Applied Mathematics & Information Sciences

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In the study of finite element model updating or damage detection, most papers usually employ transformation matrix from the master coordinates to the full-order coordinates, by either model reduction or modal expansion schemes to deal with spatially incomplete situations. This article employs the direct mode shape expansion method, by applying a hybrid vector that is constructed by measured values at master degrees of freedom (dofs) and constant values at slave dofs, to expand the measured spatially incomplete mode shape based on a series of modification factors. One theoretical development is that model updating or damage detection using Cross Model Cross Mode (CMCM) method is firstly combined with the direct mode shape expansion scheme for dealing with spatial incompleteness. The other development is a new indicator, i.e., modal strain energy change indicator (MSECI) is presented based on traditional modal strain energy method. Numerical studies have been conducted for a three-dimensional four-story frame structure with multiple damaged elements, as the measured modes are synthesized from finite element models. The numerical results reveal that the direct mode shape expansion method outperforms Guyan expansion method on higher order mode shape expansion. Implementing the CMCM method together with the direct mode shape expansion scheme, proper damge detection results can be obtained.