On the Identification of Common Fastenings of a Rectangular Plate

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.

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