Dynamic characteristics and response of low frequency cantilever beam-based FBG accelerometer under base excitation

Cantilever FBG accelerometer for low frequency application is usually modelled by single-degree-of-freedom (SDOF) system which gives linear strain-curvature relationship along the beam, even when the curvature is not linear especially when the excitation frequency is greater than fundamental frequency. This inaccurate prediction can be overcome by modelling the cantilever beam using Euler-Bernoulli (EB) theorem which considers MDOF systems. Therefore, this paper presents: (a) the validation of analytical works using EB theorem for cantilever beam and its comparison with Timoshenko (T) theorem (rotational inertia and shear force are considered) obtained from finite element method and (b) initial analysis of strain developed on cantilever beam using EB theorem and SDOF model at low frequency range. Despite the fact that the work in (a) is inequitable comparison, yet it is valid for the case of slender beam structure at low frequency range in this study. The results show that the dynamic characteristic and vibration response of a simple cantilever beam structure is not significantly affected by both rotational inertia and shear force at low frequency excitation, thus proves that the EB theorem is valid to be used in representing cantilever FBG accelerometer. In the second work (b), the strain computed from the EB theorem gives significant discrepancy in terms of value and pattern compared to SDOF model.