非光滑动力系统周期响应的数值解法

工程中有重要意义的非线性动力系统周期响应分析,一般因系统维数高、特性复杂而需要用数值方法进行。但目前有影响的打靶法、增量谐波平衡法均不能处理含弹塑性、间隙、干摩擦等非光滑因素的工程系统,计算光滑动力系统的强非线性周期响应时也常不收敛。本文分析了上述两种方法的欠缺,指出其原因在于方法中直接或隐含的Newton迭代格式。文中提出了用拟Newton迭代格式和无约束优化方法改进打靶法和增量谐波平衡法的8种方案,并对这些方案就收敛性、精度和效率进行了考核比较,给出了不同方案的适用对象,精选出了几种方案推荐工程界应用。

Numerical Analysis to the Periodic Response of Nonsmooth Dynamic Systems

The periodic response analysis, of great significance in engineering, of nonlinear dynamic systems is usually carried out by numerical methods because of the high dimension and complicated characters of the systems. The current well-known unmerical schemes like shooting and incremental harmonic balancing, however, cannot cope with the systems with nonsmooth physical factors, such as elastoplasticity, clearance and dry friction, and also fail to calculate the strong nonlinear periodic response of smooth systems sometimes. The author analyzes the above shortcomings of these schemes and points out that they come from the explicit or implicit Newton iteration in the schemes. The paper presents eight schemes based on quasi-Newton iteration and unconstrained function minimization in order to improve the shooting and the incremental harmonic balancing. The convergence, accuracy and efficiency of the new schemes are examined in the paper and four schemes of them are suggested to the engineering circle.