两种解振动反问题算法的同一性及应用

Similarity and Its Applications of Two Algorithms in Solving Inverse Problems for Vibration Engineering

根据矩阵最佳逼近与加权残值理论 ,把求解振动反问题时所使用的矩阵逼近法和极值化算法统一为不同范数定义下的最小二乘问题 ,这对部分振频和 /或振型给定情况下振动反问题的求解提供了一个有效工具。结合某大型飞机机翼颤振吹风模型的动力设计 ,本文给出了工程应用的具体数值例子。大量的算例结果表明 :与矩阵逼近法具有同一性的极值化方法计算精度和计算效率均很高 。

Based on matrix optimal approximation and weighted residuals theory, the matrix approximation and the extremal algorithm for resolving inverse problems of vibration engineering are integrated with least squares problem under definition of norms in this paper. The effective means for solving inverse problems of given partial frequencies and/or modes in vibration engineering is raised here. Combining dynamic design of wing flutter model for a giant transport aircraft, a numerical example of engineering application is presented. A large number of computation results has shown that the extremal algorithm having similtarity with matrix approximation was possessed of higher precision and efficiency. The extremal algorithm can be applied directely to engineering practice.