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\n\n \n \n \n \n \n \n Anti-plane surface waves on a half-space with depth-dependent properties.\n \n \n \n \n\n\n \n Achenbach, J. D.; and Balogun, O.\n\n\n \n\n\n\n
Wave Motion, 47(1): 59–65. January 2010.\n
Number: 1\n\n
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\n\n \n \n Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n\n\n\n
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@article{achenbach_anti-plane_2010,\n\ttitle = {Anti-plane surface waves on a half-space with depth-dependent properties},\n\tvolume = {47},\n\tissn = {0165-2125},\n\turl = {http://www.sciencedirect.com/science/article/pii/S0165212509000717},\n\tdoi = {10.1016/j.wavemoti.2009.08.002},\n\tabstract = {This paper considers the propagation of anti-plane shear waves in a half-space whose shear modulus and mass density have an arbitrary dependence on the distance from the free surface. An appropriate reformulation of the anti-plane displacement produces a governing equation for the reformulated displacement that is amenable to a solution in the high-frequency range. The boundary condition on the free surface subsequently yields an equation which relates the speed of surface waves to the wavenumber and to the functions that define the depth dependence of the shear modulus and the mass density. Restrictions for the existence of surface waves are discussed, and numerical results are presented.},\n\tnumber = {1},\n\turldate = {2018-09-16},\n\tjournal = {Wave Motion},\n\tauthor = {Achenbach, Jan D. and Balogun, Oluwaseyi},\n\tmonth = jan,\n\tyear = {2010},\n\tnote = {Number: 1},\n\tkeywords = {Antiplane surface waves, Functionally graded materials, Inhomogeneous half-space},\n\tpages = {59--65},\n}\n\n
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\n This paper considers the propagation of anti-plane shear waves in a half-space whose shear modulus and mass density have an arbitrary dependence on the distance from the free surface. An appropriate reformulation of the anti-plane displacement produces a governing equation for the reformulated displacement that is amenable to a solution in the high-frequency range. The boundary condition on the free surface subsequently yields an equation which relates the speed of surface waves to the wavenumber and to the functions that define the depth dependence of the shear modulus and the mass density. Restrictions for the existence of surface waves are discussed, and numerical results are presented.\n
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\n\n \n \n \n \n \n \n Atomic Force Acoustic Microscopy to Measure Nanoscale Mechanical Properties of Cement Pastes.\n \n \n \n \n\n\n \n Kim, J. H.; Balogun, O.; and Shah, S. P.\n\n\n \n\n\n\n
Transportation Research Record, 2141(1): 102–108. January 2010.\n
Number: 1\n\n
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\n\n \n \n Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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@article{kim_atomic_2010,\n\ttitle = {Atomic {Force} {Acoustic} {Microscopy} to {Measure} {Nanoscale} {Mechanical} {Properties} of {Cement} {Pastes}},\n\tvolume = {2141},\n\tissn = {0361-1981},\n\turl = {https://doi.org/10.3141/2141-17},\n\tdoi = {10.3141/2141-17},\n\tabstract = {The measurement of elastic properties at the nanoscale is a prerequisite to building a foundation for nanomechanics applications. At present, nanoindentation is widely used to measure the properties of elasticity. Under this method, a sample is indented with a rigid probe and the resistant force of the indentation is measured. The reduced modulus measured on the basis of the resistant force and the indentation depth is then converted to the elastic modulus of the sample. However, its spatial resolution, the distance between two consecutive locations of measurement, is limited to about 5 μm because of the area of the indented tip. Ultrasonic atomic force microscopy is an alternative method of attaining spatial resolution at the nanometer level. It uses information based on the vibrations transferred from the piezoelectric actuator at the bottom of a sample to the cantilever contacting the top surface of the sample. The cantilever makes contact with a relatively small force; as a consequence, it decreases the contact area and improves the spatial resolution. The application of atomic force acoustic microscopy to a cementitious material is described, and the results of the measurement of the elastic modulus of a cement paste are presented.},\n\tlanguage = {en},\n\tnumber = {1},\n\turldate = {2018-09-16},\n\tjournal = {Transportation Research Record},\n\tauthor = {Kim, Jae Hong and Balogun, Oluwaseyi and Shah, Surendra P.},\n\tmonth = jan,\n\tyear = {2010},\n\tnote = {Number: 1},\n\tpages = {102--108},\n}\n\n
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\n\n\n
\n The measurement of elastic properties at the nanoscale is a prerequisite to building a foundation for nanomechanics applications. At present, nanoindentation is widely used to measure the properties of elasticity. Under this method, a sample is indented with a rigid probe and the resistant force of the indentation is measured. The reduced modulus measured on the basis of the resistant force and the indentation depth is then converted to the elastic modulus of the sample. However, its spatial resolution, the distance between two consecutive locations of measurement, is limited to about 5 μm because of the area of the indented tip. Ultrasonic atomic force microscopy is an alternative method of attaining spatial resolution at the nanometer level. It uses information based on the vibrations transferred from the piezoelectric actuator at the bottom of a sample to the cantilever contacting the top surface of the sample. The cantilever makes contact with a relatively small force; as a consequence, it decreases the contact area and improves the spatial resolution. The application of atomic force acoustic microscopy to a cementitious material is described, and the results of the measurement of the elastic modulus of a cement paste are presented.\n
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\n\n \n \n \n \n \n \n Dynamic strain sensing of a model long span bridge using fiber bragg grating sensors.\n \n \n \n \n\n\n \n Zhu, Y. J.; Balogun, O.; Zhu, Y.; Zhu, S.; Xu, Y. L.; and Krishnaswamy, S.\n\n\n \n\n\n\n In 2010. \n
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@inproceedings{zhu_dynamic_2010,\n\ttitle = {Dynamic strain sensing of a model long span bridge using fiber bragg grating sensors},\n\turl = {http://ira.lib.polyu.edu.hk/handle/10397/50477},\n\tabstract = {Department of Civil and Environmental Engineering},\n\tlanguage = {en},\n\turldate = {2018-09-16},\n\tauthor = {Zhu, Y. J. and Balogun, O. and Zhu, Y. and Zhu, S. and Xu, Y. L. and Krishnaswamy, S.},\n\tyear = {2010},\n}\n\n
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\n Department of Civil and Environmental Engineering\n
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\n\n \n \n \n \n \n Generation and Propagation of Anti-Plane Surface Waves on a Body with Depth-Dependent Properties.\n \n \n \n\n\n \n Achenbach, J. D.; and Balogun, O.\n\n\n \n\n\n\n In Wu, T.; and Ma, C., editor(s),
IUTAM Symposium on Recent Advances of Acoustic Waves in Solids, of
IUTAM Bookseries, pages 33–43, 2010. Springer Netherlands\n
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\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
\n
@inproceedings{achenbach_generation_2010,\n\tseries = {{IUTAM} {Bookseries}},\n\ttitle = {Generation and {Propagation} of {Anti}-{Plane} {Surface} {Waves} on a {Body} with {Depth}-{Dependent} {Properties}},\n\tisbn = {978-90-481-9893-1},\n\tabstract = {The generation and propagation of anti-plane surface waves on an inhomogeneous half-space of depth dependent shear modulus and mass density, is discussed in this paper. The radiation of surface waves an anti-plane line load is analyzed by an application of the reciprocity theorem. Next the governing equation for free surface waves is reformulated in a form that is amenable to a surface wave solution in the high frequency range. The boundary condition on the free surface yields an equation for the velocity of surface waves, in terms of the wave number and derivatives of the functions defining the depth dependence of the shear modules and the mass density. This equation does not always have a realvalued solution, and when it does the amplitude of the corresponding wave motion does not always display the decrease with depth that would define a surface wave.Numerical examples are presented to illustrate these observations.},\n\tlanguage = {en},\n\tbooktitle = {{IUTAM} {Symposium} on {Recent} {Advances} of {Acoustic} {Waves} in {Solids}},\n\tpublisher = {Springer Netherlands},\n\tauthor = {Achenbach, Jan D. and Balogun, Oluwaseyi},\n\teditor = {Wu, Tsung-Tsong and Ma, Chien-Ching},\n\tyear = {2010},\n\tkeywords = {Depth Dependence, Line Load, Rayleigh Wave, Reciprocity Theorem, Surface Wave},\n\tpages = {33--43},\n}\n\n
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\n\n\n
\n The generation and propagation of anti-plane surface waves on an inhomogeneous half-space of depth dependent shear modulus and mass density, is discussed in this paper. The radiation of surface waves an anti-plane line load is analyzed by an application of the reciprocity theorem. Next the governing equation for free surface waves is reformulated in a form that is amenable to a surface wave solution in the high frequency range. The boundary condition on the free surface yields an equation for the velocity of surface waves, in terms of the wave number and derivatives of the functions defining the depth dependence of the shear modules and the mass density. This equation does not always have a realvalued solution, and when it does the amplitude of the corresponding wave motion does not always display the decrease with depth that would define a surface wave.Numerical examples are presented to illustrate these observations.\n
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\n\n \n \n \n \n \n \n Single-longitudinal-mode fiber Bragg grating ring laser for real-time strain monitoring.\n \n \n \n \n\n\n \n Zhu, Y.; Balogun, O.; and Krishnaswamy, S.\n\n\n \n\n\n\n In
Proceedings of the 5th European Workshop - Structural Health Monitoring 2010, pages 754–759, December 2010. \n
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\n
@inproceedings{zhu_single-longitudinal-mode_2010,\n\ttitle = {Single-longitudinal-mode fiber {Bragg} grating ring laser for real-time strain monitoring},\n\turl = {https://www.scholars.northwestern.edu/en/publications/single-longitudinal-mode-fiber-bragg-grating-ring-laser-for-real-},\n\tlanguage = {English (US)},\n\turldate = {2018-09-16},\n\tbooktitle = {Proceedings of the 5th {European} {Workshop} - {Structural} {Health} {Monitoring} 2010},\n\tauthor = {Zhu, Y. and Balogun, O. and Krishnaswamy, S.},\n\tmonth = dec,\n\tyear = {2010},\n\tpages = {754--759},\n}\n\n
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\n\n \n \n \n \n \n \n Detection of disbonding in glare composites using lamb wave approach.\n \n \n \n \n\n\n \n Huang, Q.; Balogun, O.; Yang, N.; Regez, B.; and Krishnaswamy, S.\n\n\n \n\n\n\n
AIP Conference Proceedings, 1211(1): 1198–1205. February 2010.\n
Number: 1\n\n
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\n\n \n \n Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
\n
@article{huang_detection_2010,\n\ttitle = {Detection of disbonding in glare composites using lamb wave approach},\n\tvolume = {1211},\n\tissn = {0094-243X},\n\turl = {https://aip.scitation.org/doi/abs/10.1063/1.3362193},\n\tdoi = {10.1063/1.3362193},\n\tnumber = {1},\n\turldate = {2018-09-16},\n\tjournal = {AIP Conference Proceedings},\n\tauthor = {Huang, Qiaojian and Balogun, Oluwaseyi and Yang, Ningli and Regez, Brad and Krishnaswamy, Sridhar},\n\tmonth = feb,\n\tyear = {2010},\n\tnote = {Number: 1},\n\tpages = {1198--1205},\n}\n\n
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\n\n \n \n \n \n \n \n Characterization of water‐saturated porous cement paste by a laser based ultrasonic nde technique.\n \n \n \n \n\n\n \n Yang, N.; Hong Kim, J.; Thomas, J. J.; Balogun, O.; and Krishnaswamy, S.\n\n\n \n\n\n\n
AIP Conference Proceedings, 1211(1): 1541–1548. February 2010.\n
Number: 1\n\n
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\n
@article{yang_characterization_2010,\n\ttitle = {Characterization of water‐saturated porous cement paste by a laser based ultrasonic nde technique},\n\tvolume = {1211},\n\tissn = {0094-243X},\n\turl = {https://aip.scitation.org/doi/abs/10.1063/1.3362252},\n\tdoi = {10.1063/1.3362252},\n\tnumber = {1},\n\turldate = {2018-09-16},\n\tjournal = {AIP Conference Proceedings},\n\tauthor = {Yang, Ningli and Hong Kim, Jae and Thomas, Jeffrey J. and Balogun, Oluwaseyi and Krishnaswamy, Sridhar},\n\tmonth = feb,\n\tyear = {2010},\n\tnote = {Number: 1},\n\tpages = {1541--1548},\n}\n\n
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\n\n \n \n \n \n \n \n Acoustic emission monitoring using two‐wave mixing interferometer.\n \n \n \n \n\n\n \n Zhu, Y.; Balogun, O.; and Krishnaswamy, S.\n\n\n \n\n\n\n
AIP Conference Proceedings, 1211(1): 1807–1811. February 2010.\n
Number: 1\n\n
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\n\n \n \n Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
\n
@article{zhu_acoustic_2010,\n\ttitle = {Acoustic emission monitoring using two‐wave mixing interferometer},\n\tvolume = {1211},\n\tissn = {0094-243X},\n\turl = {https://aip.scitation.org/doi/abs/10.1063/1.3362301},\n\tdoi = {10.1063/1.3362301},\n\tnumber = {1},\n\turldate = {2018-09-16},\n\tjournal = {AIP Conference Proceedings},\n\tauthor = {Zhu, Y. and Balogun, O. and Krishnaswamy, S.},\n\tmonth = feb,\n\tyear = {2010},\n\tnote = {Number: 1},\n\tpages = {1807--1811},\n}\n\n
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\n\n \n \n \n \n \n \n Real-time full-field photoacoustic imaging using an ultrasonic camera.\n \n \n \n \n\n\n \n Balogun, O.; Regez, B.; Zhang, H. F.; and Krishnaswamy, S.\n\n\n \n\n\n\n
Journal of Biomedical Optics, 15(2): 021318. March 2010.\n
Number: 2\n\n
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\n\n \n \n Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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@article{balogun_real-time_2010,\n\ttitle = {Real-time full-field photoacoustic imaging using an ultrasonic camera},\n\tvolume = {15},\n\tissn = {1083-3668, 1560-2281},\n\turl = {https://www.spiedigitallibrary.org/journals/Journal-of-Biomedical-Optics/volume-15/issue-2/021318/Real-time-full-field-photoacoustic-imaging-using-an-ultrasonic-camera/10.1117/1.3420079.short},\n\tdoi = {10.1117/1.3420079},\n\tabstract = {A photoacoustic imaging system that incorporates a commercial ultrasonic camera for real-time imaging of two-dimensional (2-D) projection planes in tissue at video rate (30 Hz) is presented. The system uses a Q-switched frequency-doubled Nd:YAG pulsed laser for photoacoustic generation. The ultrasonic camera consists of a 2-D 12×12 mm CCD chip with 120×120 piezoelectric sensing elements used for detecting the photoacoustic pressure distribution radiated from the target. An ultrasonic lens system is placed in front of the chip to collect the incoming photoacoustic waves, providing the ability for focusing and imaging at different depths. Compared with other existing photoacoustic imaging techniques, the camera-based system is attractive because it is relatively inexpensive and compact, and it can be tailored for real-time clinical imaging applications. Experimental results detailing the real-time photoacoustic imaging of rubber strings and buried absorbing targets in chicken breast tissue are presented, and the spatial resolution of the system is quantified.},\n\tnumber = {2},\n\turldate = {2018-09-16},\n\tjournal = {Journal of Biomedical Optics},\n\tauthor = {Balogun, Oluwaseyi and Regez, Brad and Zhang, Hao F. and Krishnaswamy, Sridhar},\n\tmonth = mar,\n\tyear = {2010},\n\tnote = {Number: 2},\n\tpages = {021318},\n}\n\n
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\n A photoacoustic imaging system that incorporates a commercial ultrasonic camera for real-time imaging of two-dimensional (2-D) projection planes in tissue at video rate (30 Hz) is presented. The system uses a Q-switched frequency-doubled Nd:YAG pulsed laser for photoacoustic generation. The ultrasonic camera consists of a 2-D 12×12 mm CCD chip with 120×120 piezoelectric sensing elements used for detecting the photoacoustic pressure distribution radiated from the target. An ultrasonic lens system is placed in front of the chip to collect the incoming photoacoustic waves, providing the ability for focusing and imaging at different depths. Compared with other existing photoacoustic imaging techniques, the camera-based system is attractive because it is relatively inexpensive and compact, and it can be tailored for real-time clinical imaging applications. Experimental results detailing the real-time photoacoustic imaging of rubber strings and buried absorbing targets in chicken breast tissue are presented, and the spatial resolution of the system is quantified.\n
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\n\n \n \n \n \n \n \n Interrogation of a wavelength tunable fiber Bragg grating sensor based ring laser for dynamic strain monitoring.\n \n \n \n \n\n\n \n Balogun, O.; Zhu, Y.; and Krishnaswamy, S.\n\n\n \n\n\n\n In
Smart Sensor Phenomena, Technology, Networks, and Systems 2010, volume 7648, pages 764802, April 2010. International Society for Optics and Photonics\n
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\n\n \n \n Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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@inproceedings{balogun_interrogation_2010,\n\ttitle = {Interrogation of a wavelength tunable fiber {Bragg} grating sensor based ring laser for dynamic strain monitoring},\n\tvolume = {7648},\n\turl = {https://www.spiedigitallibrary.org/conference-proceedings-of-spie/7648/764802/Interrogation-of-a-wavelength-tunable-fiber-Bragg-grating-sensor-based/10.1117/12.848979.short},\n\tdoi = {10.1117/12.848979},\n\tabstract = {Fiber Bragg gratings (FBGs) are wavelength selective optical reflectors with excellent strain sensitivity and small sensing footprint, which makes them suitable as diagnostic sensors for structural health monitoring applications. In this work, we explore the narrowband wavelength selectivity of FBGs for optical feedback in a tunable fiber ring laser. The fiber ring laser consists of an erbium doped fiber laser that is pumped with a Raman laser (980 nm) to produce population inversion and amplified spontaneous emission (ASE) in the C-band. The ASE light is used to illuminate a FBG sensor connected to the ring, and the reflected light from the sensor is fed back into the laser cavity to produce stimulated emission at the instantaneous center wavelength of the sensor. As the wavelength of the sensor shifts due mechanical or thermal strains, the wavelength of the optical output from the ring laser shifts accordingly. By combining the ring laser with a dynamic spectral demodulator for optical readout, the instantaneous wavelength of the ring laser is tracked with high temporal resolution. The fiber ring laser system offers several potential advantages in the diagnostic sensing of mechanical strains for SHM applications including, fully integrated laser and sensor system, high source power levels at the sensor wavelength, narrow spectral line-width, coherent spectral demodulation, and low system costs. In this work, we present experimental results that detail the feasibility of dynamic spectral tuning of the fiber ring laser at frequencies up to hundreds of kilohertz using a single FBG sensing element. Using multiple sensing elements, the fiber ring laser system would allow for active monitoring of dynamic strains in a multi-point sensor array configuration, which is particularly suitable for the localization of high frequency mechanical strains produced by impact loading and cracking events in structures.},\n\turldate = {2018-09-16},\n\tbooktitle = {Smart {Sensor} {Phenomena}, {Technology}, {Networks}, and {Systems} 2010},\n\tpublisher = {International Society for Optics and Photonics},\n\tauthor = {Balogun, Oluwaseyi and Zhu, Yinian and Krishnaswamy, Sridhar},\n\tmonth = apr,\n\tyear = {2010},\n\tpages = {764802},\n}\n\n
\n
\n\n\n
\n Fiber Bragg gratings (FBGs) are wavelength selective optical reflectors with excellent strain sensitivity and small sensing footprint, which makes them suitable as diagnostic sensors for structural health monitoring applications. In this work, we explore the narrowband wavelength selectivity of FBGs for optical feedback in a tunable fiber ring laser. The fiber ring laser consists of an erbium doped fiber laser that is pumped with a Raman laser (980 nm) to produce population inversion and amplified spontaneous emission (ASE) in the C-band. The ASE light is used to illuminate a FBG sensor connected to the ring, and the reflected light from the sensor is fed back into the laser cavity to produce stimulated emission at the instantaneous center wavelength of the sensor. As the wavelength of the sensor shifts due mechanical or thermal strains, the wavelength of the optical output from the ring laser shifts accordingly. By combining the ring laser with a dynamic spectral demodulator for optical readout, the instantaneous wavelength of the ring laser is tracked with high temporal resolution. The fiber ring laser system offers several potential advantages in the diagnostic sensing of mechanical strains for SHM applications including, fully integrated laser and sensor system, high source power levels at the sensor wavelength, narrow spectral line-width, coherent spectral demodulation, and low system costs. In this work, we present experimental results that detail the feasibility of dynamic spectral tuning of the fiber ring laser at frequencies up to hundreds of kilohertz using a single FBG sensing element. Using multiple sensing elements, the fiber ring laser system would allow for active monitoring of dynamic strains in a multi-point sensor array configuration, which is particularly suitable for the localization of high frequency mechanical strains produced by impact loading and cracking events in structures.\n
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\n\n \n \n \n \n \n \n Non-destructive imaging, characterization or measurement of thin items using laser-generated lamb waves.\n \n \n \n \n\n\n \n Murray, T. W.; Prada, C.; and Balogun, O.\n\n\n \n\n\n\n September 2010.\n
Inventors: _:n491 Issue: US7798000B1\n\n
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\n\n \n \n Paper\n \n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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@patent{murray_non-destructive_2010,\n\ttitle = {Non-destructive imaging, characterization or measurement of thin items using laser-generated lamb waves},\n\turl = {https://patents.google.com/patent/US7798000B1/en},\n\tabstract = {A laser-based ultrasonic technique for the inspection of thin plates and membranes employs an amplitude-modulated laser source to excite narrow bandwidth Lamb waves. The dominant feature in the acoustic spectrum is a sharp resonance peak that occurs at the minimum frequency of the first-order symmetric Lamb mode, where the group velocity of the Lamb wave goes to zero while the phase velocity remains finite. Experimental results with the laser source and receiver on epicenter demonstrate that the zero group velocity resonance generated with a low power modulated excitation source can be detected using an optical probe such as a Michelson interferometer coupled to a lock-in amplifier. This resonance peak is sensitive to the thickness and mechanical properties of plates and may be suitable, for example, for the measurement and mapping of nanoscale thickness variations.},\n\tnationality = {US},\n\tassignee = {Boston University},\n\tnumber = {US7798000B1},\n\turldate = {2018-09-16},\n\tauthor = {Murray, Todd W. and Prada, Claire and Balogun, Oluwaseyi},\n\tmonth = sep,\n\tyear = {2010},\n\tnote = {Inventors: \\_:n491\nIssue: US7798000B1},\n\tkeywords = {item, laser beam, location, predetermined, resonance peak},\n}\n\n
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\n A laser-based ultrasonic technique for the inspection of thin plates and membranes employs an amplitude-modulated laser source to excite narrow bandwidth Lamb waves. The dominant feature in the acoustic spectrum is a sharp resonance peak that occurs at the minimum frequency of the first-order symmetric Lamb mode, where the group velocity of the Lamb wave goes to zero while the phase velocity remains finite. Experimental results with the laser source and receiver on epicenter demonstrate that the zero group velocity resonance generated with a low power modulated excitation source can be detected using an optical probe such as a Michelson interferometer coupled to a lock-in amplifier. This resonance peak is sensitive to the thickness and mechanical properties of plates and may be suitable, for example, for the measurement and mapping of nanoscale thickness variations.\n
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