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E-raamat: Strain and Temperature Measurement with Fiber Optic Sensors

(Solomon Brothers, New York, USA)
  • Formaat: 294 pages
  • Ilmumisaeg: 20-Dec-2024
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781040290347
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  • Formaat: 294 pages
  • Ilmumisaeg: 20-Dec-2024
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781040290347
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Without the appropriate relationships, fiber optic sensors do not provide meaningful information. The relationship providing the bridge between the sensor output and the engineering values of strain and temperature must be established via analytical models. This book presents such models for extrinsic and intrinsic Fabry-Perot sensors and for Bragg grating sensors embedded in or mounted on the surface of isotropic or anisotropic solids or immersed in fluids. The scope of the book is limited to the theory of fiber optic strain and temperature sensors. The problem necessitates complex analytical developments. To assist the reader, the significant results are summarized in tables, and numerical examples are given illustrating the calculation procedures.

FROM THE AUTHORS' PREFACE

Sensors operating on interferometric principles and mounted inside optical fibers have recently been considered for measuring strain and temperature. Indeed, such sensors have successfully been employed for measuring pressure or temperature in fluids. Fiber optics sensors are especially adept for such measurements because sensors immersed in fluids can easily be calibrated by tests.

Unfortunately, the use of fiber optic sensors inside solids is not as straightforward. Owing to the complex interactions between the sensor and the surrounding material, the relationship between the sensor output and the parameters of interest, namely the strain and temperature inside the material, cannot be determined by simple tests. And without the appropriate relationships, fiber optic sensors do not provide meaningful information. In general, the relationship providing the bridge between the sensor output and the engineering values of strain and temperature must be established via analytical models. The major aim of this book is to present such models for extrinsic and intrinsic Fabry-Perot sensors and for Bragg grating sensors embedded in or mounted on the surface of isotropic or anisotropic solids or immersed in fluids.

The scope of the book is limited to the theory of fiber optic strain and temperature sensors. Accordingly, we have taken as our starting point the demodulated sensor signals. The hardware needed to produce these signals is not discussed. It is presumed that the reader is familiar with and has access to the sensor, light source, light detector and demodulator required for generating signals which can then be analyzed and interpreted by the methods presented in the book.

The problem necessitates complex analytical developments. To assist the reader, the significant results are summarized in tables, and numerical examples are given illustrating the calculation procedures.
Preface xi
List of Symbols
xiii
The problem
1(10)
Numerical examples
5(4)
Note on the symbols
9(2)
I Sensor strains and temperature 11(98)
Introduction
13(3)
Stresses and strains in the material
16(6)
Stresses and strains in the sensor
22(20)
Anisotropic uncoated sensor in a generally anisotropic material
42(1)
Orthotropic uncoated sensor in an orthotropic material
42(18)
Displacement continuity conditions
43(7)
Stress continuity conditions
50(10)
Transversely isotropic uncoated sensor in a transversely isotropic material
60(7)
Transversely isotropic uncoated sensor in an isotropic material
67(5)
Isotropic uncoated sensor in a transversely isotropic material
72(5)
Isotropic uncoated sensor in an isotropic material
77(3)
Sensors not embedded in a solid
80(2)
Surface mounted sensor
80(1)
Sensor immersed in a fluid
80(2)
Effects of the coating
82(22)
Out-of-plane shear applied
85(4)
Axisymmetric loading
89(3)
Non-axisymmetric in-plane loading
92(5)
Observations
97(7)
Summary of results
104(5)
Extrinsic Fabry-Perot sensors
104(2)
Plane strain and plane stress conditions
106(3)
II Optical and geometric properties of the sensor 109(22)
Introduction
111(1)
Optical properties of the sensor
112(9)
Transversely isotropic sensor
115(2)
Isotropic sensor
117(2)
Summary of results
119(2)
Geometric properties of the sensor
121(9)
Fabry-Perot sensor
121(1)
Bragg sensor
121(6)
Summary of results
127(3)
Summary of results
130(1)
III Sensor output 131(56)
Introduction
133(1)
Fabry-Perot sensor output in terms of the sensor optical and geometric properties
134(6)
Reflected light intensity---Low finesse Fabry---Perot sensor
135(3)
Reflected light intensity---High finesse Fabry---Perot sensor
138(2)
Fabry-Perot sensor output in terms of the sensor strains and temperature
140(6)
Transversely isotropic intrinsic Fabry-Perot sensor
140(1)
Isotropic intrinsic Fabry-Perot sensor
141(2)
Extrinsic Fabry-Perot sensor
143(1)
Non-embedded Fabry-Perot sensors
144(1)
Summary
145(1)
Fabry-Perot sensor output in terms of the farfield strains and temperature
146(16)
Uncoated transversely Isotropic or isotropic intrinsic Fabry-Perot sensor in a generally anisotropic material
146(1)
Transversely isotropic intrinsic Fabry-Perot sensor in a transversely isotropic material
147(2)
Transversely isotropic intrinsic Fabry-Perot sensor in an isotropic material
149(4)
Isotropic intrinsic Fabry-Perot sensor in a transversely isotropic material
153(5)
Isotropic intrinsic Fabry-Perot sensor in an isotropic material
158(1)
Extrinsic Fabry-Perot sensor
158(1)
Summary
159(3)
Bragg sensor output in terms of the sensor optical and geometric properties
162(4)
Bragg sensor output in terms of the sensor strains and temperature
166(6)
Transversely isotropic Bragg sensor
166(1)
Isotropic Bragg sensor
166(3)
Non-embedded Bragg sensors
169(1)
Summary
170(2)
Bragg sensor output in terms of the farfield strains and temperature
172(15)
Transversely isotropic intrinsic Bragg sensor in a transversely isotropic material
173(1)
Transversely isotropic intrinsic Bragg sensor in an isotropic material
173(1)
Isotropic intrinsic Bragg sensor in a transversely isotropic material
173(10)
Transversely isotropic Bragg sensor in a isotropic material
183(1)
Summary
183(4)
IV Demodulation 187(22)
Introduction
189(1)
Geoptic strain
190(2)
Demodulation
192(12)
Low finesse Fabry-Perot sensor
192(2)
High finesse extrinsic Fabry-Perot sensor
194(2)
High finesse intrinsic Fabry-Perot sensor
196(4)
Bragg sensors
200(1)
Summary
201(3)
Geoptic strain in terms of the farfield strains and temperature
204(5)
V Strain and temperature measurement 209(18)
Introduction
211(1)
Measurements of the farfield strains and temperature with seven sensors
212(3)
The effects of uncertainties
213(2)
Measurement of the farfield strains and temperature with n sensors
215(12)
The effects of uncertainties
220(7)
VI Sensor selection and calibration 227(18)
Introduction
229(1)
Sensor selection
230(7)
Sensor selection process
231(6)
Sensor properties
237(8)
Intrinsic Fabry-Perot and Bragg sensors
237(5)
Pockel constants and thermooptic coefficient for a transversely isotropic intrinsic Fabry-Perot or Bragg sensor
238(2)
Pockel constants and thermooptic coefficient for an isotropic intrinsic Fabry-Perot or Bragg sensor
240(2)
Thermooptic coefficient for an extrincisic Fabry-Perot sensor
242(1)
Summary
242(3)
VII Computer code 245(2)
Appendices 247(36)
A Transformation matrices
249(5)
A.1 Stress transformation
249(2)
A.2 Strain transformation
251(1)
A.3 Thermal expansion coefficient
252(1)
A.4 Stiffness and compliance matrices
252(1)
A.5 Optical properties
253(1)
B Stiffness and compliance matrices
254(3)
B.1 Compliance matrix
254(1)
B.1.1 Generally anisotropic material
254(1)
B.1.2 Orthotropic material
254(1)
B.1.3 Transversely isotropic material
255(1)
B.1.4 Isotropic material
255(2)
C Thermal expansion coefficient
257(2)
C.1 Generally anisotropic material
257(1)
C.2 Orthotropic material
257(1)
C.3 Transversely isotropic material
257(1)
C.4 Isotropic material
258(1)
D Continuity conditions (uncoated sensors)
259(6)
D.1 Displacements
259(3)
D.2 Stresses
262(1)
D.3 Continuity conditions at points A and B
263(2)
E Derivative of the stress function
265(2)
F Stress-strain relationship at points A and B
267(2)
F.1 Material
267(1)
F.2 Sensor
268(1)
G Solution for es5 and es6 for an orthotropic uncoated sensor in an orthotropic material
269(2)
H Solution for es2 through es4 for a transversely isotropic uncoated sensor in a transversely isotropic material
271(4)
I Continuity conditions (coated sensors)
275(1)
J Pockel constants
276(2)
J.1 Transversely isotropic material
276(1)
J.2 Isotropic material
277(1)
K Solution of the wave equation
278(2)
I Traveling wave intensity
280(1)
M Change in the geoptic strain---High finesse Fabry-Perot
281(2)
M.1 High finesse extrinsic Fabry-Perot sensors
281(1)
M.2 High finesse intrinsic Fabry-Perot sensors
282(1)
Bibliography 283(4)
Index 287
Regis J. Van Steenkiste