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Uniqueness in the determination of vibration sources in polygonal plates observing the displacement over a space‐time open set
Author(s) -
Kawano Alexandre,
Yamaoka Luís
Publication year - 2019
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201800252
Subject(s) - displacement (psychology) , uniqueness , trigonometry , interval (graph theory) , mathematics , set (abstract data type) , class (philosophy) , space (punctuation) , mathematical analysis , open set , vibration , combinatorics , computer science , physics , artificial intelligence , acoustics , psychology , psychotherapist , programming language , operating system
In this article we deal with the identification of dynamical loading over the class of all plates with polygonal shapes that admit complete systems of trigonometric polynomials. It is proved that given an open set V in the interior of a plate with one of those shapes, using the displacement measured over V for a time interval longer than a minimum value, it is possible to identify uniquely the spatial distribution of the load acting over the plate.