Experimental Evaluation of Three-Dimensional Mode Shapes and Frame-Consistent Comparison with Numerical Models

Experimental modal analysis with laser Doppler vibrometry is usually limited to the identification of monodimensional mode shapes, typically in the out-of-plane direction. This simplification restricts the understanding of the true three-dimensional deformation of a structure. In this work, we propose an experimental–computational framework to reconstruct full three-dimensional mode shapes from laser doppler vibrometry measurements. The method relies on three complementary test configurations, from which frequency response functions are extracted and combined through an algorithm to recover the complete spatial mode shape. A second contribution of this study addresses the challenge of reference frame inconsistency between experimental and numerical mode shapes. While numerical predictions are often defined in different coordinate systems, the relation between these frames is not trivial for components with complex geometry. We introduce a projection algorithm that transforms numerical mode shapes into the experimental reference frame, enabling a direct and reliable comparison. The combined approach improves the accuracy of experimental mode shape identificationand provides a systematic procedure for validation against finite element models