System condensations for inverse problems of linear dynamic structures

Abstract

A modal method combined with system condensation is presented for the assessment of selection optimality and solution accuracy in inverse problems of structural optimization and damage detection. Finite element procedures are applied to seek the structural modifications for the characteristic changes assigned from design goals or dynamic measurements. The solution convergence is related to the selection of degrees of freedom and the method of system transformation. The application of the dynamic stiffness matrix yields a frequency-dependent transformation matrix, which can be expanded into an infinite series to obtain lower-order approximations. The modal matrix may be used to project the measured data onto the mode shapes, in which case much emphasis is laid on the linear independence of the selected degrees of freedom and the condition number of the transformation matrix. The baseline structure is used to obtain an initial perturbation, which can be improved through repeated updates of the transformation. The proposed methods give excellent solutions for frequency optimization. In damage detection, however, moderate deviations from the correct structural changes are attributable to system reduction. The dynamic stiffness matrix seems recommendable over the modal matrix projection for the system transformation.