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

Abstract Background Experimental modal analysis with laser Doppler vibrometry is usually limited to the identification of mono-dimensional mode shapes, typically in the out-of-plane direction. This simplification restricts the understanding of the true three-dimensional deformation of a structure. Objective The objective of this work is to develop an experimental–computational framework for the reconstruction of full three-dimensional mode shapes using a single scanning laser Doppler vibrometer and to establish a consistent procedure for comparison with numerical mode shapes expressed in different coordinate systems. Methods The methodology combines frequency response function measurements obtained from three independent orientations of the tested component while maintaining a fixed laser head position. A reconstruction algorithm based on projection relations and rotation matrices is employed to recover the complete three-dimensional vibration shape, while an additional least-squares-based projection algorithm is introduced to project numerical mode shapes into the experimental reference frame. The methodology is experimentally validated on an air-compressor collector using a Polytec PSV-500 scanning laser Doppler vibrometer. Results The reconstructed experimental three-dimensional mode shapes showed strong agreement with numerical predictions for the first three vibration modes, with Modal Assurance Criterion values of 0.93, 0.94, and 0.85, confirming strong modal correspondence. Conclusions The proposed framework provides a cost-effective and flexible alternative to multi-head vibrometer systems for three-dimensional experimental modal analysis and enables reliable reconstruction of three-dimensional mode shapes together with consistent comparison with numerical models.