Solution for an infinite space because of the actual

This preview shows page 71 - 72 out of 82 pages.

solution for an infinite space because of the actual force and the force caused by an image force. The difference between the exact solution and this approximate approach is small. This technique was used to study the effect of attenuation and dispersion on acoustic emission waves. 123 Computer programs for Lamb’s problem with a surface source and with a buried source are available in the literature and have been used to simulate the acoustic emission waves generated by cracks and slip. Numerical solutions (displacements, velocities and accelerations) have been published 131 for Lamb’s problem with arbitrary Poisson’s ratio and with a vertical time dependent point force having time histories of the step and delta functions as well as a finite duration pulse equal to cos 2 ( π t · T –1 ) for 0.5 T t 0.5 T . An important conclusion was that “... a 10 × reduction in pulse width at a fixed pulse height yielded an increase in P and rayleigh wave amplitudes by factors of 1, 10 and 100 for displacement, velocity and strain, and acceleration, respectively.” 131 This points to the fact that the response of the typical acoustic emission transducer (which responds more to velocity or acceleration than to displacement) depends strongly on the rise time or the duration of the source. Sources Acting in or on Plates A more practical representation of an actual structure is the infinite plate, a solid bounded by two parallel planes. The analytical problem is much more complicated than the solutions for the half space or the infinite space because of the multiple reflections that are unavoidable in realistic situations. Consider the plate and source shown in Fig. 49. Even if the source is a center of compression and radiates only dilatational waves, as each dilatational wave reaches the free surface, it is reflected as both a dilatational (or longitudinal, if curvature is neglected) and an equivoluminal (or transverse) wave. Each of these two components in turn intersects the opposite surface and generates two more waves. It does not take very long to generate a very large number of reflected waves echoing back and forth between the two surfaces. The lower part of Fig. 49 shows what might be expected at a receiver several plate thicknesses from an impulsive center of a compression source. The magnitude of the individual components are a function of the path the ray takes to reach the source and can be calculated in ideal cases as noted below. The waveform at the receiver is changed considerably from the original; the task of extracting information about the source wave (given only the received wave) is considerably complicated by the presence of the multiple reflections. Early research in the effect of structure geometry on the received signal concentrated on simple bar or beam theories 77,132 and attempted to relate spectral content of the received signals to the source time history. Later, plate 96 Acoustic Emission Testing F IGURE 49. Wave propagation in a plate: (a) with rays emanating from source and striking receiver; (b) with the sum of direct and reflected waves seen by receiver.
Image of page 71

Subscribe to view the full document.

Image of page 72
  • Fall '19
  • Nondestructive testing, Acoustic Emission, Acoustic Emission Testing

{[ 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