Experimental verification of the modified spring-mass theory of fiber Bragg grating accelerometers using transverse forces

A fiber Bragg grating (FBG) accelerometer using transverse forces is more sensitive than one using axial forces with the same mass of the inertial object, because a barely stretched FBG fixed at its two ends is much more sensitive to transverse forces than axial ones. The spring-mass theory, with the assumption that the axial force changes little during the vibration, cannot accurately predict its sensitivity and resonant frequency in the gravitational direction because the assumption does not hold due to the fact that the FBG is barely prestretched. It was modified but still required experimental verification due to the limitations in the original experiments, such as the (1) friction between the inertial object and shell; (2) errors involved in estimating the time-domain records; (3) limited data; and (4) large interval ∼5 Hz between the tested frequencies in the frequency-response experiments. The experiments presented here have verified the modified theory by overcoming those limitations. On the frequency responses, it is observed that the optimal condition for simultaneously achieving high sensitivity and resonant frequency is at the infinitesimal prestretch. On the sensitivity at the same frequency, the experimental sensitivities of the FBG accelerometer with a 5.71 gram inertial object at 6 Hz (1.29, 1.19, 0.88, 0.64, and 0.31 nm/g at the 0.03, 0.69, 1.41, 1.93, and 3.16 nm prestretches, respectively) agree with the static sensitivities predicted (1.25, 1.14, 0.83, 0.61, and 0.29 nm/g, correspondingly). On the resonant frequency, (1) its assumption that the resonant frequencies in the forced and free vibrations are similar is experimentally verified; (2) its dependence on the distance between the FBG's fixed ends is examined, showing it to be independent; (3) the predictions of the spring-mass theory and modified theory are compared with the experimental results, showing that the modified theory predicts more accurately. The modified theory can be used more confidently in guiding its design by predicting its static sensitivity and resonant frequency, and may have applications in other fields for the scenario where the spring-mass theory fails.