隐式中点法对于非线性阻尼结构的稳定性

Stability of implicit midpoint algorithm for solving nonlinear damped structures

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。

Stability of the implicit midpoint algorithm for solving a equation of motion with nonlinear damping was analyzed by using the conservation of energy here. Bilinear model, a special case of nonlinear damping, was also discussed in stability analysis of this algorithm. Nonlinear dynamic analysis computation of one SDOF model and two MDOF models were performed to check the reliability of the proof process. Comparing the computation results with different time step, the stable numerical intergation method for solving dynamic equations with nonlinear damping was gained, it provided a theoretical basis for numerical stability of dynamic computation.