This paper proposes a novel method for the robust partial assignment of natural frequencies and antiresonances, together with the partial assignment of the related eigenvectors, in lightly damped linear vibrating systems. Dynamic structural modification is exploited to assign the eigenvalues, either of the system or of the adjoint system, together with their sensitivity with respect to some parameters of interest. To handle with constraints on the feasible modifications, the inverse eigenvalue problem is cast as a minimization problem and a solution method is proposed through homotopy optimization. Variables lifting for bilinear and trilinear terms, together with bilinear and double-McCormick’s constraints, are exploited to provide a convexification of the problem and to boost the attainment of the global optimum. The effectiveness of the proposed method is assessed through four numerical examples.

中文翻译：

---

通过动态结构修改对振动系统中的自然频率和反共振进行稳健分配

本文提出了一种新方法，用于在轻阻尼线性振动系统中对固有频率和反共振进行稳健的部分分配，以及相关特征向量的部分分配。利用动态结构修改来分配系统或伴随系统的特征值，以及它们对某些感兴趣参数的敏感性。为了处理对可行修改的约束，将逆特征值问题转化为最小化问题，并通过同伦优化提出了一种解决方法。双线性和三线性项的变量提升，连同双线性和双麦考密克约束，被用来提供问题的凸化并促进全局最优的实现。