinear equation, theoretic basement is given for numerical stability, in addition we can draw the conclusion that midpoint scheme is one of the best methods for this nonlinear problem.


关键词

隐式中点法 / 指数阻尼 / 能量守恒 / 数值稳定

Key words

midpoint algorithm / nonlinear damping / energy conservation / numerical stability

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导出引用
潘天林 吴 斌. 隐式中点法对于非线性阻尼结构的稳定性[J]. 振动与冲击, 2013, 32(23): 38-42
Tianlin Pan;Bin Wu. Stability of implicit midpoint algorithm applied to nonlinear damping structure[J]. Journal of Vibration and Shock, 2013, 32(23): 38-42

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