结构逆设计的物理可实现性：未知质量矩阵最小值Eigenvalue的界
On Physical Realizability for Inverse Structural Designs: Bounding the Least Eigenvalue of an Unknown Mass Matrix
摘要：
在结构工程分析领域，一个常见的要求是计算已经经历更新的结构的模态频率，无论是自然的（如材料降解），还是由于人为的影响（通过沿结构放置点质量）。除此要求外，通常只能访问截断模态测试结果。本文给出了线弹性系统中完全不可观测质量矩阵第一特征值的解析界。这样做允许工程师继续修改线性弹性系统，而不需要直接访问质量矩阵。这是因为通常很难确切知道什么样的负质量扰动是允许的，因为完整的质量矩阵是一个未知量。最后，本文的分析将通过假设只访问底层系统的左和右特征向量来进行-这两个特征向量都可以通过物理实验获得，因此边界不仅在物理上可实现，而且在实践中也可实现。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
