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OPTICS LETTERS / Vol. 39, No. 11 / June 1, 2014
Mechanical impedance measurement and damage detection using noncontact laser ultrasound Hyeonseok Lee, Hyeong Uk Lim, Jung-Wuk Hong, and Hoon Sohn* Department of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, South Korea *Corresponding author: [email protected] Received December 17, 2013; accepted April 6, 2014; posted April 22, 2014 (Doc. ID 203026); published May 19, 2014 This Letter proposes a mechanical impedance (MI) measurement technique using noncontact laser ultrasound. The ultrasound is generated by shooting a pulse laser beam onto a target structure, and its response is measured using a laser vibrometer. Once ultrasound propagation converges to structural vibration, MI is formed over the entire structure. Because noncontact lasers are utilized, this technique is applicable in harsh environments, free of electromagnetic interference, and able to perform wide-range scanning. The formation of MI and its feasibility for damage detection are verified through thermo-mechanical finite element analysis and lab-scale experiments. © 2014 Optical Society of America OCIS codes: (280.3375) Laser induced ultrasonics; (120.4290) Nondestructive testing. http://dx.doi.org/10.1364/OL.39.003130
In recent years, structural health monitoring (SHM) techniques have become important to detect structural damage and enhance the structural safety of critical infrastructure. Among various damage detection approaches, mechanical impedance (MI) measurement has been widely used for detecting the presence of incipient damage. An electromechanical impedance (EMI) technique has evolved into as a preferable method of measuring MI changes by attaching piezoelectric transducers and utilizing their electromechanical coupling properties [1–4]. The EMI technique is known to be sensitive to various sizes of structural defects and it requires a relatively simple hardware configuration [5]. However, there are several problems associated with EMI measurement using piezoelectric transducers. First, because piezoelectric transducers are directly attached to a target structure, they are vulnerable to harsh environments, such as high temperature, corrosive or radioactive conditions, and are not conformable to curved surfaces [6]. For example, the variability of the bonding condition between the piezoelectric transducer and the host structure can deteriorate the robustness and repeatability of EMI measurement [7]. Furthermore, the EMI waveform can be distorted by the cross talk between the excitation and sensing transducers or temperatureinduced variations of transducer capacitance [8]. This study first develops a laser-based mechanical impedance (LMI) technique which enables noncontact measurement of MI using laser ultrasound. An Nd:Yag pulse laser is used to generate ultrasound responses on a target structure, and a laser vibrometer measures LMI responses after the ultrasound converges to a steadystate. A numerical analysis at multiscale hierarchical levels allows the modeling of thermomechanical effect of laser ultrasound and the formation of the corresponding LMI responses. The effectiveness and feasibility of the proposed technique is experimentally verified through damage detection applications for a plate structure and multiple notches. The uniqueness of this study is that the proposed LMI technique enables the measurement of MI of a target structure without sensor placement. Therefore, it can 0146-9592/14/113130-04$15.00/0
be applied under harsh environmental conditions, and it can scan MI of the target structure with high spatial resolution. For efficient numerical analysis of LMI formation, this study utilizes the multiscale approach to partition a thermomechanical computation process into multiple steps in a time and spatial domain. It helps one reduce the simulation time in calculating LMI responses induced by an ultrashort laser pulse. Figure 1 shows an overview of the proposed noncontact LMI measurement. When a solid surface of a target structure is illuminated by a high-power pulse laser, a localized temperature expansion and compression is formed at an infinitesimal area of the surface and generates ultrasound [9]. The generated ultrasound initially travels forward from the laser incidence point and reflected from the structural boundaries. Eventually, the forwarding and reflecting waves are superimposed and converged to structural vibration (i.e., LMI). Here, a laser Doppler vibrometer enables the measurement of LMI by measuring the out-of-plane surface velocity [10–12]. The LMI can be described as a frequency response function (FRF) between the ultrasound generation and sensing points. The pulse laser beam is acting as an impulse input that induces MI on the target surface.
Fig. 1.
Schematic diagram of LMI measurement.
© 2014 Optical Society of America
June 1, 2014 / Vol. 39, No. 11 / OPTICS LETTERS
3131
Equation (1) shows an analytical FRF for a simply edgesupported plate [13] Gx; y; x0 ; y0 ∞ X ∞ 4 X sinkm x0 sinkn y0 sinkm x sinkn y ; Lx Ly m1 n1 Dfk2m k2n 2 − k4f g (1) where Lx , km and x0 are a plate length, wave numbers, and the coordinate of the impulse excitation point in the x direction, respectively. Ly , kn and y0 are defined similarly in the y direction. D is flexural rigidity and kf ω2 ρh∕D1∕4 Here, ω is the angular velocity, ρ is the density, and h is the height of the plate. The convolution integral of the input impulse signal and Gx; y; x0 ; y0 is the analytical solution of the LMI response. The LMI induced by the interaction between the excitation laser beam and the target structure can be identified through thermomechanical numerical analysis. The governing equations for thermomechanical analysis are composed of (a) the equation of motion in a local form and (b) the local balance equation of entropy ρü i −
∂ τ pi ; ∂xj ij
T 0 s_ −
∂qi ; ∂xi
(2)
where ρ is the density, T 0 is the equilibrium temperature, and s_ is the entropy rate. Using i–j index notations, τij are ̈ stresses, pi are body forces, ui are accelerations, and ∂qi ∕∂xi are divergences of thermal fluxes. Application of virtual work and temperature to Eq. (2) yields formulations for actual finite element (FE) analysis of LMI responses. This thermomechanical analysis is computationally expensive since the duration of the pulse laser is of the order of nanosecond, so the time step should be in the sub nanosecond range. In addition, the ultrashort excitation laser pulse makes it difficult to obtain an accurate heat flux profile on the thermal source. To overcome these limitations, this study adopts a two-step multiscale approach [14] in thermomechanical FE analysis to enhance the computation efficiency in solving the coupled thermomechanical problems of LMI. In this two-step approach, a microscale model with the dimensions in micrometer is first employed to obtain a temperature distribution profile on the surface when the laser-induced heat flux is irradiated on the infinitesimal area on a target structure. Then, the captured temperature profile is applied at nodal points as an input laser source in the FE model of the target structure. A subsequent thermomechanical analysis solves the governing equations associated with the interaction between the laser heat and the ultrasound. Numerical simulation of LMI formation is conducted using FEAP [15], a research purpose FE program. Figure 2(a) shows the FE model of an aluminum plate used in this thermomechanical simulation. The FE model is a simply edge-supported aluminum plate with 3D solid elements. The material properties are as follows: Young’s modulus E 70 GPa, Poisson’s ratio ν 0.345, density
Fig. 2. FE modeling of an aluminum plate and laser-induced thermal excitation (dimensions in millimeter). (a) Partitioning of the aluminum plate. (b) Spatial and temporal implementation of laser excitation.
ρ 2769 kgm−3 , and damping coefficient ξ 2.5M 10−6 K, where M and K are structural mass and stiffness matrices, respectively. The absorptivity of the specimen is assumed to be 5.2% [14]. The dimensions of the plate are 450 mm × 90 mm × 3 mm. The mesh size is set to 1 mm for all directions. The LMI is excited and measured at 150 mm away from the left and right ends, respectively. Both points are located at the center of the plate. The laser beam size, pulse energy, and duration are 20 mm2 , 10 mJ, and 8 ns, respectively. This is equivalent to a heat flux of 158.9 GW∕m2 applied to an excitation position. Using the two-step approach in thermomechanical simulation, the temperature gradient equivalent to the input heat flux is applied at multiple nodal points inside the beam area, as shown in Fig. 2(b). To further reduce the computation time for the thermomechanical simulation, the entire FE model is divided into two subregions. First, a 100 mm × 90 mm area around the laser excitation point is designated as the thermomechanical region. In this region, the effect of a laser-induced heat source on the formation of ultrasound is significant, so an implicit time integration scheme is applied to obtain a precise waveform considering the thermomechanical interaction. On the other hand, the effect of the incident heat source becomes marginal as a measurement point moves far away from the heat source. Therefore, only mechanical response is considered for this region, and an explicit time integration scheme is applied to reduce computation costs. Figure 3 shows a general agreement between numerical and experimental LMI responses obtained for 10–15 kHz. The experimental LMI response is induced and measured using a Nd:Yag pulse laser (Quantel, Brilliant Ultra) and a laser Doppler vibrometer (Polytec, OFV-551). Both the numerical and experimental LMI responses clearly show resonant peaks of LMI. Since the vibrometer measures only out-of-plane velocity responses, mainly flexural vibration components are captured.
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Fig. 3. Comparison of the numerical and experimental LMI responses. Fig. 6. LMI response changes due to damage type 1.
Next, the proposed LMI technique is applied to the detection of two different damage types in Figs. 4 and 5. For damage type 1 in Fig. 4, three notches are sequentially introduced. For damage type 2 in Fig. 5, a 30 mm notch is initiated at the middle bottom portion of the plate, grown to 60 mm, and finally to 90 mm. Each notch is 30 mm long, 1 mm deep, and 1 mm wide. Figures 6 and 7 show signal changes induced by damage types 1 and 2, respectively. The frequency range of 10–15 kHz is zoomed for a better comparison. A significant change in resonance peaks is observed, indicating the possibility of using LMI measurement for damage detection. In this study, a damage index (DI) is defined as follows. DIf i ; f j
~ − f¯ i f j ω − f¯ j 1 X f i ω ω ; 1 − max ω~ N − 1 i;j σf iσf j
(3)
where f i is ith LMI response, f¯i and σ f i are the mean and standard deviation of f i , respectively, N is the total number of data points, and ω~ is a frequency shift.
Fig. 7. LMI response changes due to damage type 2.
Tables 1 and 2 show the DI values obtained for damage types 1 and 2 over the frequency range of 10–70 kHz. This frequency range is divided into six subfrequency ranges with a frequency interval of 10 kHz for a closer look. As the number or length of the damage increases, the DI value monotonically increases for all frequency ranges. These observations suggest that LMI measurement can be used for effective damage detection. Although LMI responses are obtained only from a single pair of laser excitation and sensing points in this study, the proposed technique can be easily extended for multipoint measurements by scanning either the excitation or sensing laser beams. This additional scanning feature will improve the spatial resolution for damage detection. Table 1. DI Values for Damage Type 1
Fig. 4. Dimensions of the target plate and damage type 1: effect of notch number increases.
Freq. (kHz) State 10–20 Intact 1 Notch 2 Notches 3 Notches
20–30
30–40
40–50
50–60
60–70
0 0 0 0 0 0 0.0377 0.0925 0.126 0.1037 0.2024 0.1815 0.1119 0.1048 0.1586 0.2295 0.2470 0.2007 0.1215 0.1559 0.2462 0.2696 0.2838 0.2075
Table 2. DI Values for Damage Type 2 Freq. (kHz) State 10–20
Fig. 5. Dimensions of the target plate and damage type 2: effect of notch length increases.
Intact 30 mm 60 mm 90 mm
20–30
30–40
40–50
50–60
60–70
0 0 0 0 0 0 0.1116 0.1329 0.1363 0.1712 0.2569 0.2301 0.1588 0.1625 0.1906 0.2633 0.2835 0.2638 0.2039 0.2273 0.2513 0.3566 0.2905 0.2782
June 1, 2014 / Vol. 39, No. 11 / OPTICS LETTERS
In conclusion, a noncontact laser technique for MI measurement and damage detection is proposed. The formation of LMI has been confirmed through multiscale thermomechanical FE analysis. The general trend of the numerical simulation matches with the experimental result, indicating that LMI can successfully be formed using a laser source. The feasibility of the proposed LMI technique for damage detection is experimentally verified with increasing damage number and damage length. The DI value increases as the damage progresses. This research was supported by the Mid-Career Researcher Program through the National Research Foundation of Korea (NRF) (No. 2010-0017456). References 1. C. Liang, F. P. Sun, and C. A. Rogers, J. Intell. Mater. Syst. Struct. 5, 12 (1994). 2. J. W. Ayres, F. Lalande, Z. Chaudhry, and C. A. Rogers, Smart Mater. Struct. 7, 599 (1998). 3. G. Park, H. Sohn, C. R. Farrar, and D. J. Inman, Shock Vib. Dig. 35, 451 (2003).
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4. B. L. Grisso and D. J. Inman, Smart Struct. Syst. 4, 305 (2008). 5. V. Giurgiutiu, Structural Health Monitoring with Piezoelectric Wafer Active Sensors (Elsevier, 2008), p. 120. 6. H. Lee, J. Yang, and H. Sohn, Struct. Health Monit. 11, 684 (2012). 7. S. Bhalla and S. Moharana, J. Intell. Mater. Syst. Struct. 24, 33 (2012). 8. N. Sepehry, M. Shamshirsaz, and A. Bastani, Struct. Health Monit. 10, 171 (2011). 9. C. B. Scruby and L. E. Drain, Laser Ultrasonics: Techniques and Applications (Taylor & Francis, 2008), p. 76. 10. W. J. Staszewski, B. C. Lee, L. Mallet, and F. Scarpa, Smart Mater. Struct. 13, 251 (2004). 11. P. Castellini, M. Martarelli, and E. P. Toamasini, Mech. Sys. Sig. Pro. 20, 1265 (2006). 12. M. Salman and K. G. Sabra, J. Acoust. Soc. Am. 133, 1245 (2013). 13. J. Cuenca, F. Gautier, and L. Simon, J. Sound Vib. 322, 1048 (2009). 14. W. Liu and J. W. Hong, Proc. SPIE 8545, 854501 (2012). 15. R. L. Taylor, FEAP—A Finite Element Analysis Program, Version 8.2 User Manual (University of California at Berkeley, 2008).
OPTICS LETTERS / Vol. 39, No. 11 / June 1, 2014
Mechanical impedance measurement and damage detection using noncontact laser ultrasound Hyeonseok Lee, Hyeong Uk Lim, Jung-Wuk Hong, and Hoon Sohn* Department of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, South Korea *Corresponding author: [email protected] Received December 17, 2013; accepted April 6, 2014; posted April 22, 2014 (Doc. ID 203026); published May 19, 2014 This Letter proposes a mechanical impedance (MI) measurement technique using noncontact laser ultrasound. The ultrasound is generated by shooting a pulse laser beam onto a target structure, and its response is measured using a laser vibrometer. Once ultrasound propagation converges to structural vibration, MI is formed over the entire structure. Because noncontact lasers are utilized, this technique is applicable in harsh environments, free of electromagnetic interference, and able to perform wide-range scanning. The formation of MI and its feasibility for damage detection are verified through thermo-mechanical finite element analysis and lab-scale experiments. © 2014 Optical Society of America OCIS codes: (280.3375) Laser induced ultrasonics; (120.4290) Nondestructive testing. http://dx.doi.org/10.1364/OL.39.003130
In recent years, structural health monitoring (SHM) techniques have become important to detect structural damage and enhance the structural safety of critical infrastructure. Among various damage detection approaches, mechanical impedance (MI) measurement has been widely used for detecting the presence of incipient damage. An electromechanical impedance (EMI) technique has evolved into as a preferable method of measuring MI changes by attaching piezoelectric transducers and utilizing their electromechanical coupling properties [1–4]. The EMI technique is known to be sensitive to various sizes of structural defects and it requires a relatively simple hardware configuration [5]. However, there are several problems associated with EMI measurement using piezoelectric transducers. First, because piezoelectric transducers are directly attached to a target structure, they are vulnerable to harsh environments, such as high temperature, corrosive or radioactive conditions, and are not conformable to curved surfaces [6]. For example, the variability of the bonding condition between the piezoelectric transducer and the host structure can deteriorate the robustness and repeatability of EMI measurement [7]. Furthermore, the EMI waveform can be distorted by the cross talk between the excitation and sensing transducers or temperatureinduced variations of transducer capacitance [8]. This study first develops a laser-based mechanical impedance (LMI) technique which enables noncontact measurement of MI using laser ultrasound. An Nd:Yag pulse laser is used to generate ultrasound responses on a target structure, and a laser vibrometer measures LMI responses after the ultrasound converges to a steadystate. A numerical analysis at multiscale hierarchical levels allows the modeling of thermomechanical effect of laser ultrasound and the formation of the corresponding LMI responses. The effectiveness and feasibility of the proposed technique is experimentally verified through damage detection applications for a plate structure and multiple notches. The uniqueness of this study is that the proposed LMI technique enables the measurement of MI of a target structure without sensor placement. Therefore, it can 0146-9592/14/113130-04$15.00/0
be applied under harsh environmental conditions, and it can scan MI of the target structure with high spatial resolution. For efficient numerical analysis of LMI formation, this study utilizes the multiscale approach to partition a thermomechanical computation process into multiple steps in a time and spatial domain. It helps one reduce the simulation time in calculating LMI responses induced by an ultrashort laser pulse. Figure 1 shows an overview of the proposed noncontact LMI measurement. When a solid surface of a target structure is illuminated by a high-power pulse laser, a localized temperature expansion and compression is formed at an infinitesimal area of the surface and generates ultrasound [9]. The generated ultrasound initially travels forward from the laser incidence point and reflected from the structural boundaries. Eventually, the forwarding and reflecting waves are superimposed and converged to structural vibration (i.e., LMI). Here, a laser Doppler vibrometer enables the measurement of LMI by measuring the out-of-plane surface velocity [10–12]. The LMI can be described as a frequency response function (FRF) between the ultrasound generation and sensing points. The pulse laser beam is acting as an impulse input that induces MI on the target surface.
Fig. 1.
Schematic diagram of LMI measurement.
© 2014 Optical Society of America
June 1, 2014 / Vol. 39, No. 11 / OPTICS LETTERS
3131
Equation (1) shows an analytical FRF for a simply edgesupported plate [13] Gx; y; x0 ; y0 ∞ X ∞ 4 X sinkm x0 sinkn y0 sinkm x sinkn y ; Lx Ly m1 n1 Dfk2m k2n 2 − k4f g (1) where Lx , km and x0 are a plate length, wave numbers, and the coordinate of the impulse excitation point in the x direction, respectively. Ly , kn and y0 are defined similarly in the y direction. D is flexural rigidity and kf ω2 ρh∕D1∕4 Here, ω is the angular velocity, ρ is the density, and h is the height of the plate. The convolution integral of the input impulse signal and Gx; y; x0 ; y0 is the analytical solution of the LMI response. The LMI induced by the interaction between the excitation laser beam and the target structure can be identified through thermomechanical numerical analysis. The governing equations for thermomechanical analysis are composed of (a) the equation of motion in a local form and (b) the local balance equation of entropy ρü i −
∂ τ pi ; ∂xj ij
T 0 s_ −
∂qi ; ∂xi
(2)
where ρ is the density, T 0 is the equilibrium temperature, and s_ is the entropy rate. Using i–j index notations, τij are ̈ stresses, pi are body forces, ui are accelerations, and ∂qi ∕∂xi are divergences of thermal fluxes. Application of virtual work and temperature to Eq. (2) yields formulations for actual finite element (FE) analysis of LMI responses. This thermomechanical analysis is computationally expensive since the duration of the pulse laser is of the order of nanosecond, so the time step should be in the sub nanosecond range. In addition, the ultrashort excitation laser pulse makes it difficult to obtain an accurate heat flux profile on the thermal source. To overcome these limitations, this study adopts a two-step multiscale approach [14] in thermomechanical FE analysis to enhance the computation efficiency in solving the coupled thermomechanical problems of LMI. In this two-step approach, a microscale model with the dimensions in micrometer is first employed to obtain a temperature distribution profile on the surface when the laser-induced heat flux is irradiated on the infinitesimal area on a target structure. Then, the captured temperature profile is applied at nodal points as an input laser source in the FE model of the target structure. A subsequent thermomechanical analysis solves the governing equations associated with the interaction between the laser heat and the ultrasound. Numerical simulation of LMI formation is conducted using FEAP [15], a research purpose FE program. Figure 2(a) shows the FE model of an aluminum plate used in this thermomechanical simulation. The FE model is a simply edge-supported aluminum plate with 3D solid elements. The material properties are as follows: Young’s modulus E 70 GPa, Poisson’s ratio ν 0.345, density
Fig. 2. FE modeling of an aluminum plate and laser-induced thermal excitation (dimensions in millimeter). (a) Partitioning of the aluminum plate. (b) Spatial and temporal implementation of laser excitation.
ρ 2769 kgm−3 , and damping coefficient ξ 2.5M 10−6 K, where M and K are structural mass and stiffness matrices, respectively. The absorptivity of the specimen is assumed to be 5.2% [14]. The dimensions of the plate are 450 mm × 90 mm × 3 mm. The mesh size is set to 1 mm for all directions. The LMI is excited and measured at 150 mm away from the left and right ends, respectively. Both points are located at the center of the plate. The laser beam size, pulse energy, and duration are 20 mm2 , 10 mJ, and 8 ns, respectively. This is equivalent to a heat flux of 158.9 GW∕m2 applied to an excitation position. Using the two-step approach in thermomechanical simulation, the temperature gradient equivalent to the input heat flux is applied at multiple nodal points inside the beam area, as shown in Fig. 2(b). To further reduce the computation time for the thermomechanical simulation, the entire FE model is divided into two subregions. First, a 100 mm × 90 mm area around the laser excitation point is designated as the thermomechanical region. In this region, the effect of a laser-induced heat source on the formation of ultrasound is significant, so an implicit time integration scheme is applied to obtain a precise waveform considering the thermomechanical interaction. On the other hand, the effect of the incident heat source becomes marginal as a measurement point moves far away from the heat source. Therefore, only mechanical response is considered for this region, and an explicit time integration scheme is applied to reduce computation costs. Figure 3 shows a general agreement between numerical and experimental LMI responses obtained for 10–15 kHz. The experimental LMI response is induced and measured using a Nd:Yag pulse laser (Quantel, Brilliant Ultra) and a laser Doppler vibrometer (Polytec, OFV-551). Both the numerical and experimental LMI responses clearly show resonant peaks of LMI. Since the vibrometer measures only out-of-plane velocity responses, mainly flexural vibration components are captured.
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Fig. 3. Comparison of the numerical and experimental LMI responses. Fig. 6. LMI response changes due to damage type 1.
Next, the proposed LMI technique is applied to the detection of two different damage types in Figs. 4 and 5. For damage type 1 in Fig. 4, three notches are sequentially introduced. For damage type 2 in Fig. 5, a 30 mm notch is initiated at the middle bottom portion of the plate, grown to 60 mm, and finally to 90 mm. Each notch is 30 mm long, 1 mm deep, and 1 mm wide. Figures 6 and 7 show signal changes induced by damage types 1 and 2, respectively. The frequency range of 10–15 kHz is zoomed for a better comparison. A significant change in resonance peaks is observed, indicating the possibility of using LMI measurement for damage detection. In this study, a damage index (DI) is defined as follows. DIf i ; f j
~ − f¯ i f j ω − f¯ j 1 X f i ω ω ; 1 − max ω~ N − 1 i;j σf iσf j
(3)
where f i is ith LMI response, f¯i and σ f i are the mean and standard deviation of f i , respectively, N is the total number of data points, and ω~ is a frequency shift.
Fig. 7. LMI response changes due to damage type 2.
Tables 1 and 2 show the DI values obtained for damage types 1 and 2 over the frequency range of 10–70 kHz. This frequency range is divided into six subfrequency ranges with a frequency interval of 10 kHz for a closer look. As the number or length of the damage increases, the DI value monotonically increases for all frequency ranges. These observations suggest that LMI measurement can be used for effective damage detection. Although LMI responses are obtained only from a single pair of laser excitation and sensing points in this study, the proposed technique can be easily extended for multipoint measurements by scanning either the excitation or sensing laser beams. This additional scanning feature will improve the spatial resolution for damage detection. Table 1. DI Values for Damage Type 1
Fig. 4. Dimensions of the target plate and damage type 1: effect of notch number increases.
Freq. (kHz) State 10–20 Intact 1 Notch 2 Notches 3 Notches
20–30
30–40
40–50
50–60
60–70
0 0 0 0 0 0 0.0377 0.0925 0.126 0.1037 0.2024 0.1815 0.1119 0.1048 0.1586 0.2295 0.2470 0.2007 0.1215 0.1559 0.2462 0.2696 0.2838 0.2075
Table 2. DI Values for Damage Type 2 Freq. (kHz) State 10–20
Fig. 5. Dimensions of the target plate and damage type 2: effect of notch length increases.
Intact 30 mm 60 mm 90 mm
20–30
30–40
40–50
50–60
60–70
0 0 0 0 0 0 0.1116 0.1329 0.1363 0.1712 0.2569 0.2301 0.1588 0.1625 0.1906 0.2633 0.2835 0.2638 0.2039 0.2273 0.2513 0.3566 0.2905 0.2782
June 1, 2014 / Vol. 39, No. 11 / OPTICS LETTERS
In conclusion, a noncontact laser technique for MI measurement and damage detection is proposed. The formation of LMI has been confirmed through multiscale thermomechanical FE analysis. The general trend of the numerical simulation matches with the experimental result, indicating that LMI can successfully be formed using a laser source. The feasibility of the proposed LMI technique for damage detection is experimentally verified with increasing damage number and damage length. The DI value increases as the damage progresses. This research was supported by the Mid-Career Researcher Program through the National Research Foundation of Korea (NRF) (No. 2010-0017456). References 1. C. Liang, F. P. Sun, and C. A. Rogers, J. Intell. Mater. Syst. Struct. 5, 12 (1994). 2. J. W. Ayres, F. Lalande, Z. Chaudhry, and C. A. Rogers, Smart Mater. Struct. 7, 599 (1998). 3. G. Park, H. Sohn, C. R. Farrar, and D. J. Inman, Shock Vib. Dig. 35, 451 (2003).
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4. B. L. Grisso and D. J. Inman, Smart Struct. Syst. 4, 305 (2008). 5. V. Giurgiutiu, Structural Health Monitoring with Piezoelectric Wafer Active Sensors (Elsevier, 2008), p. 120. 6. H. Lee, J. Yang, and H. Sohn, Struct. Health Monit. 11, 684 (2012). 7. S. Bhalla and S. Moharana, J. Intell. Mater. Syst. Struct. 24, 33 (2012). 8. N. Sepehry, M. Shamshirsaz, and A. Bastani, Struct. Health Monit. 10, 171 (2011). 9. C. B. Scruby and L. E. Drain, Laser Ultrasonics: Techniques and Applications (Taylor & Francis, 2008), p. 76. 10. W. J. Staszewski, B. C. Lee, L. Mallet, and F. Scarpa, Smart Mater. Struct. 13, 251 (2004). 11. P. Castellini, M. Martarelli, and E. P. Toamasini, Mech. Sys. Sig. Pro. 20, 1265 (2006). 12. M. Salman and K. G. Sabra, J. Acoust. Soc. Am. 133, 1245 (2013). 13. J. Cuenca, F. Gautier, and L. Simon, J. Sound Vib. 322, 1048 (2009). 14. W. Liu and J. W. Hong, Proc. SPIE 8545, 854501 (2012). 15. R. L. Taylor, FEAP—A Finite Element Analysis Program, Version 8.2 User Manual (University of California at Berkeley, 2008).
