Force inversion in floating plate dynamics

Abstract

An axisymmetric floating plate of infinite extent is subjected to prescribed dynamics under the action of a point load. The problem of inverting the forcing is studied mathematically with a view to classifying its properties within the framework of integral equations. In the process, the floating plate problem is shown to be moderately ill-posed and the rate of change of the forcing is shown to initially be directly proportional to the acceleration of the plate. This latter result is incorporated into the numerical study that follows. Throughout the paper, a model problem is used as an analytical and numerical benchmark.

Uniqueness in the determination of vibration sources in rectangular Germain–Lagrange plates using displacement measurements over line segments with arbitrary small length

“…For the recovery of the distribution Q, given by (8), that is, for the recovery of the sequence (Q m,n ) m,n∈N , we divide the problem into two cases, when (L 1 /L 2 ) 2 belongs to Q and when it does not.…”

“…Concerning plates specifically, to our best knowledge, there are relatively few papers dealing with uniqueness proofs and determination of loads. In [8], the plate is unbounded and the loading is of the form P(t )δ ξ , where δ ξ stands for a unit point force applied at ξ , which is assumed to be known. The inverse problem was to determine the function of time P, from knowledge of the displacement of the plate at ξ .…”