非光滑机械动力系统数值积分的精度分析

采用 Taylor级数展开方法 ,分析了常用的线性多步法在非光滑机械动力系统中的计算精度特性 ,建立了一个非光滑的机械振动系统检验模型 ,给出了典型的计算实例 ,并提出了几种改善计算精度的措施。分析表明 ,在计算非光滑的机械动力系统时 ,线性多步法类的数值积分方法出现降阶现象 ,计算精度会大大降低。采用光滑函数过渡、自适应变步长技术及隐式和预测校正等方法 ,可以有效地提高数值计算精度 ,而提高方法的阶次不能有效提高精度

Analysis on precision of numerical integration method for piecewise- smooth dynamics of mechanical systems

The precision of numerical integration method for piecewise smooth dynamics of mechanical systems is studied using Taylor series expansion. The properties of the general linear multistep method(LMM) for piecewise smooth dynamics of mechanical systems are analyzed and a picewise smooth vibration model is introduced. Some numerical experiments on the vibration model are made and several improved integration methods are presented. The analyses show that the order of the general LMM may be reduced when the LMM is used to calculate piecewise smooth dynamics systems, and the precision of LMM is decreased. The precision of integration can be evidently improved by using smooth function transition, adaptive step size change method, implicit integration and predictor corrector method. Increasing the order of the LMM may not improve the precision in this case.