This paper proposes a novel indirect, two-stage approach for model updating in linear vibrating systems, exploiting measured natural frequencies, antiresonances and uncertain or incomplete data of the mode shapes. In the first stage, the technique relies on the partial eigenstructure assignment paradigm and recasts model updating into a non-linear, non-convex minimization that simultaneously updates the mass and stiffness matrices. Uncertainty on mode shapes is formulated through interval (bounds) where they should belong. The inverse eigenvalue problem is solved through homotopy optimization, improved through variables lifting and McCormick's constraints. The unknown parameters are normalized introducing Jacobian matrices, computed through the complex step derivatives, to improve the numerical conditioning of the problem and speed up the computation. In the second stage, the damping matrix is identified through the generalized formulation of proportional damping provided by the Caughey's series.

Two challenging experimental test-cases are solved and prove the method effectiveness: the linearized multibody model of a flexible manipulator and a structure made by a cantilever beam plus a lumped spring-mass system.

本文提出了一种新颖的间接两阶段方法，用于线性振动系统中的模型更新，利用实测的固有频率，反共振以及模态形状的不确定或不完整数据。在第一阶段，该技术依赖于局部特征结构分配范式，并将模型更新重铸为非线性，非凸最小化，同时更新质量和刚度矩阵。模式形状的不确定性是通过它们应属于的间隔（范围）来表示的。特征值反问题通过同伦优化解决，通过变量提升和McCormick的约束得到改善。未知参数通过引入雅可比矩阵进行归一化，该雅可比矩阵是通过复数阶导数计算的，改善问题的数值条件并加快计算速度。在第二阶段，通过Caughey系列提供的比例阻尼的广义公式来确定阻尼矩阵。

解决了两个具有挑战性的实验用例，并证明了该方法的有效性：柔性机械手的线性多体模型和由悬臂梁加集总弹簧质量系统制成的结构。