Designing possibility of a seismometer using Fiber Bragg Grating and metal bellows

In this study, we have theoretically investigated designing possibility of a seismometer using Fiber Bragg Grating (FBG) and Metal Bellows pairs attached on a mechanical system. This new seismometer can record earthquakes according to sensitivity of fiber optic to changes in physical parameters such as stress and strain. Firstly, in order to understand the quantity and quality of sensor performance, with a mathematically brief description, the effect of stress and strain on the FBG reflection spectrum is examined. FBG is an intrinsic sensing element which can be photo-inscribed into a silica fiber. The basic principle of this operation commonly uses FBG based sensor system. The operation is monitoring of the shift in wavelength of the Bragg signal following changing in stress, strain and also temperature. The Bragg wavelength, or resonance condition of a Grating, is                                              
                                                                                                                                                                    (1)
The wavelength of the optical signal reflected by the Bragg Grating depends on the FBG physical parameters ( the fiber's effective refractive index, and  is the wave length of the FBG). These parameters are changed if the Grating is subjected to mechanical deformation or temperature variation. The measured strain response at constant temperature is
                                                                                                                                             (2)
                                                                                                                                                              (3)
The structure of the seismometer consists of an inertial mass, supported by a L-shaped aluminum cantilever beam, connected to the structure base by metal bellows and an FBG element. In case of ground acceleration, the inertial mass moves in the vertical direction, imposing a compressed or stretch of the optical fiber. This deformation induces variation on the FBG Bragg wavelength. From the system work-energy concept analysis, the seismometer undamped natural frequency can be written as:
                                                                                                                                                 (4)
with natural frequency about 7.8 Hz. Ideally, we can consider a seismometer as a black box whose input is ground motion (represented by a kinematic variable: displacement, velocity or acceleration) and its output is displacement Bragg wavelength. Assuming a ground acceleration ,, by using the frequency range of 2011 (M_W 6.0) Rigan earthquake waveform, strain (5) and displacement of amplitudes Bragg wavelength (6) and phase change (7) for different angular frequencies and amplitudes of the ground acceleration (for different damping coefficient 0.4, 0.6, 0.8, 1) are obtained. The relationships between them are investigated and for different angular frequencies, they are plotted and compared.
                                                                                                                                              (5)
                                                                                                                                      (6)
                                                                                                                                                                    (7)
As  (undamped), the solution has an increasing amplitude as , which is called resonance. If  (under damped), the signal tend to ring at near seismometer period. For  the signal is critically damped and oscillation is minimized. For  (overdamped), no oscillations occur, but the mass returns to rest more slowly. The possibility of designing a seismometer is investigated which works in near critical damping (0.6, optimal damping coefficient) which records a part of earthquake waves with frequency close to the natural frequency of the seismometer with the maximum amplitude and without phase-shift. Also, to prove performance and ability of seismometer with the mentioned method two other earthquakes, 2010 (M_W 6.4) Rigan earthquake and 2011 (M_W 7.8) Saravan earthquakes were investigated. Also each of the above events recorded and processed at the same time by several seismic stations and compared with seismometer Fiber Bragg Grating. A seismometer which uses Fiber Bragg Grating has a few number of advantages such as immunity to electromagnetic interference, their capability to transmit signal over long distance without any additional amplifiers, highly accurate and digital output, lighter weight, high sensitivity, low power consumption, lower cost and a wide range of dynamics.