Abstract–

A rectangular plate pivotally mounted on two opposite edges is considered. It is shown that one of the plate fastenings at the other two edges is determined up to a permutation of the fastenings at these edges uniquely from five natural frequencies. It is also shown that four eigenfrequencies for such a recovery is not enough. The corresponding counterexample is given. It was previously shown that the general boundary conditions at the two edges of a rectangular plate can be uniquely determined by 9 eigenfrequencies. The method used earlier was based on the reconstruction of the matrix accurate to linear row transformations. Such a matrix is restored up to linear transformations of strings by a vector determined up to a constant factor and made up of 10 fourth-order minors of such a matrix. The method used in this work is based on the restoration of elastic canonical boundary conditions for which it is assumed that the stiffness coefficients of elastic fastenings can be zero or infinity.

中文翻译：

---

关于矩形板常见紧固件的识别

摘要-

考虑可枢转地安装在两个相对边缘上的矩形板。示出了，在其他两个边缘处的板紧固件之一被确定为直到五个边缘处的在这些边缘处的紧固件的唯一排列。还显示出用于这种恢复的四个本征频率是不够的。给出了相应的反例。先前已经表明，矩形板两个边缘的一般边界条件可以由9个本征频率唯一地确定。较早使用的方法是基于精确到线性行变换的矩阵重构。这样的矩阵可以通过由一个常数因子决定的向量恢复到字符串的线性变换，该向量由该矩阵的10个四阶次要元素组成。