Modal Expansion using Strain Mode Shapes

Reduction/expansion approaches have been conventionally used in correlation and validation studies. Recently, these approaches have also been used to extract full-filed results on structures using limited set of data measured. The expansion techniques are used to expand real-time data measured on components of vehicle chassis, utility scale wind turbines, and helicopter rotors. The resulted full-field data is used to monitor structures and determine their durability. With the advances in Digital Image Correlation (DIC), researchers are able to readily extract strain mode shapes of structures. However, the conventional reduction/expansion techniques are usually limited to displacement, velocity, or acceleration data. This can hinder correlation studies that compare the strain data between two models. Furthermore, this limitation does not allow researchers to expand strain-gage measured data for full-field structural monitoring and durability analysis. In the current paper, a reduction/expansion technique has been developed to reduce/expand strain data. In this technique, measured strain at limited locations is expanded using strain mode shapes to extract full-field results on the entire surface and within the structure. This technique can also be used to reduce data for correlation studies. In order to demonstrate the merit of the approach, the proposed strain expansion approach was applied to the finite element model of a cantilever beam subjected to sinusoidal and impact excitations. The results show that the proposed approach can effectively expand the strain measured at limited locations. The approach could accurately predict the strain at locations where no sensors were placed.