## 3 Experimental Procedures  
Lamb-wave attenuation tests followed procedures similar to those described previously [48]. For generating symmetric mode waves, an ultrasonic transducer (Olympus V101, 0.5 MHz, 25 mm diameter, Olympus NDT, Waltham, MA, USA; NDT Systems C-16, 2.25 MHz, 13 mm diameter, NDT Systems, Huntington Beach, CA, USA; FC500, 2.25 MHz, 19 mm diameter, AC375L, 12.7 mm diameter, Acoustic Emission Technology Corp., Sacramento, CA, USA) was mounted to an edge of a sample plate. For asymmetric mode waves, two types were used. One was an Olympus V103 (1 MHz, 12.7 mm diameter, Olympus NDT), and the other was an NDT Systems C16. Olympus V221, 10 MHz, 6.4 mm diameter, was also used for a comparison. The ultrasonic transducer was mounted to an edge of a sample plate using a 6.4-mm thick aluminum hex rod, providing an incident angle of 60\({}^{\circ}\). This incident angle was selected for obtaining repeatable and robust transducer attachment, as the sample plate needs to be turned over for two-sided detection. This process affects the sensor position accuracy, which is estimated to be better than \(\pm\)1 mm. The transducer was attached to a sample plate using a mechanical jig or with a cyanoacrylate adhesive. This experimental set-up is shown in Figure 2a. The V103 transmitter was attached to a PVC plate edge with two U-shaped jigs (see insert photograph for an enlarged view). The KRN receiver was positioned vertically using a large U-shaped holder, which was held with brass plates. The total force on the sensor tip was 10.5 N. Another method for asymmetric wave generation used a point-contact transmitter (KRNBB-PCP transducer with 1-mm diameter active area, KRS Services, Richland, WA, USA), mounted vertically on a plate. Contact location was either in the middle of a large plate or within 5 mm from an edge. This was also used with edge mounting. These transmitters were usually driven by high-voltage pulses (280-320 V) or by low-voltage (\(\pm\)20 V) pulses from a waveform generator with an amplifier. Single sinewave and Gaussian pulse shapes were used depending on the degree of attenuation. These low-voltage pulses were tried when a certain frequency range was targeted, but some tests resulted in unsatisfactory outcomes due to weak signals. Longer sinewave excitation was used on a large Al plate, as will be subsequently described. The transmitting sensitivities of V101 and NDT C16 are shown in Figure 2b [49]. The unit is in dB in reference to 1 nm/V. The high-voltage pulse spectrum is also plotted. The sum of the sensor and pulse spectra yielded the displacement output, which reached a peak of 10 to 20 nm with a risetime of less than 0.2 us and decay time of about 1 us. These spectra showed that V101 was suitable for frequencies below 500 kHz, whereas NDT C16 produced high-frequency output. When a transmitter was attached to a plate through a hex rod for asymmetric wave generation, the hex rod changed its output. The use of the hex rod provided an efficient reflection path of the initial pulse with 2-us time delay, enhancing the signal output below 400 kHz. Relative frequency spectra of V103 and NDT C16 outputs with the hex rod are shown in Figure 2c. The two spectra are similar to each other, with a dip at 271 or 276 kHz, suggesting strong effects of the hex rod. These dips were absent without the hex rod. As a transmitter, these can be considered equivalent. Lamb-wave vibration developed following wave propagation of at least 100 mm, but usually a travel distance of 125 or 150 mm was needed for fuller development of Lamb modes. This is reflected in the increase of peak amplitude. In most of the tests, the wave propagation distance ranged from 150 to 400 mm in 50-mm steps, or 125 to 300 mm in 25-mm steps. The upper limit of the propagation distance was imposed by the arrival of reflected waves. In some tests, signal amplitude started to increase for unknown reasons at larger distances before any reflections could arrive. Such data were discarded.