A self-demodulated fiber Bragg grating for investigating impact-induced transient responses of phononic crystal beams

This work presents a fiber Bragg grating (FBG) displacement sensing system to experimentally investigate the dynamic behaviors of phononic crystal (PC) beams through impact-induced early short time or long time transient responses. Based on the couple-mode theory and the optical transfer matrix (T-matrix) formulation, we first show that it is feasible to achieve linear displacement sensing using a single FBG without extra demodulators such as matching gratings. To validate its effectiveness, the proposed self-demodulated FBG system is applied to measure the point-wise transient displacement responses of a cantilever PC beam subjected to steel ball impacts. To demonstrate the transient sensing performance, the measured early short time transient responses are compared with the corresponding ones predicted by the method of reverberation-ray matrix (MRRM) theoretically and the finite element method (FEM) numerically. The excellent agreements verify together the experimental, theoretical and numerical results. Finally, conducting Fast-Fourier transform (FFT) to the early short time or long time transient responses gives the frequency responses that clearly show the existence of the band gaps. In addition to providing a new displacement sensing method using the self-demodulated FBGs, this work also offers another route to investigate the band structures of PC beams through the frequency responses transformed from the early short time transient responses, long before the structural damping becomes dominant.