Some of the sources useful for modeling acoustic

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Some of the sources useful for modeling acoustic emission sources are discussed in this section. The discussion here is limited to the results; the interested reader is referred to the second edition of the Nondestructive Testing Handbook 114 or to the original references 56,116,117,125-126 for details. Concentrated Force The displacements in an infinite medium caused by a concentrated force acting in an arbitrary direction at the origin and having an arbitrary time history g ( t ) have been solved and are given elsewhere. 116 A plot of the normalized displacements as a function of the normalized time for an impulsive force applied to the body in the 1 direction are shown in Fig. 47. These plots assume that c 2 = c 1 ÷ 2. Figure 47a shows the displacement u 1 at a position directly under the applied force. The first disturbance to arrive is an impulse caused by a compressive wave. Following the impulse is a displacement that increases linearly with time until the transverse wave arrives at t = r · c 2 –1 . At that time, the displacement u 1 decreases to zero and the point experiences no further motion. The solution shows that the displacement u 2 and u 3 are identically zero at this point. 116 The displacement u 1 at a point abreast of the applied force ( x 1 = x 3 = 0) is shown in Fig. 47b. The displacements u 2 and u 3 are also identically zero. Fig. 47b shows no evidence of the impulsive compressive wave but a step increase in the displacement does arrive at t = r · c 1 –1 . However the transverse wave causes an impulsive displacement at t = r · c 2 –1 . The displacements u 1 and u 2 at a point x 1 = x 2 = r and x 3 = 0 are shown in Figs. 47c and 47d. These plots show impulsive waves arriving at t = r · c 1 –1 and t = r · c 2 –1 as well as the linearly increasing displacement between the two waves. If one examines the published solutions, 116 it is found that the impulsive terms decrease as r –1 whereas the terms involving step functions decrease as r –2 . Thus, the linearly changing displacement in the plots of Fig. 47 will be evident when observed near the source. This part decreases rapidly as the observation point moves away from the source. In the far field, only the impulsive terms will be important. If the impulsive force is replaced by a step force acting in the 1 direction, then the solution may be obtained by replacing 93 Fundamentals of Acoustic Emission Testing F IGURE 46. Attenuation due to surface coating 3.2 mm (0.125 in.) on a thick Unified Numbering System A92219 wrought aluminum alloy. 124 Insulation glued on Insulation sprayed on No insulation 0.4 dB·mm –1 (10 dB·in. –1 ) 0.3 dB·mm –1 (8 dB·in. –1 ) Attenuation, dB·mm –1 (dB in. –1 ) 0.76 (3.0) 0.51 (2.0) 0.25 (1.0) 0 0 200 400 600 800 1000 1200 Frequency (kHz)
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the displacements in Fig. 47 with the corresponding velocities: u 1 du 1 ( dt ) –1 ; u 2 du 2 ( dt ) –1 ; and u 3 du 3 ( dt ) –1 . Thus, the plots in Fig. 47 also represent the velocity of a point in the infinite solid subjected to a concentrated force applied at the origin with a step time history.
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  • Fall '19
  • Nondestructive testing, Acoustic Emission, Acoustic Emission Testing

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