Non-linear sensitivity analysis of mechanical structures using modal data

This paper presents a new procedure for determining the revised modal properties (eigenvalues and mass-normalized eigenvectors) in a structural modification analysis. The procedure is based on expressing the eigenvectors of the modified structure as a linear combination of the eigenvectors of the original structure and employs the stationary property of the Rayleigh quotient to determine the modified structure's eigenvalues. It has the same theoretical basis as first- and second-order sensitivity analysis, but here the non-linear effects contributed by all high-order terms [generally assumed to be small relative to the effect contributed by first- and second-order terms (1–6)] are preserved in full. Hence, the usual shortcoming of sensitivity analysis—that it is limited to small modifications—is overcome. A special feature of this procedure is that the exact modal properties of the modified structure are determined without solving the generalized eigenvalue problem for the modified structure. Thus, this procedure can greatly reduce the computation cost and increase the efficiency of structural modification analysis (or reanalysis) during a structural optimization process. Numerical examples demonstrate the superconvergence characteristic of the technique. The limitations caused by modal and coordinate incompleteness, and the sensitivity of this technique with respect to simulated measurement errors, are investigated by using a finite element model of a steel frame structure and a ten-degrees-of-freedom mass-spring model.