基于灵敏度矩阵的结构分布质量识别

Structural distribution mass recognition based on sensitivity matrix

为获得结构系统的质量分布的位置及大小等信息,提出了一种基于灵敏度矩阵的结构分布质量识别方法。首先分析了质量矩阵变化引起的系统模态改变,然后利用质量矩阵变化后的模态特征方程,推导了结构质量灵敏度系数矩阵的计算公式。将质量灵敏度矩阵代入到质量变化前后的偏差与质量变化系数之间的关系式中,建立了基于灵敏度矩阵的结构分布质量识别理论模型,以求解结构的质量变化系数,实现质量变化定位和大小的定量分析。采用三质点动力体系模型的数值分析结果表明,所提方法识别效果显著。为了将该方法应用到工程实践中,选用了悬臂梁结构于指定位置假定质量变化,并通过对比质量变化系数的设定值与计算值来验证理论分析。验证结果的相对误差均低于5%,表明所提方法是可行的。

In order to obtain the position and size of the mass distribution of the structural system, a method of structural distribution quality identification based on sensitivity matrix is proposed.Firstly, the change of system mode caused by the change of mass matrix is analyzed, and then the formula of structure mass sensitivity coefficient matrix is deduced by means of the modal characteristic equation after the change of mass matrix.By bringing the mass sensitivity matrix into the relationship between the deviation before and after the mass change and the mass change coefficient, a theoretical model of structural distribution quality identification based on the sensitivity matrix is established to solve the mass change coefficient of the structure and realize the quantitative analysis of the location and size of the mass change.The numerical analysis of the three-particle dynamic system model is adopted, and the results show that the proposed method is effective.The cantilever beam structure is selected to assume the mass change at the designated position, and the theoretical analysis is verified by comparing the set and calculated values of the mass change coefficient.The purpose of this method is to apply it to engineering practice.The relative errors of the validation results are less than 5%,which shows that the proposed method is feasible.