An Expansion Method Dealing with Spatial Incompleteness of Measured Mode Shapes of Beam Structures

Obtaining mode shape values at rotational degrees of freedom (dofs) is a challenge from dynamic test of beam structures, for the reason that rotational dofs are usually difficult to be measured. This article proposes an expansion method to deal with spatial incompleteness of measured mode shapes of beam structures. One improvement is that the constrained linear least squares is combined into traditional expansion procedure proposed by Liu (2011), to estimate modeling errors in a physical meaning interval; and the initial guesses on mode-correction coefficients could be obtained using a non-iterative technique for improving the convergence of the approach. A cantilever beam is used to investigate the proposed method by establishing two numerical models: one is a beam finite element model as a baseline; the other is the model to represent real structure with different stiffness distribution compared with the baseline. One can conclude from numerical results that the approach has a better convergence performance than traditional expansion method, and spatially incomplete measured modes for beam structures, including higher order modes, can be expand properly and to be fundamental modal data for model updating or damage detection of beam structures.