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Uniqueness in the determination of loads in multi-span beams and plates

Published online by Cambridge University Press:  10 January 2018

ALEXANDRE KAWANO
Affiliation:
Escola Politecnica, University of Sao Paulo, Sao Paulo, Brazil email: akawano@usp.br
ANTONINO MORASSI
Affiliation:
Polytechnic Department of Engineering and Architecture, Università degli Studi di Udine, Udine, Italy email: antonino.morassi@uniud.it

Abstract

Most of the results available on the inverse problem of determining loads acting on elastic beams or plates under transverse vibration refer to single beam or single plate. In this paper, we consider the determination of sources in multi-span systems obtained by connecting either two Euler–Bernoulli elastic beams or two rectangular Kirchhoff–Love elastic plates. The material of the structure is assumed to be homogeneous and isotropic. The transverse load is of the form g(t)f(x), where g(t) is a known function of time and f(x) is the unknown term depending on the position variable x. Under slight a priori assumptions, we prove a uniqueness result for f(x) in terms of observations of the dynamic response taken at interior points of the structure in an arbitrary small interval of time. A numerical implementation of the method is included to show the possible application of the results in the practical identification of the source term.

Type
Papers
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

A. Kawano acknowledges the support provided by CNPq Proc. 304972/2013-4 and Fapesp Proc. 2017/06452-1; 2017/07189-2. A. Morassi gratefully acknowledges the financial support of the National Research Project PRIN 2015TTJN95 “Identification and monitoring of complex structural systems”.

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