In a typical optic fiber Bragg grating (FBG) strain measurement, unless made in an ideal static laboratory environment, the presence of vibration or often disturbance always exists, which often creates spurious multiple peaks in the reflected spectrum, resulting in a nonunique determination of strain value. We attempt to investigate the origin of this phenomenon by physical arguments and simple numerical simulation. We postulate that the fiber gratings execute small-amplitude transverse, vibrations changing the optical path in which the reflected light traverses slightly and nonuniformly. Ultimately, this causes the multipeak reflected spectrum.
We suggest using distributed fiber Bragg sensors systems which were developed locally at Langley Research Center carefully placed on the wing surface to collect strain component information at each location. Then we used the fact that the rate change of slope in the definition of linear strain is very small and can be treated as a constant. Thereby the strain distribution information of a morphed surface can be reduced into a distribution of local slope information of a flat surface. In other words a morphed curve surface is replaced by the collection of individual flat surface of different slope. By assembling the height of individual flat surface, the morphed curved surface can be approximated. A more sophisticated graphic routine can be utilized to restore the curved morphed surface. With this information, the morphed wing can be further adjusted and controlled. A numerical demonstration is presented.
Conventional finite element approaches for modeling delaminations in laminated composite structures use the Heaviside unit step function at the interfacial nodes in the delaminated zone of the structure to model the possible jumps in the displacement field during “breathing” of the delaminated layers. In quantum mechanics, the Fermi-Dirac distribution applies to Fermion particles whose characteristics are half-integer spins. The present paper uses the Fermi-Dirac distribution function to model a smoother transition in the displacement and the strain fields of the delaminated interfaces during the opening and closing of the delaminated layers under vibratory loads. This paper successfully shows that the Fermi-Dirac distribution function can be used to more accurately model the dynamic effects of delaminations in laminated composite structures. Optimizing the parameters in the Fermi-Dirac distribution function can lead to more accurate modeling of the dynamic and transient behavior of the delaminated zones in laminated composite structures. Further applications of the Fermi-Dirac distribution function in other physics based dynamic models are suggested. This paper also effectively demonstrates how hybrid sensors comprising of out of plane displacement sensors and in plane strain sensors can effectively map a composite structure to detect and locate the delaminated zones. It also shows how simple mode shapes can be used to determine the locations of single and multiple delaminations in laminated composite structures.
The reflected signature of an optical fiber Bragg grating is analyzed using the transfer function method. This approach is capable to cast all relevant quantities into proper places and provides a better physical understanding. The relationship between reflected signal, number of periods, index of refraction, and reflected wave phase is elucidated. The condition for which the maximum reflectivity is achieved is fully examined. We also have derived an expression to predict the reflectivity minima accurately when the reflected wave is detuned. Furthermore, using the segmented potential approach,
this model can handle arbitrary index of refraction profiles and compare the strength of optical reflectivity of different profiles. The condition of a non-uniform grating is also addressed.
By adopting the basic principle of the reflection (and transmission) of a plane polarized electromagnetic wave incident normal to a stack of films of alternating refractive index, a simple numerical code was written to simulate the maximum reflectivity (transmittivity) of a fiber optic Bragg grating corresponding to various non- uniform strain conditions including photo-elastic effect in certain cases.