Optimal reconstruction of mode shapes using nonuniform strain sensor spacing

In this paper, a theoretical and practical technique for the reconstruction of the static and dynamic deflection curves of a cantilever beam with one free end is presented. In practice a limited number of strain sensors is used, so the sensor layout is important for the accuracy of the result. A new approach for finding an optimized number and placement of FBG strain sensors is described, and it is shown that five well placed readings suffice to precisely reconstruct the modes up to the 3rd which are significant in lots of applications. The method is validated by comparing dynamic shape estimations with experimental results