AE03.pdf

At asymptotically large source to receiver distances

This preview shows page 15 - 17 out of 17 pages.

At asymptotically large source-to-receiver distances, the time of signal arrival equals the time of source event plus the ratio of distance to V g b ( ω ): (46) where V g b is the group velocity: (47) Group velocity depends on plate material and thickness and on the branch in question and the frequency of interest but not on source type or distance. Time of arrival is different for different branches and frequencies. Thus, at any time t , there are several modes contributing to the waveform, all with different effective amplitudes Q and all with different frequencies. The result is a complex beat pattern. Extracting the modal amplitudes Q from that pattern is difficult because each such mode, having a different frequency, has been affected differently by the transducer sensitivity, the amplifier gain and the source function. Conversely, the waveform in the frequency domain can be understood as an interference pattern between the many branches that have the same frequency but different amplitudes Q and different arrival times. In either domain, the waveform is complex, because there are so many interfering branches at the same point. The best way to analyze these waveforms is in neither the frequency domain nor the time domain but rather by means of a simultaneous time and frequency decomposition. If signal processing can effect this decomposition, the only remaining interferences would be at the occasional places where two branches have the same group velocity and frequency. Much signal processing literature tries to optimize such decompositions. Work has focused on the spectrogram, that is, on the square of the short time fourier transform, and on the wigner transform. The simplest analysis of time versus frequency, the spectrogram, has been found to be adequate. A spectrogram calculated from a theoretical waveform (an evaluation of Eq. 34) is shown in Fig. 4, where amplitudes concentrated along the loci of frequency versus arrival time are evident. Similar spectrograms are V d dk b b g = ω Time of signal arrival Time of source event Distance g = + ( ) V b ω Q k k Q k k b eff stepload ( ) = ( ) ( ) 1 2 ω Q k W h 1 2 2 stepload sign ( ) = ( ) ( ) ρ M v F kdk Q k J kr k t k b b b = × ( ) ( ) [ ] × ( ) [ ] ( ) – cos 0 stepload 0 π ω ω 1 2 1 118 Acoustic Emission Testing F IGURE 4. Spectrogram obtained from a theoretical acoustic emission waveform. Amplitudes are confined to specific loci in the space of time versus frequency. 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 100 200 300 400 500 600 700 800 Frequency (MHz) Time (μs) S0 A0 Legend S0 = asymmetric S wave A0 = symmetric P wave
Image of page 15

Subscribe to view the full document.

shown in this NDT Handbook volume’s chapter on source location. From such spectrograms, the distance to the source can be extracted by comparing the times of arrival of different modes of known group velocity. For example, it is clear that the rayleigh wave arrives around time t R = 325 μs. The S0 mode arrives around t S0 = 60 μs. Thus, distance of the source can be calculated: (48) By analyzing multiple points in such plots, it is possible in principle to obtain highly accurate source distances.
Image of page 16
Image of page 17
  • Fall '19
  • Acoustic Emission

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern