Quasi distributed strain sensing in cantilever beams by use of modal interference

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1 Quasi distributed strain sensing in cantilever beams by use of modal interference *S.K.Ghorai and Dilip Kumar Department of Electronics and Communication Engineering, Birla Institute of Technology, Mesra,Ranchi * ABSTRACT A quasi distributed strain sensing method based on intermodal interference (LP 1 ) in a single mode birefringent fiber is presented for measurement of strain of an array of simply supported beam and cantilever beam. A frequency modulated optical signal was launched into the fiber and the amplitude of the beat frequencies due to interference of signals were measured using FFT method. Results for different loading conditions are presented. 1. INTRODUCTION Fiber optic sensing of strain in concrete beam and advanced structure has been attractive for the past few years, as it permits real time and in situ measurement. Distributed fiber optic sensing has the advantages of continuous monitoring the mechanical parameters of structures and this would allow the alleviating action to be taken in good time before any potentially damaging condition. Several different types of fiber optic sensors have been reported for measurement of strain in different types of beams or structures. Fiber Bragg grating sensors have created great current interest for monitoring strain in composite structures [1,]. In these sensors intracore gratings are written within the fiber and there is a change in the Bragg wavelength under the loading condition. The advantage of these sensors is that their measurements are independent of source intensities and losses. However the disadvantage is that their manufacturing process is quite difficult because of stringent requirements. Recently long period fiber gratings (LPFGs) written by the high frequency CO large pulses have been demonstrated to reduce the fabrication difficulties and to increase load sensitivity [3]. But their writing efficiency depends on the precise control of focusing and these are affected by cross-sensitivity during simultaneous measurement of measurands. A quasi distributed strain sensor based on OTDR (Optical time domain reflectometry ) has been proposed for measuring strain in a long structure [4]. Several reflectors are built in the core of optical fiber with suitable reflection coefficient. However the sensor system would be expensive and technological complexity would be present during implementation. A low cost 1 x N star coupler distribution strain fiber optic sensors has been demonstrated in a white light interferometer system for measuring strain in smart materials and structure [5]. The advantage of such low coherence interferometers was its ability to facilitate the absolute measurements and it provides an in-service monitor for tracking structure response to characterize fatigue and to assess damage. A double interferometer quasi distributed intrinsic fiber optic strain sensor has been reported for measurement of structural strains based on white light interferometry [6]. It consists of a self-referencing interferometer and interrogator. The reference arm in the sensing module was eliminated and a single optical fiber was used both for sensing as well as for referencing. This would eliminate the error associated with the lead in fiber phase changes. Another white light quasi-distributed fiber optic strain sensor based on a Mach-Zehnder optical path interrogator has been used to measure/monitor strain distribution in smart structure [7]. The sensor architecture provides the redundancy owing to its bidirectional interrogation of sensor ring. However in these two beam interferometric sensors the reference and sensing arms are placed at different locations, which can lead to error in the measurement. Distributed sensors based on Brillouin scattering have been reported for strain distribution in cantilever beam [8-1]. By analyzing the Brillouin back scattered light power spectrum, the strain and the measurement position have been determined for a beam to which a concentrated load is applied. In this method, strain measurement error is minimized for a uniform strain distribution but it increases when the strain difference becomes large and also the spatial resolution is limited.

2 In the present paper we report a quasi distributed strain sensor for measuring strain in an array of simply supported beam and cantilever beam. It is based on the interference of two lower order modes in SM (single mode) fiber. The beat frequencies produced due to the interference of LP 1 modes were measured using Fourier transform method, where a frequency modulated continuous wave (FMCW) was launched in a biefringent SM fiber. By measuring the amplitude and frequency of the beat signal strain and position of the corresponding beam were determined.. EXPERIMENTAL SET UP Fig.1. shows the fiber optic sensing scheme for measurement of quasi distributed strain at different fiber lengths. The set up comprises of a cantilever and simply supported beam at different locations. The simply supported beam was positioned at fiber length of 3.meter from the detection end, and the cantilever at.meter. A single mode birefringent fiber (LB-13, Oxford Electronics) was attached to the beam using suitable adhesive. The beams were made of plastic (Arcylic-Rod). The dimension of the beam used for simply supported beam was 51.cm x 3.cm x.6 cm, and for the cantilever one 4.cm x 3.cm x.6 cm. The loads were applied at the center of the beam in case of simply supported beam and at the extreme end in case of the cantilever beam, by use of weights. FIBER W W POWER SUPPLY L D C P Photodetector FUNCTION GENERATOR PC C P RAMP SIGNAL MEGAZOOM OSCILOSCOPE Fig. 1. Experimental Set-up: LD-Laser diode, CP-Coupler Optical couplers have been connected to both ends of the fiber and those were then coupled to the Laser diode (Ando Electric, AQ-1318, 85 nm) and a Si photodetector ( Melles Griot) respectively. The Laser diode has been modulated by a saw tooth signal of 5 Hz from a function generator. The fiber was characterized by cutoff wavelength 13 nm. So at 85 nm, by changing launching condition, lowest order modes LP 1 were excited. The photodetector output was fed to the oscilloscope (Agilent 5461D Megazoom) where digital signal processing was performed using FFT. There is a specific harmonic corresponding to the beam position at a fixed fiber length from the detection end, whose amplitude changes in linear way on application of load. By measuring the amplitude variations of those specific harmonics, the strains produced on the beams were determined.

3 3. SENSOR PRINCIPLE In a single fiber if the V-parameter is set in the range.45 V 3.8, then LP 1 mode would propagate through the fiber. A small perturbation due to strain at one point of the fiber causes a coupling of light to the other mode. The phase delay due to the different mode velocities leads to a beat frequency. This phase difference may be written as Φ = ( β )L 1 (1) where β and β 1 are the propagation constants of LP 1 modes respectively, L is the distance of light propagation along the fiber. Assuming, under loading condition the strain in fiber is due to longitudinal strain, change in phase is given by, β ( Φ) = ( β β1) + L ( β β L L 1 ) Under weakly guiding approximation, the propagation constant β ( =,1) can be expressed in terms of normalized propagation constant as β = k [ n + b ( n n )] 1 where k, n 1, and n are the free space wave vector, core and cladding refractive index respectively. Assuming the fiber as homogeneous material in elasticity, the refractive index variation under strain can be written as [11] n L n = L 3 [ p σ ( p + p )] where p 11, p 1 are Strain Optic Coefficients (.1 and.7) for fused silica, σ is the Poisson s ratio (.17). For weekly guiding fibers, b can be expressed as a function of normalized frequency V [1] (3) () (4) b V = L L σ whereν = p 1 ν + σ ( p ( n + n ) 1 11 b V + p ) 1 (5) Using the above equations finally we get β L k = Lβ ν b 4 4 { n + b ( n n )} + V δ 4 1 V (6) where δ=σ(n 1 n )+ 4 ν/(n 1 n 4 ) The values of b and b / V can be obtained by solving the eigen value equations for LP lm modes which are given by [13], 1/ 1/ J [ (1 ) ] [ ] ( 1 ) 1/ l 1 V b 1/ Kl 1 Vb V b = Vb ; l 1 1/ J [ V (1 b)] K [ Vb ] l l (7) 1/ 1/ J1[ V (1 b) ] K1[ Vb ] V ( 1 b) 1/ = Vb 1/ 1/ 1/ J [ V (1 b) ] K [ Vb ] ; l = (8)

4 Substituting the values of β/ L, we find the differential phase shift due to strain. If the laser frequency is modulated by a current ramp, then instantaneous frequency can be written as, ω(t)=ω +Ωt (9) where ω is the constant frequency and Ω is a modulation constant. If mode conversion occurs at a distance L, from the fiber end due to strain, then time difference between the modes LP 1 and LP 11 is, τ= (β - β 1 ) L / ω or, τ=λ L / C Lp (1) where, beat length Lp = π / (β - β 1 ) When the two beams interfere, the beat signal generated is, S( t) = P cos θ + P1 sin θ + P P1 sin θ cos( ω t + Φ) (11) where P & P 1 are powers of LP 1 modes respectively, ω=ωτ, is the beat frequency and θ is the angle of orientation of polarizer at the detector end. From the values of ω, one can obtain the distance L, the point of disturbance, which is given by, CL P L = ω λ Ω Change in amplitude of the beat frequency in the power spectrum provides the information about the measurand (strain). (1) 4. RESULTS AND DISCUSSION An elliptical core birfringent fiber (LB-3, Oxford-Electronics) was used in our experiment. The interference patterns recorded for simply supported beam under different loading condition are shown in fig.. and those for cantilever beam are shown in fig.3. (a)

5 (b). (c) Fig.. Interference patterns and FFT recorded for simply supported beam under different loading conditions: (a) for no load, (b) for 5gm & (c) for gm. (a) (b) Fig. 3. Interference patterns and FFT recorded for cantilever beam under different loading conditions: (a) for5 gm, (b) for 5gm The harmonics of the corresponding patterns are also shown after performing FFT (Fast Fourier Transform). The beat frequencies obtained from the fiber parameters were 9Hz for the simply supported beam and 67Hz for the cantilever beam. The central point of the simply supported beam from the photodetector was at 3.m and that for cantilever beam was at

6 .m. The birfringent fiber that was used in our experiment had the following parameters: n 1 =1.461, n =1.456, V=.36 at?=13nm At the operating wave length of 85nm. V-parameter comes out to be 3.6. Using these fiber parameters normalized propagation constants b (for LP 1 ) and b 1 (for LP 11 ) were obtained as b =.738 and b 1 =.35. The beat length of fiber at 85 nm, L p came out to be.44mm. Substituting these values in equation (11) the power spectrum was obtained through FFT operation. The peak of the spectrum obtained corresponds to the 4 th harmonic (for simply supported beam) and 3 ed harmonic (for cantilever beam) of the modulating signal. (a) no load (b) 5gm (c) gm Fig.4. Interference patterns for simply supported beam under different loading condition. The results were in good agreement with our experimental work. The phase informations of the fringe patterns were retrieved using Fourier transform method. The interference patterns were captured using CCD camera and are shown in fig.4. for simply supported beam. The gray level values of the pixel of a selected size of the pattern were determined using an image processing algorithm. Those were Fourier transformed and filtered in the spatial frequency domain. After filtering the fundamental component of the spectrum inverse Fourier transform was applied. The obtained phase was unwrapped to obtain the phase distribution of the pattern. Fig.5 (a) &(b) show the phase distributions obtained from the fringe patterns of the fig,4 (a) & (b). Normalized phase Normalized phase Y (pixels) (a) X (pixels) Y (pixels) (b) X (pixels) Fig 5. Phase distributions of fringe patterns of fig. 4 (a) & (c).

7 Fig.6. (a) shows the variation in amplitude of beat frequency (3 ed harmonic) in case of cantilever beam and fig.6.(b) shows the variation in case of simply supported beam under different loading conditions. With proper calibration the strain applied to a particular beam can be determined through the measurement of the amplitude of beat frequency. Amplitude of bear frequency (dbv) Relative strain (µstrain) Amplitude of bear frequency (dbv) Relative strain (µstrain) Fig.6(a) Amplitude of beat frequency vs applied strain in cantilever beam. CONCLUSION We have demonstrated a FMCW method based on LP 1 mode interference in a birefringent fiber for strain measurement in an array of simply supported beam and cantilever beam at different locations. The amplitude of beat frequency obtained through FFT operation of the interference signal has provided the information about the strain applied to the beams. Measurement sensitivity would depend on the mode coupling into the birefringent fiber. The method can be used for fully distributed system in structural monitoring application. ACKNOWLEDGEMENT: The authors deeply acknowledge the ISRO (VSSC) for providing the necessary financial support. Fig.6(b). Amplitude of beat frequency vs applied strain in simply supported beam. REFERENCES: 1. Cure monitoring of smart composites using Fiber Bragg Grating based embedded sensors: V. M. Murukeshan, P. Y. Chan, L. S. Ong, and L. K. Seah, Sensor Actuat, Vol No.A 8, 153 (1999).. Intracore fiber Bragg grating for strain measurement in embedded composite structures: V. M. Murukeshan, P. Y. Chan, L. S. Ong, A. Asundi, Appl. Opt., Vol. No. 4, 145 (1). 3. Novel Fiber-Optic Sensors Based on Long-Period Fiber Grating Written by High-Frequency CO Laser Pulses: Y. J. Rao, Y P Wang, Z. L. Ran, and T. Zhu, J. Lightwave Technol.,Vol No 1, 13(3). 4. A Novel distributed fiber optic strain sensor: M.J.Garica, J.A. Ortega, J.A.Chavez, J.Salazar, and Antoni Turo, IEEE trans.instrum.meas,vol No 51, 685 () 5. 1x N star coupler as a distributed fiber-optic strain sensor in a white-light interferometer: Libo Yuna and Limin Zhou, Appl. Opt., Vol. No. 37, 4168 (1998)

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