Vibrations of an elastic strip with a rough boundary |
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Authors: | A. O. Vatul’yan P. S. Uglich |
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Affiliation: | (1) Rostov State University, ul. Zorge 5, Rostov-on-Don, 3440090, Russia |
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Abstract: | A plane problem of steady-state forced vibrations of an elastic strip whose lower boundary contains a rough segment is considered. Using Green’s functions for a strip, the problem is reduced to a system of integral equations with integrals over the rough boundary, which is solved by the boundary-element method. The inverse problem of determining the shape of the rough boundary segment from the data on the displacement field of a certain part of the upper boundary is formulated. By the linearization procedure, the inverse problem is reduced to a Fredholm integral equation of the first kind with a smooth kernel, which is solved by Tikhonov’s regularization method. |
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