论文标题
关于逆结构设计的物理可靠性：界定未知质量矩阵的最低特征值
On Physical Realizability for Inverse Structural Designs: Bounding the Least Eigenvalue of an Unknown Mass Matrix
论文作者
论文摘要
在结构工程分析的领域中，一个共同的要求是计算经过更新的结构的模态频率，即自然（例如材料降解），或者是由于人为影响（通过沿结构放置点质量）所致。除了此要求外，通常只能访问截短的模态测试结果。在本文中，我们为线性弹性系统完全未观察到的质量基质的第一个特征值得出了分析界限。这样做可以使工程师继续修改线性弹性系统，而无需直接访问质量矩阵。这是因为鉴于完整的质量矩阵是未知的数量，通常很难确切地知道哪些负质量扰动是可以允许的。最终，本文中的分析将仅假设仅对基础系统的左右特征向量访问，这两者都可以通过物理实验获得，以便界限不仅可以在物理上实现，而且实际上可以实现。
In the field of structural engineering analysis, a common requirement is to calculate the modal frequencies of a structure that has undergone an update, either naturally (such as from material degradation), or due to man-made influences (by placing point masses along a structure). In addition to this requirement, it is common to only have access to truncated modal testing results. In this paper, we derive analytical bounds for the first eigenvalue of a completely unobserved mass matrix for linear elastic systems. Doing so allows engineers to proceed with modifying linear elastic systems, without requiring direct access to the mass matrix. This is because it is often difficult to know exactly what negative mass perturbations are allowable, given that the full mass matrix is an unknown quantity. Ultimately, the analysis in this paper will proceed by assuming only access to the left and right eigenvectors of the underlying system - which are both possible to obtain via physical experiments, so that the bounds are not only physically realizable, but also practically realizable.
