Abstract

A theoretical analysis of fiber Bragg grating (FBG)-based plane strain monitoring of aerostat envelope structures is presented. Plane strain analysis of FBG-based aerostat envelope structures is much more complex than the case along the axis of the optical fiber because the effect of transverse stress on the FBG should be taken into consideration. To achieve accurate strain measurement of the aerostat envelope, a theoretical model is set up by using two perpendicular fibers in the monitoring. An analytical formula that evaluates the relationship between the strain measured by FBG sensors and the real one in the aerostat envelope is established. On the other hand, the real strain of aerostat envelope strain is affected by two unknown parameters, axial transfer rate KL and the radial transfer rate KR. An equation is derived to calculate the axial transfer rate KL. Then, the finite element method results show that KR is a very small value, but it cannot be ignored in accurate measurement. This paper would lay a theoretical groundwork for the research and design of FBG sensors in the structural health monitoring of aerostat envelope structures.

© 2013 Optical Society of America

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References

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  1. D. Huang, H. Zhao, Y. Qiu, and J. Chen, “Modeling and simulation analysis of stratospheric aerostat envelop,” Comput. Simul. 30, 150–153 (2013).
  2. M. D. Todd, G. A. Johnson, and S. T. Vohra, “Deployment of a fiber Bragg grating-based measurement system in a structural health monitoring application,” Smart Mater. Struc. 10, 534–539 (2001).
    [CrossRef]
  3. H. Zhao, Q. Wang, Y. Qiu, J. Chen, Y. Wang, and Z. Fan, “Strain transfer of surface-bonded fiber Bragg grating sensors for aerostat envelope structural health monitoring,” J. Zhejiang Univ. Sci. A 13, 538–548 (2012).
  4. R. B. Wagreich, W. A. Atia, H. Singh, and J. S. Sirkis, “Effects of diametric load on fibre Bragg gratings fabricated in low birefringent fibre,” Electron. Lett. 32, 1223–1224 (1996).
    [CrossRef]
  5. R. Gafsi and M. A. El-Sherif, “Analysis of induced-birefringence effects on fiber Bragg gratings,” Opt. Fiber Technol. 6, 299–323 (2000).
    [CrossRef]
  6. J. Zhao, X. Zhang, Y. Huang, and X. Ren, “Experimental analysis of birefringence effects on fiber Bragg gratings induced by lateral compression,” Opt. Commun. 229, 203–207 (2004).
    [CrossRef]
  7. G. Luyckx, E. Voet, N. Lammens, and J. Degrieck, “Strain measurements of composite laminates with embedded fibre Bragg gratings: criticism and opportunities for research,” Sensors 11, 384–408 (2011).
    [CrossRef]
  8. K. T. Lau, “Fibre-optic sensors and smart composites for concrete applications,” Mag. Concr. Res. 55, 19–34 (2003).
    [CrossRef]
  9. R. V. Steenkiste and L. Kollar, “Effect of the coating on the stresses and strains in an embedded fiber optic sensor,” J. Compos. Mater. 32, 1680–1711 (1998).
    [CrossRef]
  10. K. Nagano, S. Kawakami, and S. Nishida, “Change of the refractive index in an optical fiber due to external forces,” Appl. Opt. 17, 2080–2085 (1978).
    [CrossRef]
  11. W. Morey, G. Meltz, and W. Glenn, “Fiber optic Bragg grating sensors,” Fiber Optic Laser Sensors 1169, 98–107 (1989).
  12. A. Kersey, M. Davis, H. Patrick, M. LeBlanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
    [CrossRef]
  13. M. Lai, D. Karalekas, and J. Botsis, “On the effects of the lateral strains on the fiber Bragg grating response,” Sensors 13, 2631–2644 (2013).
    [CrossRef]
  14. C. Liu, P. Chen, H. Li, and H. Tu, “Application of the fiber Bragg grating transverse effect in measurement of plain strain,” Opt. Optoelectron. Technol. 6, 29–32 (2008).
  15. D. C. Betz, G. Thursby, B. Culshaw, and W. J. Staszewski, “Advanced layout of a fiber Bragg grating strain gague rosette,” J. Lightwave Technol. 24, 1019–1026 (2006).
    [CrossRef]
  16. Q. Wang, Y. Qiu, H. Zhao, J. Chen, Y. Wang, and Z. Fan, “Analysis of strain transfer of six-layer surface-bonded fiber Bragg gratings,” Appl. Opt. 51, 4129–4138 (2012).
    [CrossRef]
  17. F. Ansari and Y. Libo, “Mechanics of bond and interface shear transfer in optical fiber sensors,” J. Eng. Mech. 124, 385–394 (1998).
    [CrossRef]
  18. D. S. Li, H. N. Li, L. Ren, and G. B. Song, “Strain transferring analysis of fiber Bragg grating sensors,” Opt. Eng. 45, 024402 (2006).
    [CrossRef]

2013

D. Huang, H. Zhao, Y. Qiu, and J. Chen, “Modeling and simulation analysis of stratospheric aerostat envelop,” Comput. Simul. 30, 150–153 (2013).

M. Lai, D. Karalekas, and J. Botsis, “On the effects of the lateral strains on the fiber Bragg grating response,” Sensors 13, 2631–2644 (2013).
[CrossRef]

2012

H. Zhao, Q. Wang, Y. Qiu, J. Chen, Y. Wang, and Z. Fan, “Strain transfer of surface-bonded fiber Bragg grating sensors for aerostat envelope structural health monitoring,” J. Zhejiang Univ. Sci. A 13, 538–548 (2012).

Q. Wang, Y. Qiu, H. Zhao, J. Chen, Y. Wang, and Z. Fan, “Analysis of strain transfer of six-layer surface-bonded fiber Bragg gratings,” Appl. Opt. 51, 4129–4138 (2012).
[CrossRef]

2011

G. Luyckx, E. Voet, N. Lammens, and J. Degrieck, “Strain measurements of composite laminates with embedded fibre Bragg gratings: criticism and opportunities for research,” Sensors 11, 384–408 (2011).
[CrossRef]

2008

C. Liu, P. Chen, H. Li, and H. Tu, “Application of the fiber Bragg grating transverse effect in measurement of plain strain,” Opt. Optoelectron. Technol. 6, 29–32 (2008).

2006

D. S. Li, H. N. Li, L. Ren, and G. B. Song, “Strain transferring analysis of fiber Bragg grating sensors,” Opt. Eng. 45, 024402 (2006).
[CrossRef]

D. C. Betz, G. Thursby, B. Culshaw, and W. J. Staszewski, “Advanced layout of a fiber Bragg grating strain gague rosette,” J. Lightwave Technol. 24, 1019–1026 (2006).
[CrossRef]

2004

J. Zhao, X. Zhang, Y. Huang, and X. Ren, “Experimental analysis of birefringence effects on fiber Bragg gratings induced by lateral compression,” Opt. Commun. 229, 203–207 (2004).
[CrossRef]

2003

K. T. Lau, “Fibre-optic sensors and smart composites for concrete applications,” Mag. Concr. Res. 55, 19–34 (2003).
[CrossRef]

2001

M. D. Todd, G. A. Johnson, and S. T. Vohra, “Deployment of a fiber Bragg grating-based measurement system in a structural health monitoring application,” Smart Mater. Struc. 10, 534–539 (2001).
[CrossRef]

2000

R. Gafsi and M. A. El-Sherif, “Analysis of induced-birefringence effects on fiber Bragg gratings,” Opt. Fiber Technol. 6, 299–323 (2000).
[CrossRef]

1998

F. Ansari and Y. Libo, “Mechanics of bond and interface shear transfer in optical fiber sensors,” J. Eng. Mech. 124, 385–394 (1998).
[CrossRef]

R. V. Steenkiste and L. Kollar, “Effect of the coating on the stresses and strains in an embedded fiber optic sensor,” J. Compos. Mater. 32, 1680–1711 (1998).
[CrossRef]

1997

A. Kersey, M. Davis, H. Patrick, M. LeBlanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

1996

R. B. Wagreich, W. A. Atia, H. Singh, and J. S. Sirkis, “Effects of diametric load on fibre Bragg gratings fabricated in low birefringent fibre,” Electron. Lett. 32, 1223–1224 (1996).
[CrossRef]

1989

W. Morey, G. Meltz, and W. Glenn, “Fiber optic Bragg grating sensors,” Fiber Optic Laser Sensors 1169, 98–107 (1989).

1978

Ansari, F.

F. Ansari and Y. Libo, “Mechanics of bond and interface shear transfer in optical fiber sensors,” J. Eng. Mech. 124, 385–394 (1998).
[CrossRef]

Askins, C.

A. Kersey, M. Davis, H. Patrick, M. LeBlanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Atia, W. A.

R. B. Wagreich, W. A. Atia, H. Singh, and J. S. Sirkis, “Effects of diametric load on fibre Bragg gratings fabricated in low birefringent fibre,” Electron. Lett. 32, 1223–1224 (1996).
[CrossRef]

Betz, D. C.

Botsis, J.

M. Lai, D. Karalekas, and J. Botsis, “On the effects of the lateral strains on the fiber Bragg grating response,” Sensors 13, 2631–2644 (2013).
[CrossRef]

Chen, J.

D. Huang, H. Zhao, Y. Qiu, and J. Chen, “Modeling and simulation analysis of stratospheric aerostat envelop,” Comput. Simul. 30, 150–153 (2013).

Q. Wang, Y. Qiu, H. Zhao, J. Chen, Y. Wang, and Z. Fan, “Analysis of strain transfer of six-layer surface-bonded fiber Bragg gratings,” Appl. Opt. 51, 4129–4138 (2012).
[CrossRef]

H. Zhao, Q. Wang, Y. Qiu, J. Chen, Y. Wang, and Z. Fan, “Strain transfer of surface-bonded fiber Bragg grating sensors for aerostat envelope structural health monitoring,” J. Zhejiang Univ. Sci. A 13, 538–548 (2012).

Chen, P.

C. Liu, P. Chen, H. Li, and H. Tu, “Application of the fiber Bragg grating transverse effect in measurement of plain strain,” Opt. Optoelectron. Technol. 6, 29–32 (2008).

Culshaw, B.

Davis, M.

A. Kersey, M. Davis, H. Patrick, M. LeBlanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Degrieck, J.

G. Luyckx, E. Voet, N. Lammens, and J. Degrieck, “Strain measurements of composite laminates with embedded fibre Bragg gratings: criticism and opportunities for research,” Sensors 11, 384–408 (2011).
[CrossRef]

El-Sherif, M. A.

R. Gafsi and M. A. El-Sherif, “Analysis of induced-birefringence effects on fiber Bragg gratings,” Opt. Fiber Technol. 6, 299–323 (2000).
[CrossRef]

Fan, Z.

Q. Wang, Y. Qiu, H. Zhao, J. Chen, Y. Wang, and Z. Fan, “Analysis of strain transfer of six-layer surface-bonded fiber Bragg gratings,” Appl. Opt. 51, 4129–4138 (2012).
[CrossRef]

H. Zhao, Q. Wang, Y. Qiu, J. Chen, Y. Wang, and Z. Fan, “Strain transfer of surface-bonded fiber Bragg grating sensors for aerostat envelope structural health monitoring,” J. Zhejiang Univ. Sci. A 13, 538–548 (2012).

Friebele, E.

A. Kersey, M. Davis, H. Patrick, M. LeBlanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Gafsi, R.

R. Gafsi and M. A. El-Sherif, “Analysis of induced-birefringence effects on fiber Bragg gratings,” Opt. Fiber Technol. 6, 299–323 (2000).
[CrossRef]

Glenn, W.

W. Morey, G. Meltz, and W. Glenn, “Fiber optic Bragg grating sensors,” Fiber Optic Laser Sensors 1169, 98–107 (1989).

Huang, D.

D. Huang, H. Zhao, Y. Qiu, and J. Chen, “Modeling and simulation analysis of stratospheric aerostat envelop,” Comput. Simul. 30, 150–153 (2013).

Huang, Y.

J. Zhao, X. Zhang, Y. Huang, and X. Ren, “Experimental analysis of birefringence effects on fiber Bragg gratings induced by lateral compression,” Opt. Commun. 229, 203–207 (2004).
[CrossRef]

Johnson, G. A.

M. D. Todd, G. A. Johnson, and S. T. Vohra, “Deployment of a fiber Bragg grating-based measurement system in a structural health monitoring application,” Smart Mater. Struc. 10, 534–539 (2001).
[CrossRef]

Karalekas, D.

M. Lai, D. Karalekas, and J. Botsis, “On the effects of the lateral strains on the fiber Bragg grating response,” Sensors 13, 2631–2644 (2013).
[CrossRef]

Kawakami, S.

Kersey, A.

A. Kersey, M. Davis, H. Patrick, M. LeBlanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Kollar, L.

R. V. Steenkiste and L. Kollar, “Effect of the coating on the stresses and strains in an embedded fiber optic sensor,” J. Compos. Mater. 32, 1680–1711 (1998).
[CrossRef]

Koo, K.

A. Kersey, M. Davis, H. Patrick, M. LeBlanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Lai, M.

M. Lai, D. Karalekas, and J. Botsis, “On the effects of the lateral strains on the fiber Bragg grating response,” Sensors 13, 2631–2644 (2013).
[CrossRef]

Lammens, N.

G. Luyckx, E. Voet, N. Lammens, and J. Degrieck, “Strain measurements of composite laminates with embedded fibre Bragg gratings: criticism and opportunities for research,” Sensors 11, 384–408 (2011).
[CrossRef]

Lau, K. T.

K. T. Lau, “Fibre-optic sensors and smart composites for concrete applications,” Mag. Concr. Res. 55, 19–34 (2003).
[CrossRef]

LeBlanc, M.

A. Kersey, M. Davis, H. Patrick, M. LeBlanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Li, D. S.

D. S. Li, H. N. Li, L. Ren, and G. B. Song, “Strain transferring analysis of fiber Bragg grating sensors,” Opt. Eng. 45, 024402 (2006).
[CrossRef]

Li, H.

C. Liu, P. Chen, H. Li, and H. Tu, “Application of the fiber Bragg grating transverse effect in measurement of plain strain,” Opt. Optoelectron. Technol. 6, 29–32 (2008).

Li, H. N.

D. S. Li, H. N. Li, L. Ren, and G. B. Song, “Strain transferring analysis of fiber Bragg grating sensors,” Opt. Eng. 45, 024402 (2006).
[CrossRef]

Libo, Y.

F. Ansari and Y. Libo, “Mechanics of bond and interface shear transfer in optical fiber sensors,” J. Eng. Mech. 124, 385–394 (1998).
[CrossRef]

Liu, C.

C. Liu, P. Chen, H. Li, and H. Tu, “Application of the fiber Bragg grating transverse effect in measurement of plain strain,” Opt. Optoelectron. Technol. 6, 29–32 (2008).

Luyckx, G.

G. Luyckx, E. Voet, N. Lammens, and J. Degrieck, “Strain measurements of composite laminates with embedded fibre Bragg gratings: criticism and opportunities for research,” Sensors 11, 384–408 (2011).
[CrossRef]

Meltz, G.

W. Morey, G. Meltz, and W. Glenn, “Fiber optic Bragg grating sensors,” Fiber Optic Laser Sensors 1169, 98–107 (1989).

Morey, W.

W. Morey, G. Meltz, and W. Glenn, “Fiber optic Bragg grating sensors,” Fiber Optic Laser Sensors 1169, 98–107 (1989).

Nagano, K.

Nishida, S.

Patrick, H.

A. Kersey, M. Davis, H. Patrick, M. LeBlanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Putnam, M.

A. Kersey, M. Davis, H. Patrick, M. LeBlanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Qiu, Y.

D. Huang, H. Zhao, Y. Qiu, and J. Chen, “Modeling and simulation analysis of stratospheric aerostat envelop,” Comput. Simul. 30, 150–153 (2013).

Q. Wang, Y. Qiu, H. Zhao, J. Chen, Y. Wang, and Z. Fan, “Analysis of strain transfer of six-layer surface-bonded fiber Bragg gratings,” Appl. Opt. 51, 4129–4138 (2012).
[CrossRef]

H. Zhao, Q. Wang, Y. Qiu, J. Chen, Y. Wang, and Z. Fan, “Strain transfer of surface-bonded fiber Bragg grating sensors for aerostat envelope structural health monitoring,” J. Zhejiang Univ. Sci. A 13, 538–548 (2012).

Ren, L.

D. S. Li, H. N. Li, L. Ren, and G. B. Song, “Strain transferring analysis of fiber Bragg grating sensors,” Opt. Eng. 45, 024402 (2006).
[CrossRef]

Ren, X.

J. Zhao, X. Zhang, Y. Huang, and X. Ren, “Experimental analysis of birefringence effects on fiber Bragg gratings induced by lateral compression,” Opt. Commun. 229, 203–207 (2004).
[CrossRef]

Singh, H.

R. B. Wagreich, W. A. Atia, H. Singh, and J. S. Sirkis, “Effects of diametric load on fibre Bragg gratings fabricated in low birefringent fibre,” Electron. Lett. 32, 1223–1224 (1996).
[CrossRef]

Sirkis, J. S.

R. B. Wagreich, W. A. Atia, H. Singh, and J. S. Sirkis, “Effects of diametric load on fibre Bragg gratings fabricated in low birefringent fibre,” Electron. Lett. 32, 1223–1224 (1996).
[CrossRef]

Song, G. B.

D. S. Li, H. N. Li, L. Ren, and G. B. Song, “Strain transferring analysis of fiber Bragg grating sensors,” Opt. Eng. 45, 024402 (2006).
[CrossRef]

Staszewski, W. J.

Steenkiste, R. V.

R. V. Steenkiste and L. Kollar, “Effect of the coating on the stresses and strains in an embedded fiber optic sensor,” J. Compos. Mater. 32, 1680–1711 (1998).
[CrossRef]

Thursby, G.

Todd, M. D.

M. D. Todd, G. A. Johnson, and S. T. Vohra, “Deployment of a fiber Bragg grating-based measurement system in a structural health monitoring application,” Smart Mater. Struc. 10, 534–539 (2001).
[CrossRef]

Tu, H.

C. Liu, P. Chen, H. Li, and H. Tu, “Application of the fiber Bragg grating transverse effect in measurement of plain strain,” Opt. Optoelectron. Technol. 6, 29–32 (2008).

Voet, E.

G. Luyckx, E. Voet, N. Lammens, and J. Degrieck, “Strain measurements of composite laminates with embedded fibre Bragg gratings: criticism and opportunities for research,” Sensors 11, 384–408 (2011).
[CrossRef]

Vohra, S. T.

M. D. Todd, G. A. Johnson, and S. T. Vohra, “Deployment of a fiber Bragg grating-based measurement system in a structural health monitoring application,” Smart Mater. Struc. 10, 534–539 (2001).
[CrossRef]

Wagreich, R. B.

R. B. Wagreich, W. A. Atia, H. Singh, and J. S. Sirkis, “Effects of diametric load on fibre Bragg gratings fabricated in low birefringent fibre,” Electron. Lett. 32, 1223–1224 (1996).
[CrossRef]

Wang, Q.

H. Zhao, Q. Wang, Y. Qiu, J. Chen, Y. Wang, and Z. Fan, “Strain transfer of surface-bonded fiber Bragg grating sensors for aerostat envelope structural health monitoring,” J. Zhejiang Univ. Sci. A 13, 538–548 (2012).

Q. Wang, Y. Qiu, H. Zhao, J. Chen, Y. Wang, and Z. Fan, “Analysis of strain transfer of six-layer surface-bonded fiber Bragg gratings,” Appl. Opt. 51, 4129–4138 (2012).
[CrossRef]

Wang, Y.

Q. Wang, Y. Qiu, H. Zhao, J. Chen, Y. Wang, and Z. Fan, “Analysis of strain transfer of six-layer surface-bonded fiber Bragg gratings,” Appl. Opt. 51, 4129–4138 (2012).
[CrossRef]

H. Zhao, Q. Wang, Y. Qiu, J. Chen, Y. Wang, and Z. Fan, “Strain transfer of surface-bonded fiber Bragg grating sensors for aerostat envelope structural health monitoring,” J. Zhejiang Univ. Sci. A 13, 538–548 (2012).

Zhang, X.

J. Zhao, X. Zhang, Y. Huang, and X. Ren, “Experimental analysis of birefringence effects on fiber Bragg gratings induced by lateral compression,” Opt. Commun. 229, 203–207 (2004).
[CrossRef]

Zhao, H.

D. Huang, H. Zhao, Y. Qiu, and J. Chen, “Modeling and simulation analysis of stratospheric aerostat envelop,” Comput. Simul. 30, 150–153 (2013).

Q. Wang, Y. Qiu, H. Zhao, J. Chen, Y. Wang, and Z. Fan, “Analysis of strain transfer of six-layer surface-bonded fiber Bragg gratings,” Appl. Opt. 51, 4129–4138 (2012).
[CrossRef]

H. Zhao, Q. Wang, Y. Qiu, J. Chen, Y. Wang, and Z. Fan, “Strain transfer of surface-bonded fiber Bragg grating sensors for aerostat envelope structural health monitoring,” J. Zhejiang Univ. Sci. A 13, 538–548 (2012).

Zhao, J.

J. Zhao, X. Zhang, Y. Huang, and X. Ren, “Experimental analysis of birefringence effects on fiber Bragg gratings induced by lateral compression,” Opt. Commun. 229, 203–207 (2004).
[CrossRef]

Appl. Opt.

Comput. Simul.

D. Huang, H. Zhao, Y. Qiu, and J. Chen, “Modeling and simulation analysis of stratospheric aerostat envelop,” Comput. Simul. 30, 150–153 (2013).

Electron. Lett.

R. B. Wagreich, W. A. Atia, H. Singh, and J. S. Sirkis, “Effects of diametric load on fibre Bragg gratings fabricated in low birefringent fibre,” Electron. Lett. 32, 1223–1224 (1996).
[CrossRef]

Fiber Optic Laser Sensors

W. Morey, G. Meltz, and W. Glenn, “Fiber optic Bragg grating sensors,” Fiber Optic Laser Sensors 1169, 98–107 (1989).

J. Compos. Mater.

R. V. Steenkiste and L. Kollar, “Effect of the coating on the stresses and strains in an embedded fiber optic sensor,” J. Compos. Mater. 32, 1680–1711 (1998).
[CrossRef]

J. Eng. Mech.

F. Ansari and Y. Libo, “Mechanics of bond and interface shear transfer in optical fiber sensors,” J. Eng. Mech. 124, 385–394 (1998).
[CrossRef]

J. Lightwave Technol.

D. C. Betz, G. Thursby, B. Culshaw, and W. J. Staszewski, “Advanced layout of a fiber Bragg grating strain gague rosette,” J. Lightwave Technol. 24, 1019–1026 (2006).
[CrossRef]

A. Kersey, M. Davis, H. Patrick, M. LeBlanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

J. Zhejiang Univ. Sci. A

H. Zhao, Q. Wang, Y. Qiu, J. Chen, Y. Wang, and Z. Fan, “Strain transfer of surface-bonded fiber Bragg grating sensors for aerostat envelope structural health monitoring,” J. Zhejiang Univ. Sci. A 13, 538–548 (2012).

Mag. Concr. Res.

K. T. Lau, “Fibre-optic sensors and smart composites for concrete applications,” Mag. Concr. Res. 55, 19–34 (2003).
[CrossRef]

Opt. Commun.

J. Zhao, X. Zhang, Y. Huang, and X. Ren, “Experimental analysis of birefringence effects on fiber Bragg gratings induced by lateral compression,” Opt. Commun. 229, 203–207 (2004).
[CrossRef]

Opt. Eng.

D. S. Li, H. N. Li, L. Ren, and G. B. Song, “Strain transferring analysis of fiber Bragg grating sensors,” Opt. Eng. 45, 024402 (2006).
[CrossRef]

Opt. Fiber Technol.

R. Gafsi and M. A. El-Sherif, “Analysis of induced-birefringence effects on fiber Bragg gratings,” Opt. Fiber Technol. 6, 299–323 (2000).
[CrossRef]

Opt. Optoelectron. Technol.

C. Liu, P. Chen, H. Li, and H. Tu, “Application of the fiber Bragg grating transverse effect in measurement of plain strain,” Opt. Optoelectron. Technol. 6, 29–32 (2008).

Sensors

M. Lai, D. Karalekas, and J. Botsis, “On the effects of the lateral strains on the fiber Bragg grating response,” Sensors 13, 2631–2644 (2013).
[CrossRef]

G. Luyckx, E. Voet, N. Lammens, and J. Degrieck, “Strain measurements of composite laminates with embedded fibre Bragg gratings: criticism and opportunities for research,” Sensors 11, 384–408 (2011).
[CrossRef]

Smart Mater. Struc.

M. D. Todd, G. A. Johnson, and S. T. Vohra, “Deployment of a fiber Bragg grating-based measurement system in a structural health monitoring application,” Smart Mater. Struc. 10, 534–539 (2001).
[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

Strain transfer analysis of the single fiber.

Fig. 2.
Fig. 2.

Strain transfer analysis of double fiber.

Fig. 3.
Fig. 3.

(a) 3D model of the substrate-packaging FBG. (b) Cross section of the substrate-packaging FBG. (c) Longitudinal section of the substrate-packaging FBG. (d) Stress distribution of the substrate-packaging FBG.

Fig. 4.
Fig. 4.

Finite element mesh of the substrate-packaging FBG.

Fig. 5.
Fig. 5.

Influence of the thickness of upper adhesive layer on axial strain transfer rate.

Fig. 6.
Fig. 6.

Influence of the thickness of bottom adhesive layer on axial strain transfer rate.

Fig. 7.
Fig. 7.

Influence of the Young’s modulus of the substrate on axial strain transfer rate.

Fig. 8.
Fig. 8.

Influence of the thickness of the substrate on axial strain transfer rate.

Fig. 9.
Fig. 9.

Influence of the Young’s modulus of the substrate on radial strain transfer rate.

Fig. 10.
Fig. 10.

Influence of the shear modulus of the adhesive layer on radial strain transfer rate.

Tables (1)

Tables Icon

Table 1. Parameters of the FBG Sensor

Equations (46)

Equations on this page are rendered with MathJax. Learn more.

{KL=εL1εxKR=εR1εy.
λ1=2neffΛ,
dλ1=2neff·dΛ+2Λ·dneff.
dλ1λ1=dneffneff+dΛΛ.
dΛΛ=εL1.
dneffneff=neff22[p12υ(p11+p12)]ε,
PL=neff22[p12υ(p11+p12)].
dλ1Lλ1=(1PL)εL1=(1PL)KLεx.
dneffneff=neff22[p121υ2υ(p11+p12)]ε.
PR=neff22[p121υ2υ(p11+p12)].
dλ1Rλ1=(1PR)εR1=(1PR)KRεy.
dλ1λ1=dλ1Lλ1+dλ1Rλ1=(1PL)KLεx+(1PR)KRεy.
G=1PR1PL.
dλ1λ1=(1PL)(εL1+GεR1).
εR1=μεL1.
dλ1λ1=εL1(1PL)(1μG).
{dλ1λ1=(1PL)KLεx+(1PR)KRεydλ1λ1=εtest1·(1PL)(1μG),
εtest1=KLεx+GKRεy1μG.
dλ2Lλ2=(1PL)εL2=(1PL)KLεy,
dλ2Rλ2=(1PR)εR1=(1PR)KRεx.
dλ2λ2=dλ2Lλ2+dλ2Rλ2=(1PL)KLεy+(1PR)KRεx.
dλ2λ2=εtest2(1PL)(1μG),
{εtest1=KLεx+GKRεy1μGεtest2=KLεy+GKRεx1μG.
{εx=(1Gυ)(εtext1KLGKRεtext2)KL2(GKR)2εy=(1Gυ)(εtext2KLGKRεtext1)KL2(GKR)2.
πrg2σg=πrg2(σg+dσg)+πrgdxτ(x,rg),
dσgdx=τ(x,rg)rg.
dσadx=πrgτ(x,rg)Waτ(x,ra)Waraπrg22,
dσcdx=Waτ(x,ra)Wcτ(x,rc)rcra,
dσbdx=τ(x,rc)τ(x,rb)rbrc.
τ(x,r)={πrg2Wadσgdx(War12πrg2)dσadx(rg<r<ra)πrg2WcdσgdxWaWc(Wara12πrg2)dσadx(rra)dσcdx(ra<r<rc)πrg2WcdσgdxWaWc(Wara12πrg2)dσadx(rcra)dσcdx(rrc)dσbdx(rc<r<rb).
τ(x,r)={Eg[πrg2Wadεgdx+(War12πrg2)EaEgdεadx](rg<r<ra)Eg[πrg2Wcdεgdx+WaWc(Wara12πrg2)EaEgdεadx+(rra)EcEgdεcdx](ra<r<rc)Eg[πrg2Wcdεgdx+WaWc(Wara12πrg2)EaEgdεadx+(rcra)EcEgdεcdx+(rrc)EbEgdεbdx](rc<r<rb).
dεgdxdεadxdεcdxdεbdx.
WaWc(Wara12πrg2)EaEgdεadxo(dεgdx)(rrc)EbEgdεbdxo(dεgdx).
τ(x,r)={πrg2EgWadεgdx(rg<r<ra)[πrg2EgWc+(rra)Ec]dεgdx(ra<r<rc)[πrg2EgWc(rcra)Ec]dεgdx(rc<r<rb).
τ(x,r)=Gpγ(x,r)=G(ur+wx)Gdudr,
{rgraGadudrdr=rgraπrg2EgWadεgdxdrrarcGcdudrdr=rarc[πrg2EgWc+(rra)Ec]dεgdxdrrcrbGbdudrdr=rcrb[πrg2EgWc(rcra)Ec]dεgdxdr,
{uaug=πrg2Eg(rarg)GaWadεgdxucua=rcraGc[πrg2EgWc+12(rcra)Ec]dεgdxubuc=rbrcGb[πrg2EgWc+(rcra)Ec]dεgdx,
umug=[πrg2(rargWaGa+rcraWcGc+rbrcWcGb)Eg+(rcra)(rcra2Gc+rbrcGb)Ec]dεgdx=1γ2dεgdx,
ξ=1[πrg2(rargWaGa+rcraWcGc+rmrcWcGm)Eg+(rcra)(rcra2Gc+rmrcGm)Ec].
d2εg(x)dx2ξ2εg(x)=ξ2εm.
εf(x)=C1eξx+C2eξx+εm,
εg(L)=εg(L)=0.
ε˙g(0)=0.
C1=C2=εm2cosh(ξL).
εg(x)=(1cosh(ξx)cosh(ξL))εm.
KL=εg(x)εm=1cosh(ξx)cosh(ξL).

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