A strain-wavelength modelling of low-frequency cantilever fibre Bragg grating accelerometer

Abstract

The accuracy of single-degree-of-freedom (SDOF) model in describing the beam motion of low-frequency cantilever fibre Bragg grating (FBG) accelerometer can be further explored, since the SDOF model is limited to fundamental vibration modes. Therefore, this paper addresses the aforementioned limitation by introducing a modal model of the cantilever Euler-Bernoulli (EB) beam into the wavelength shift equation. This modal model (FBG-MM) considered five vibration modes. The convergent series of eigenfunction for cantilevered EB beam was solved using a standard modal expansion theory. The curvature of the cantilevered beam resulted from dual differentiation of the eigenfunction (with respect to x) is then related to the strain and wavelength of the FBG. The computed wavelength shift using FBG-MM was compared with the SDOF model. The experimental results where the harmonic base excitation occurring at five different frequencies were also discussed. The simulation results showed that the wavelength shift exhibited more reasonable behaviour along the beam particularly when the excitation frequency exceeded the second bending mode (596.67 Hz). The FBG-MM and experimental wavelength shift showed convincing correlation only when the excitation frequency came close to the fundamental frequency. On the other hand, there was no agreement at low excitation frequencies due to stiffness issues of the cantilever beam and the capability of the optical spectrum analyser. In future, the improvement of this study will focus on introducing a tip mass on the cantilever beam for increasing the accelerometer sensitivity and representing the cantilever beam using Timoshenko model.