Ultrasonic transmission measurements

If the distortion of the interface by the higher harmonics generated can be neglected as a higher-order effect, the interface vibration is sinusoidal with the excitation frequency. Its displacement amphtude ao is determined by the stress and displacement continuity of the waves of fundamental frequency at the interface. If the transmission of the fundamental frequency shows no hysteresis relative to the interface vibration, we get the result ao=fiBi/k, fiBi = 2 /fi] — e. Here k=colVi is the wavenumber and Vl is the compressional sound velocity in the aluminum plates [10]. The strain amphtude in the interface is the ratio of Oq to the thickness of the interface, i.e., the interface strain amphtude is directly proportional to bi. 

4 show the cahbrated measure of the interface strain vibration bi and the strain amphtudes of the transmitted waves of fundamental frequency and its second and third harmonic i, 2, and 3 as a function of the incident strain amphtude i. The sohd hues represent a hnear fit of Ebi and 1, a quadratic fit of 2, and a cubic fit of 3 of the first 12 measuring points up to a strain level 1.3x10. The strain amphtudes of the first six measured data points of the third harmonic were below the noise level. The experimentally observed power laws for 1, 2, and 3 render it possible to relate them to an expansion of the stress-strain curve which displays no hysteresis [9]. In this case 

With further increases of the input strain beyond 1.3x10, the interface changes its dynamic behavior because the strain amplitude of the interface vibration is no longer linear with the excitation and the transmitted harmonics change their relative phases. Furthermore their amplitudes no longer follow a power series expansion. We relate this behavior to a hysteresis and increasing viscoelasticity in the interface. The evaluation of the transmitted waves to obtain interface restoring forces has to take the phases explicitly into account The in- 

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Thompson, R. B., Fiedler, C. J., and Buck, O. (1984). Inference of fatigue crack closure stresses from ultrasonic transmission measurements. In Nondestructive methods for materials property determination (ed. C. O. Ruud and R. B. Thompson), pp. 161-70. Plenum Press, New York. [278]... 

Acoustic and elastic properties are directly concerned with seismic wave propagation in marine sediments. They encompass P- and S-wave velocity and attenuation and elastic moduli of the sediment frame and wet sediment. The most important parameter which controls size and resolution of sedimentary structures by seismic studies is the frequency content of the source signal. If the dominant frequency and bandwidth are high, fine-scale structures associated with pore space and grain size distribution affect the elastic wave propagation. This is subject of ultrasonic transmission measurements on sediment cores (Sects. 2.4 and 2.5). At lower frequencies larger scale features like interfaces with different physical properties above and below and bed-forms like mud waves, erosion zones and ehatmel levee systems are the dominant structures imaged... 

I 25 Calibration and Evaluation of Nonlinear Ultrasonic Transmission Measurements... 

Fig. 25.2 Ultrasonic transmission measurement results for a sample of two aluminum plates 4 mm thick bonded together by an adhesive epoxy layer of 30 p,m thickness showing the transmitted strain amplitude s- of the fundamental frequency versus the input strain amplitude and the linear fit of the first 12 measuring points.

Before the tensile test the samples were investigated by ultrasonic transmission measurements as described in Section 25.2. The peak power of the RF-car-rier pulse (again 10-30 cycles, center frequency 2.25 MHz) was swept from 0 up to 3.6 kW and back to zero. The transmitted ultrasonic signal was detected by a broadband receiver probe, recorded, and Fourier-transformed. The dependence of the resulting amplitude and phase spectra on the transmitting pulse power was recorded. Figs. 25.11 and 25.12 show the results obtained for two of the specimens, one with a weak and one with a strong bond of 5.5 and... 

After the ultrasonic measurements the specimens were loaded until fracture to obtain the tensile strength. During the loading procedure nonlinear ultrasonic transmission measurements with an excitation peak power of 1.86 kW were carried out Figs. 25.13 and 25.14 show the results. The amplitudes of the transmitted waves of fundamental frequency (Fig. 25.13) and of the second and the third harmonic (Fig. 25.14) are plotted in arbitrary units as recorded by the receiver probe. The horizontal axis represents the number of measuring points... 

Fig. 25.14 Ultrasonic transmission measurement results (excitation RF peak power 1.85 kW) carried out on samples of two aluminum plates 5 mm thick bonded together by an adhesive epoxy layer of 30-50 pm thickness during quasi-static tension loading (displacement rate 0.5 pm s ) until fracture. The amplitudes of the second and the third...

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