彭凡　王樑　肖健

摘 要：研究质量时变系统的动态载荷识别技术，引入广义模态概念，在初瞬时的模态空间中利用模态叠加法得到部分解耦的动力学方程，结合考虑质量变化效应的虚拟变形法和Duhamel积分，构建反演动态力的2种分析途径.一种是基于加速度反演的连锁递推格式，另一种是基于位移和加速度反演的正则化求解格式.分析2个动载荷作用下的变质量多自由度系统，利用Euler中点辛差分方法求得系统的响应，将其叠加随机噪声以模拟测点响应，然后，应用2种模态力反求格式反演动载荷.研究结果表明，连锁递推格式计算效率高，但对加速度测量噪声敏感；正则化求解格式的稳健性较高.

关键词：变质量；动态载荷；反问题；递归计算；正则化

中图分类号：O326；O347.1 文献标识码：A

Abstract：The technique of the load identification of mass variable system was studied. The generalized modal concept applied on time-varying system was introduced， and the method of modal superposition was used to give dynamic equations with partially decoupled in initial modal space defined at initial instant. Based on both virtual distortion method （VDM） accounting for the effect of mass change and the Duhamel integration in initial modal space， two approaches to identify modal forces were constructed： one is the recursive calculation pattern formulated on the basis of modal acceleration， and the other is the regularized solution by the direct discretization of Duhamel integration with modal displacement and acceleration. A mass variable system with 16 degrees of freedom subjected to two external loads was analyzed. The responses were calculated by applying Euler midpoint symplectic difference method and added with random noise to simulate measured signals. Two dynamic loads were identified by two inversion approaches of modal forces. The comparison of results has indicated that regularized solution format has a higher numerical robust than the recursive calculation pattern， but the latter is sensitive to the noise of measurement.

Key words：time-varying mass；dynamic loads；inverse problems； recursive calculation； regularization

许多工程领域存在质量等振动参数随时间发生变化的动力学问题 [1-5].质量时变系统的动力学响应分析方法主要包括2类，一类是直接积分法，包括Newmark法和各类差分算法[6]；另一类是基于短时时不变假设的模态叠加法[7-8].与动力响应分析相对应的是质量时变振动系统的载荷反求，如考虑质量快速减少的运载工具的脉动推力反求，这在工程上也是非常有意义的课题.针对时不变结构的动态载荷识别，已经发展了较为丰富的方法与技术[9].然而，关于时变结构的动态载荷识别方法的研究还较少，张青霞等[10]将车桥系统视为质量时变系统，移动荷载的反求转化为移动质……