In this paper we present a numerical method for an inverse problem of nondestructive testing for a composite system formed by the connection of a steel beam and a reinforced concrete beam. The small vibrations of the composite beam are governed in space by two second order and two fourth order dierential operators, which are coupled in the lower order terms by two coecients which express the shearing and axial stiness of the connection. Our inverse problem is to determine these stiness coecients by using Neumann type boundary data measured at one end of the beam and transversal displacements given in an interior portion of the beam axis. We recast the inverse problem as a constrained variational issue and an iterated projected gradient method is proposed for the numerical solution of the minimizing problem. Suitable clip-o and mollifier operators are introduced in order to describe the constrained conditions. The eectiveness of method and the sensitivity of the results to errors in the measured data are tested on the basis of an extensive series of numerical experiments.

Numerical method for an inverse dynamical problem for composite beams

MORASSI, Antonino;
2007-01-01

Abstract

In this paper we present a numerical method for an inverse problem of nondestructive testing for a composite system formed by the connection of a steel beam and a reinforced concrete beam. The small vibrations of the composite beam are governed in space by two second order and two fourth order dierential operators, which are coupled in the lower order terms by two coecients which express the shearing and axial stiness of the connection. Our inverse problem is to determine these stiness coecients by using Neumann type boundary data measured at one end of the beam and transversal displacements given in an interior portion of the beam axis. We recast the inverse problem as a constrained variational issue and an iterated projected gradient method is proposed for the numerical solution of the minimizing problem. Suitable clip-o and mollifier operators are introduced in order to describe the constrained conditions. The eectiveness of method and the sensitivity of the results to errors in the measured data are tested on the basis of an extensive series of numerical experiments.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/853056
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