Long base optical fiber extensometers sense structural geometrical nonlinearities

With the development of interferometric optical fiber sensors (OFS), very long base extensometers are commercially available. They are very interesting for dynamic structural health monitoring, as their length is similar to bridge dimensions; thus structural behaviour instead of local particularities is sensed. Recent research focused on the sheath of the optical fiber so as to enable the sensor to be continuously attached to the structure. We focused our work on the use of this type of OFS for structural health monitoring. Assuming that the sensor is a Fabry-Perot cavity continuously attached to the structure and read by low-coherence interferometry, the measurement is the integration of the curvature along the optical fiber between the partial mirrors included in the fiber. For long-base extensometers, curvature differs from Euclidian distance and calculations showed that structural linear approximations may not be valid anymore. More precisely, the dynamic response of OFS depends on the geometrical nonlinearities of the structure. If dynamical equations governing the beam are linear, OFS, like every sensor, enable determining the structural modes. If the nonlinearities are not negligible, the Fourier transform of the OFS measurements contains the structural eigenfrequencies (also detected by accelerometers), on top of which unexpected frequencies appear. These additional frequencies are combinations of the structural ones. The amplitude of the peaks depends on the degree of the geometrical nonlinearity, the length and location of the OFS. From that point of view, long base optical fiber extensometers sense structural geometrical nonlinearities. Numerical simulations are given in the case of after-shock vibrations of free-free beam.