Fiber Bragg grating (FBG) sensors are often applied as Lamb wave detectors for structural health monitoring (SHM) systems. Analyzing the measured signal for the identification of structural damage requires a high signal-to-noise ratio (SNR) because of the low-amplitude Lamb waves. This paper applies a two-dimensional ultrasonic horn between the structure and a remotely bonded FBG sensor to increase the amplitudes of the measured signal. Experimentally we test a variety of ultrasonic geometries and demonstrate a 100% increase in the measured ultrasonic signal amplitude using a metallic ultrasonic horn with step-down geometry. A bonding procedure for the combined ultrasonic horn and optical fiber is also developed that produces repeatable signal measurements. For some horn geometries, an additional vibration signal at the Lamb wave excitation frequency is observed in the measurements. Laser Doppler vibrometry (LDV) measurements and finite element analysis demonstrate that the signal is due to the natural vibration of the horn. The experimental results demonstrate that using an aluminum ultrasonic horn to focus wave is an excellent method to increase the sensitivity of the FBG to the small amplitude Lamb wave, provided the horn vibration characteristics are taken account in the design of the measurement system.
The passive pitch-catch technique based on ultrasonic Lamb waves propagating through a thin structure is often utilized in structural health monitoring (SHM) applications [1,2]. Various sensors can be used for the detector, including fiber Bragg grating (FBG) sensors, piezoelectric transducers, and laser Doppler vibrometers [3–5]. As the Lamb wave propagates from the actuator to the detector, the propagating Lamb waves can be converted to other modes or frequencies, or attenuated or distorted due to the presence of damage in the structure. The detected waveforms can then be demodulated to identify the location and form of the damage [6,7]. However, analyzing and demodulating the detected signal for damage detection can be difficult because it requires a high signal-to-noise ratio (SNR) due to the low amplitude of the Lamb waves. The SNR is especially critical when FBG sensors are used as the detector, because the small contact area between the optical fiber and the structure surface leads to a relatively poor sensitivity as compared with some conventional disc-type sensors. However, FBG sensors possess other advantages as Lamb wave detectors, including their strong directionality and ability to be multiplexed in large numbers in a single optical fiber.
Ultrasonic Lamb wave detection in large structures is even more challenging since the wave amplitude decreases with propagation distance from the actuation source. Therefore, previous researchers have focused the propagating Lamb waves in the structure to increase the amount of signal energy extracted from the structure. This focusing can be achieved through structural features such as thickness changes or bends. For example, Ramdhas et al.  demonstrated that bends in thin-walled structures can generate higher energy symmetric and antisymmetric guided modes with waveforms identical to the original symmetric (S0) and antisymmetric (A0) Lamb waves, however with different propagation velocities. Similar trapping of guided waves through thinning and curvature of the structure cross section has also been demonstrated [9,10].
Another method to amplify Lamb waves in the structure is to add an additional device such as an elastic metamaterial, to focus the wave energy. Yan et al.  and Tol et al.  demonstrated focusing of low-frequency A0 Lamb waves through gradient-index phononic crystal lens designs, however limitations in fabrication processes for these elastic metamaterials restrict their use to frequencies below 100 kHz. Plano-concave aspherical lenses have also been applied to control and focus A0 Lamb waves, changing the effective plate thickness to modulate the wavefront [13,14]. Slice lenses are easy to fabricate and are low-profile. However, plano-concave lens can only control highly dispersive Lamb waves for which the wavenumber strongly depends on the plate thickness.
An alternate approach to increasing the SNR is to amplify the detector response to the arriving Lamb wave. Specifically for the case of a FBG sensor as the detector, researchers have amplified the collected signal by refraction and resonant-type waveguides  and resonant structures . Many of these devices are bulky, three-dimensional devices.
Remote bonding of an FBG sensor has also been demonstrated recently as an alternative method to increase the FBG SNR [17–19]. The S0 and A0 Lamb waves are converted at the adhesive location into guided longitudinal, L01, traveling waves in a single-mode optical fiber. The L01 mode retains the same waveform as the original S0 and A0 Lamb waves and is nondispersive at sub-MHz frequencies.
This paper investigates the potential of further increasing the sensitivity of a FBG sensor for Lamb wave detection by combining geometrical amplification using an ultrasonic horn with the remote bonding configuration. The ultrasonic horn is easy to fabricate and bond to the host plate and focuses both symmetric and antisymmetric modes for detection by the FBG. Specifically, the fundamental Lamb wave modes propagating through an aluminum plate are coupled into an ultrasonic horn through an adhesive bond and then into an optical fiber through a second adhesive bond. The combined approach is experimentally tested for both polymer and metallic ultrasonic horns of various geometries.
Measurement of Lamb Waves With Fiber Bragg Grating Sensor.
A generic testbed, shown in Fig. 1, was designed to measure the relative amplification of the Lamb wave signal from a flat plate through an ultrasonic horn and into the optical fiber. Lamb waves propagating through an aluminum plate are captured by an adhesively bonded optical fiber and converted into a L01 mode propagating along the optical fiber. The waveform of the L01 mode is then measured by a FBG sensor further along the fiber. This process of converting Lamb waves into the L01 mode into the optical fiber has been well documented in previous studies [17–19].
The number of ultrasonic horns bonded to the plate and their geometries varied between tests. Lamb waves in the aluminum plate are excited by a piezoelectric actuator (PZT 1) and propagate through the 0.8 mm thick aluminum plate, then are coupled to the ultrasonic horn. All ultrasonic horns are bonded radially from the PZT at a distance of 150 mm (more details on the bonding procedure are provided in the titled “Bonding Procedure”). The ultrasonic horns are bonded with cyanoacrylate (CA) adhesive (Loctite®) to the aluminum plate with a rectangular bond of dimensions 5 mm × a mm, as shown in Fig. 1, where a is the maximum width of the ultrasonic horn. The dimensions of the 6061 aluminum plate are 609.6 mm × 609.6 mm. An elastomeric damping material (Dynamat®) is used to cover the boundary of the aluminum plate on both top and bottom surfaces, to reduce boundary reflections.
The FBG sensor in all experiments is a 10 mm long grating written in a 125 μm diameter SMF-28 optical fiber with a 15 μm thick polyimide coating. The optical fiber is bonded on the surface of the ultrasonic horn using the same liquid CA adhesive, as shown in Fig. 1. The length of bond area for the optical fiber to the horn is 10 mm and the width is b mm, where b is the minimum width of the ultrasonic horn.
The PZT is actuated with a 5.5 cycle Hanning windowed burst excitation at 300 kHz. The PZT actuates in the radial mode and therefore generates primarily symmetric Lamb waves. The excitation frequency is chosen to only generate the fundamental symmetric, S0, mode in the aluminum plate. The excitation signal is transferred to an arbitrary waveform generator (AWG), which is input to the PZT through a voltage amplifier. The oscilloscope is synchronized with the waveform generator by the trigger function. The propagating S0 mode is converted into propagating modes in the ultrasonic horn, and then into the L01 mode in the optical fiber which is bonded to the other end of the ultrasonic horn (see Fig. 1). The L01 mode propagates along the optical fiber to the FBG. The distance along the optical fiber between the adhesive bond edge and FBG sensor is fixed at 100 mm.
The edge-filtering method, shown in Fig. 2, is applied to measure the output signal of the FBG sensor. The narrowband output of the tunable laser (TUNICS PLUS) is initially set to the midpoint of the FBG ascending edge of the reflected spectrum. The variation of axial strain in the optical fiber due to the L01 mode induces a wavelength shift in the FBG reflected spectrum, which produces a change in the portion of the light reflected from the FBG and therefore a variation in the optical power measured at the photodetector (PD). The change of voltage is converted to strain by first measuring the reflected spectrum by sweeping the tunable laser output and calculating the slope of the spectral edge shown in Fig. 2. The other end of the optical fiber is submersed in an index matching gel to reduce back reflections. The same FBG was used for all experiments.
For each test, two reference measurements were collected. The first was from a PZT sensor (PZT 2) bonded directly to the plate to measure any variations in the PZT actuator (PZT 1) output between tests. The second used a reference FBG in an optical fiber directly bonded to the aluminum plate to measure the signal output without an ultrasonic horn. For this measurement, the optical fiber was disconnected from the circulator and replaced with the reference optical fiber, shown as the dashed line in Fig. 1.
Ultrasonic Horn Selection.
Initial ultrasonic geometries were printed from Acrylonitrile Butadiene Styrene (ABS) using a 3D printer to rapidly fabricate a large number of ultrasonic horn geometries and thicknesses for initial testing. The 3D printer prints in 0.127 mm layers and extrudes ABS at a raster width of 0.254 mm. A step-down geometry was used, with the dimension variables shown in Fig. 3. Each horn geometry was printed in two thicknesses, 0.6 and 1.2 mm. The specific geometries tested are listed in Table 1. The goal of these experiments was to test the role of the step-down ratio (a/b), maximum width, a, and the thickness on the signal amplification.
|Shape||a (mm)||b (mm)||c (mm)||d (mm)|
|Shape||a (mm)||b (mm)||c (mm)||d (mm)|
After the initial screening of ABS samples, a small number of geometries were selected to be fabricated in 6061 aluminum. The metal ultrasonic horns were waterjet cut with an accuracy of ±0.08 mm. In addition to the step-down geometries, aluminum horns were also fabricated with an exponential-decay keeping the same step-down ratio, shown in Fig. 4. The specific geometries fabricated are listed in Table 2. All of the geometries were fabricated in two thicknesses, 0.4 and 0.63 mm. These two thicknesses are thinner than the aluminum plate.
One of the most critical steps in the experimental setup is the bonding of the ultrasonic horn because the quality of the bond affects the coupling of the Lamb wave to the ultrasonic horn. Preliminary testing demonstrated that the signal amplitude varied between tests of the same ultrasonic horn when it was removed and rebonded to the aluminum plate. Therefore, it is necessary to have a repeatable bonding procedure such that the results from the different test cases could be compared. The bonding procedure shown in Fig. 5 was therefore developed through multiple trials and was applied to all specimens in this paper.
A rectangle is first drawn by a water-ink pen on the aluminum plate to mark the specific area where the ultrasonic horn is to be bonded (Fig. 5(a)); the width of this area depends on the maximum width, a, of the horn and the length is 5 mm. Then Kapton tape is applied to prevent adhesive from spreading to the surrounding area of the aluminum plate (Fig. 5(b)). CA adhesive is painted onto the edge of the bottom tape (Fig. 5(c)) and is spread using a glass plate (Fig. 5(d)). The bottom Kapton tape is then removed (Fig. 5(e)). Kapton film is placed on the bottom surface of the horn and fixed in position using two pieces of Kapton tape (Fig. 5(f)). The exposed bonding area between the ultrasonic horn and aluminum plate is bonded using CA adhesive (Fig. 5(g)). A fixed weight is applied on a portion of the ultrasonic horn to give a consistent pressure (Fig. 5(h)). The adhesive is then cured at room temperature for 24 h. After removing the Kapton film and tapes, the optical fiber is bonded to upper surface of the horn. A polyester film is first placed between the horn and the aluminum plate to protect from CA adhesive overflow, (Fig. 5(i)). The optical fiber is fixed to the horn and polyester film by Kapton tape. The CA adhesive is applied along 10 mm of the optical fiber (Fig. 5(j)) and allowed to cure at room temperature for 24 h. The final configuration is shown in Fig. 5(k).
In order to verify that the procedure did produce repeatable, high quality bonds between the ultrasonic horn and the aluminum plate, it was applied to bond 20 ultrasonic horns to glass slides. Photographs of representative bond regions with and without the revised bonding procedure are shown in Fig. 6. The photographs show that revising the bond procedure produced a much more uniform distribution of adhesive in the bond region for both the ABS and aluminum horns. Between the multiple specimens, the average thickness of the CA adhesive using the original bonding procedure was 0.11 mm ± 0.05 mm (measured with a caliper). Revising the bonding procedure reduced the average thickness of the CA adhesive to 0.07 mm ± 0.01 mm.
Acrylonitrile Butadiene Styrene Ultrasonic Horns.
A total of 14 acoustic horns were manufactured by 3D printing. Their specific dimensions are shown in Table 1. A second PZT sensor (PZT 2 in Fig. 1) is used to normalize the input Lamb wave excited from the actuator (PZT 1) over the multiple days of the experiment. The maximum deviation of signal collected by PZT 2 was 5%. Figure 7 shows the peak-to-peak amplitude of the output FBG response for the different ABS ultrasonic horn shapes. The peak-to-peak amplitude is defined as the maximum amplitude of the windowed signal. The reference case is that of an optical fiber bonded directly to the plate, without the ABS horn.
The thicker horns (t = 1.2 mm) consistently produce signal amplitudes smaller than the thinner horns (t = 0.6 mm) and the reference case. Therefore, we will discuss the results of the t = 0.6 mm thickness horns only. Shape A.1, is the rectangular case, without any step-down in the geometry. As expected, the amplitude collected for this case is lower than the reference case, because the ABS material attenuates the propagating wave more than aluminum, while there is no geometrical amplification in the horn. This case was included as a second reference case.
The measured signal amplitude for the step-down geometries (shapes A.2-7) are shown in Fig. 7. The measured signal amplitudes are inversely proportional to the total area of the geometries from A.2-7, demonstrating that there was a strong geometrically induced amplification of the waves. Among those geometries, shapes A.2 and A.3 (t = 0.6 mm) are the two that produced larger amplitudes than the reference case, with a 20% and 15% amplitude increase, respectively.
However, it is critical to evaluate not only the signal amplitude but also how well the signal waveform is preserved during the amplification process. Therefore, we examine the waveform of the collected signals using A.2 and A.3 ultrasonic horns for both thicknesses. Figure 8 plots the input excitation signal to the PZT actuator (PZT 1) and the subsequent FBG responses for these two shapes. The PZT excites both S0 and A0 Lamb waves in the aluminum plate, however we only consider the S0 mode, which is the first to arrive.
The theoretical velocity of the S0 mode in the aluminum 6061 plate is 5340 m/s and that of the L01 mode in the optical fiber is 5110 m/s (ν = 0.33, ρ = 2700 kg/m3, E = 69 GPa) . The theoretically estimated velocity of S0 mode for t = 1.2 and 0.6 mm ABS ultrasonic horns are 1474 m/s and 1604 m/s, respectively, calculated from the dispersion curve based on an infinite plate of ABS material (ν = 0.35, ρ = 950 kg/m3, E = 2.23 GPa). The A0 Lamb wave is an evanescent wave at 300 kHz for these two thicknesses and therefore does not propagate into the horn. Therefore, the theoretical arrival time of the original S0 mode wave packet for the reference case without a horn at the FBG is 53 μs, shown by the dashed line in Fig. 8, which matches the experimentally arrival time well. The theoretical arrival time for the t = 1.2 and 0.6 mm ABS ultrasonic horns are 68 μs and 66 μs, respectively, which again matches the experimentally measured arrival time well. However, the output FBG responses of the ultrasonic horn cases presented in Fig. 8 shows some difference as compared with the input excitation signal, in particular vibrations following the original wave packet are detected by the FBG. Therefore, the wave propagation through the ultrasonic horns is further investigated using laser Doppler vibrometry (LDV).
Figure 9 shows the LDV experimental setup used to measure the wave propagation at the surface of the bonded ultrasonic horn on the aluminum plate. The horn of shape A. 2 (t = 0.6 mm) was selected for analysis since it produced the highest signal amplification. The aluminum plate is placed under the 3D LDV sensor (Polytec® MSA-100-3D) head on the xy precision stage. The x-direction is aligned with the propagation direction, the y-direction in the plane of the plate perpendicular to the propagation direction, and the z-direction perpendicular to the surface of the plate. The input excitation signal from the waveform generator is time-synchronized with the output measurement of the 3D LDV. The 3D LDV scanning region matches the shape of the horn and is as the solid line in Fig. 9. The scan area is spray-coated with a thin layer of white powder (Weld Check® Developer, CRC) in order to create uniform light scattering from the surface of the specimen, because the aluminum plate is highly reflective.
Figures 10(a)–10(c) plots the x-directional surface velocity of shape A.2 (t = 0.6 mm) ultrasonic horn sample at different times. This in-plane displacement is the main component for the S0 mode Lamb wave. Figure 10(a) plots the surface deformation of the ultrasonic horn at 40.8 μs when the S0 Lamb wave in the plate is starting to couple into the ultrasonic horn through the bonded section. The Lamb wave couples into the horn approximately as a plane wave. The wave propagating in the horn beyond the bonded section then decays rapidly, as shown in Fig. 10(b). However, some amplification of the wave can be seen in Fig. 10(c) as the wave re-focuses at the beginning of the channel, indicated by the arrow. We also plot the z-directional surface velocity of the ultrasonic horn in Figs. 10(d)–10(f). Clearly an unintended out-plane mode is excited by the coupled Lamb wave as well as the in-plane mode. Moreover, the same focusing of this wave occurs as for the in-plane component in Fig. 10(f). This out-of-plane component is most likely a source of the vibrations in the FBG signal after the first wave packet.
Acrylonitrile Butadiene Styrene Numerical Simulations.
To further understand the difference in amplification between the two ABS horn thicknesses, finite element simulations were performed in ansys. The model was limited to cover only the mode conversion from the aluminum plate to the ABS sheet, not focusing within the horn, so a rectangular ABS sheet was modeled. The model geometry is shown in Fig. 11, consisting of the aluminum plate, the ABS sheet and a layer of CA adhesive between them. The density of the CA adhesive is 1070 kg/m3, the modulus is 1.26 GPa, and the thickness is the same as the experiments. The size of ABS sheet is 20 × 40 mm2 and the thickness varied from 0.2 to 1.2 mm. In-plane displacement excitation (S0 mode) was applied at a line source on the plate as a 300 kHz, 5.5 cycle Hanning windowed wave. The model mesh size and time-step was 0.5 mm and 0.17 μs.
Figure 12 plots the results of this simulation for the 1.2 mm horn thickness. The waveforms are plotted for three locations in the model (shown in Fig. 11): a reference point on the aluminum plate (1), and points near the front (2), and rear (3) edges of the ABS sheet. The time of arrival is different for the three locations. The in-plane and out-of-plane components of the waves are plotted in Figs. 12(a) and 12(b). Both S0 and A0 modes are seen in the plate, arriving approximately 10 μs apart. The in-plane displacements are highest in the aluminum plate (1) but are also converted into a S0 mode in the ABS horn. At location 2, the waveform is complex due to reflections from the horn boundary; however, the wave is reduced to the original 5 cycle envelope, followed by a lower amplitude vibration, by location 3. Out-of-plane displacements are also measured at location 2 in the ABS horn, therefore the Lamb waves are converted to both S0 and A0 modes in the horn. The amplitude of the A0 mode in the ABS is much higher than the S0 mode; however, the A0 mode decays rapidly since it is an evanescent wave.
Next the thickness of the ABS horn was varied in the simulations. The mesh size was reduced to 0.2 mm to be sufficient for the thinner horns. The peak-to-peak amplitude of the S0 mode in the ABS horn is plotted in Fig. 13 for each thickness. The amplitude was calculated at the center of the ABS horn in Fig. 11. The simulations confirm that the expected amplitude is higher for the 0.6 mm horn thickness than for the 1.2 mm thickness, which was observed experimentally. However, the amplitude is not a monotonic function of horn thickness.
To understand the amplitude increase for the 0.4 and 0.6 mm thickness cases, Fig. 14 plots the total deformation at two time-steps for the 0.6 mm horn thickness. In the first step (Fig. 14(a)), the S0 mode has arrived at the horn and is starting to propagate along the horn. However, at the second step (Fig. 14(b)), 5 μs later, most of the energy of the mode has not yet propagated along the horn. This effect was also observed in the time-domain plots, as the S0 mode in the horn arrived significantly later for the 0.4 and 0.6 mm cases than for the other cases. Therefore, for some thickness cases, a significant portion of the wave energy in the horn is trapped at the beginning of the horn, and constructively interferes with the rest of the incoming S0 mode in the aluminum plate, prior to propagating along the horn. This resonance behavior is similar the predictions of the theoretical model proposed by Huang and Balusu  for coupling of the ultrasonic modes from a plate through the adhesive layer to the optical fiber (without an ultrasonic horn).
Aluminum Ultrasonic Horns.
The experimental measurements from the ABS horns demonstrate the potential of the horn geometry to amplify the wave amplitude at the FBG. However, the LDV measurements of Fig. 10 highlight the rapid decay of the S0 mode in the ABS horns, not predicted in the numerical simulations. This decay is most likely to due to inherent damping in the ABS material (not included in the numerical simulations). Therefore, we next fabricated metallic ultrasonic horns using those geometries. We fabricated horns with shapes A.2 and A.3 using 6061 aluminum, in order to reduce the effect of material damping. The ABS horns with thickness t = 0.6 mm better amplified the Lamb wave signal than the horns with thickness t = 1.2 mm. Therefore, we fabricated the aluminum horns with a thickness of t = 0.6 mm and a smaller thickness of t = 0.4 mm. We also tested two different focus channel designs, step-down and exponential-decay. The specific dimensions of these geometries are defined in Figs. 3 and 4 and Table 2.
Figures 15(a)–15(c) plot the output FBG responses for the shapes B.1, B.2, and B.4 with t = 0.63 mm thickness. Figures 15(d)–15(f) plot the response for the same shapes, but for t = 0.4 mm thickness. The ultrasonic horn of shape B.3 demonstrated a lower signal amplification as compared with the reference signal and the other cases, therefore we only discuss shapes B.1, B.2, and B.4 in the rest of this section.
The theoretical velocity of the S0 mode for the t = 0.63 and 0.4 mm aluminum ultrasonic horns are 5345 m/s and 5350 m/s, respectively. Therefore, the theoretical arrival time for the signal at the FBG location is 53.3 μs for both thicknesses, indicated with dashed lines in Fig. 15. We observe the arrival of the S0 mode in the plots of Fig. 15, slightly delayed from the theoretical arrival time. This delay is likely due to the fact that the horn geometry is not accounted for in the theoretical arrival time approximation. Similar to the previous results, the metallic ultrasonic horns amplified the first arriving wave packet, however vibration of the horn can still be seen in the signal. Both the signal and the vibration have higher amplitudes than those of the ABS horns. The increased vibration amplitude is consistent with the decreased material damping of aluminum as compared with ABS. For shape B.4, the noise wave packet is overlapped with the first-wave package in the result of thickness 0.63 mm horn. The shape B.2 produced the best result. Figure 16 shows the peak-to-peak amplitude of the first-arriving wave packets for the aluminum horn data. Overall, these results demonstrate that we can tune the ultrasonic horn geometry in order to optimize the waveform and amplitude of the wave signals extracted from the horn using an FBG.
To further analyze the metal horns, we performed the same 3D LDV measurements as for the ABS horns. The 3D LDV measurements were performed for the B.2 aluminum horn since it had the best performance. The results of the x-directional surface velocity are plotted in Figs. 17(a)–17(c). In Fig. 17(a), the Lamb wave couples to the bottom side of horn from the aluminum plate and then gradually focuses in the horn, demonstrating that this horn geometry can amplify the signal. In Figs. 17(b) and 17(c), when the wave enters to the channel the wave energy focuses. The measured z-directional surface velocity at different times are plotted in Figs. 17(d)–17(f). The metal ultrasonic horn has a strong out-of-plane displacement, meaning that the in-plane S0 mode is also coupled to an out of plane vibration in the horn. Interestingly, the plane wave motion seen in Fig. 17(d) eventually transforms into a torsional rotation, as clearly seen in Fig. 17(f).
To further understand this vibration, we performed modal analysis of the horn using the finite element method (ansys). The horn was meshed as a single layer of with 0.25 × 0.25 mm2 brick elements and the bond area to the plate was set with fixed boundary conditions. The horn of shape B.2 was calculated to have 28 natural frequencies in the range of 280–350 kHz. The modes of vibration for at these frequencies were of two different types of motion. Figures 18(a) and 18(b) plot these two representative cases at 297 kHz and 302 kHz, respectively. The mode at 302 kHz (Fig. 18(b)) is a longitudinal mode, close to that observed in the LDV measurements of Figs. 17(d) and 17(e). The mode at 297 kHz (Fig. 18(a)) is a torsional mode, close to that of Fig. 17(f). Therefore, while the modes are too closely spaced in frequency to know exactly which one is excited experimentally, the out-of-plane displacements excited in the metal horns are clearly natural vibration modes of the horn.
This paper demonstrates that ultrasonic horns can be used to amplify the coupling of Lamb waves in a remotely bonded optical fiber for detection by a FBG sensor. A signal amplification of 100% was demonstrated for one of the metallic horn geometries tested. As the signal amplitude is often a serious limitation for the use of FBG sensors to detect Lamb waves, this amplification is a significant benefit.
However, the use of the ultrasonic horn as an intermediate step between the thin-walled structure and the optical fiber also introduced additional signal due to resonant vibration of the horn at the same frequency as the Lamb wave. For some geometries, this vibration signal partially overlapped the signal to be measured. For many structural health applications, it would be difficult to separate these two signals for analysis of the Lamb wave signal itself.
Future work will investigate alternate methods to amplify the signal while reducing distortion of the waveform. For example, this paper only considered focusing using a step-down and exponential-decay channel design. It is expected that further improvements would be seen by optimizing the profile of the horn. The role of the horn thickness is also a complex one that deserves further investigation.
The authors thank the Office of Naval Research (ONR) (Nos. N00014-18-1-2515 and N00014-17-1-2764) for financial support of this research.
Conflict of Interest
There are no conflicts of interest.