振动系统动力学设计迭代算法及解的存在性讨论

An Iterative Algorithm of Dynamic Design and Existence Condition of Solution for Vibration Systems

振动系统动力学设计被抽象为高维广义非线性特征值反问题。若系统构成以可变参数表示 ,则可构造一个非线性多元函数。基于多元函数极小原理 ,提出了一套求解这一特征值反问题的迭代算法。该算法不受系统给定阶数和给定方向的限制 ,也适用于具有重特征值的退化情况 ,系统或结构的构成材料可以是任意的。文中同时讨论了解的存在条件 ,且以显式表达 ,可方便地应用于工程实际。结合某直升机旋翼桨叶的动力学设计 ,给出了应用的数值算例。大量数值仿真结果及应用实践表明 ,本文算法具很好的收敛性 。

The dynamic design of vibration system is considered as an inverse problem for nonlinear generalized eigenvalue in this paper. If variable parameters P=(p 1,p 2,...,p s) are contained in the vibration system, a nonlinear multivariate function can be constructed. Based on minimizing the function, an iterative algorithm for solving the inverse eigenvalue problem is presented here. The method is not limited in the prescribed order of vibration frequency and the given direction. The iterative algorithm is suitable to degenerated case with multiple eigenvalue, too. The material of the systems or the structures is arbitrary. Existence condition of solution is discussed. Explicit formulation for existence is obtained. The expression can be conveniently applied to engineering. Combining dynamic design for a type of helicopter rotor blade, numerical examples in engineering application are given. The results for a large number of numerical experiments and practice in engineering shows that the iterative method has a good convergence and a high accuracy.