ncku-talk2011-01-10

NCTS(South)/ NCKU Math Colloquium

DATE 2011-01-10　15:10-16:00

PLACE R204, 2F, NCTS, NCKU

SPEAKER Gen Nakamura（Department of Math, Hokkaido University）

TITLE Inverse Spectral Problem for Identifying Damage in Steel-Concrete Composite Beams

ABSTRACT I will deal with an inverse problem of nondestructive testing for steel-concrete structures based on eigenvalue and eigenfunction measurements. The composite system is formed by the connection of a steel beam and a reinforced concrete beam. The small vibrations of the composite beam are described by a one dimensional model in which a coupling takes place between longitudinal and bending motions.
The motion is governed in space by two second order and two fourth order differential operators, which are coupled in the lower order terms by the shearing, $k$, and axial, $\mu$, stiffness coefficients of the connection. The coefficients $k$ and $\mu$ define the mechanical model of the connection between the steel beam and the concrete beam and contain direct information on the integrity of the system.
In this talk, I will present a study the inverse problem of determining $k$ and $\mu$ by finite spectral data associated to a given set of boundary conditions. The inverse problem is transformed to a variational problem for a cost function which includes eigenvalue data and transversal displacements of eigenfunctions. A projected gradient method which uses the analytical expressions of the first partial derivatives of the eigenvalues and eigenfunctions is proposed for identifying the unknown coefficients. Several numerical results based on this method both for numerically simulated data and experimental data are presented and discussed.

NCTS(South)/ NCKU Math Colloquium

DATE	2011-01-10　15:10-16:00

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	Gen Nakamura（Department of Math, Hokkaido University）

TITLE	Inverse Spectral Problem for Identifying Damage in Steel-Concrete Composite Beams

ABSTRACT	I will deal with an inverse problem of nondestructive testing for steel-concrete structures based on eigenvalue and eigenfunction measurements. The composite system is formed by the connection of a steel beam and a reinforced concrete beam. The small vibrations of the composite beam are described by a one dimensional model in which a coupling takes place between longitudinal and bending motions. The motion is governed in space by two second order and two fourth order differential operators, which are coupled in the lower order terms by the shearing, $k$, and axial, $\mu$, stiffness coefficients of the connection. The coefficients $k$ and $\mu$ define the mechanical model of the connection between the steel beam and the concrete beam and contain direct information on the integrity of the system. In this talk, I will present a study the inverse problem of determining $k$ and $\mu$ by finite spectral data associated to a given set of boundary conditions. The inverse problem is transformed to a variational problem for a cost function which includes eigenvalue data and transversal displacements of eigenfunctions. A projected gradient method which uses the analytical expressions of the first partial derivatives of the eigenvalues and eigenfunctions is proposed for identifying the unknown coefficients. Several numerical results based on this method both for numerically simulated data and experimental data are presented and discussed.