A perturbation approach for the identification of uncertain structures

This paper deals with the identification of linear structural systems with random parameters. The stiffness matrix of a four-storey shear frame structure is assumed to be linearly dependent on a random parameter ruling the damage evolution of the columns. The evaluation of natural frequencies and the mode-shapes is in the context of random eigenvalue problems in structural dynamics. Using a Taylor expansion of the mass and stiffness matrices, a perturbation technique is first applied to derive the asymptotic solution up to the second order. Then, the evaluation of the statistic of the frequencies and mode-shapes is derived up to the second order. Finally a stochastic identification technique is proposed to characterize the statistics of the random parameter.