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Attenuation by energy loss mechanisms in all of the

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Attenuation by Energy Loss Mechanisms In all of the mechanisms discussed above, the total mechanical energy of all of the waves (original and reflected, scattered, diffracted, dispersed) remains constant if the solid is an elastic medium. However, wave propagation in real media is usually not conservative. That is, mechanical energy associated with motion (kinetic energy) and the elastic deformation (potential energy) is not conserved. Mechanical energy can be converted to thermal energy by thermoelastic coupling. It can also be lost through (1) plastic deformation if the medium is stressed past its elastic limit, (2) creating new surfaces if a crack is extended, or (3) interactions with dislocation motion. Losses can be associated with (1) viscoelastic material behavior prevalent in plastics, (2) friction between surfaces that slip and (3) incompletely bonded inclusions or fibers in composite materials. Losses can be caused by magnetoelastic interactions, by interactions with conduction electrons in metals or by paramagnetic electron and nuclear spin systems. 122 Regardless of the particular mechanism causing the loss of mechanical energy, the amplitude of a wave will decrease as the wave propagates through the medium. If the medium and the loss mechanism are homogeneous, then the losses occur uniformly as the wave travels through the 90 Acoustic Emission Testing F IGURE 42. Attenuation caused by dispersion for a wave in an aluminum beam. Displacement (ratio) 1 0 –1 Time (relative scale)
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medium. If the wave is a simple harmonic function, the particle displacement can be described as below: (107) where A is the length (meter) of the wave at x = 0, k is the wave number (equal to ω · c –1 ), t is time (second), x is the coordinate (meter) measured in the direction of wave travel and α is the loss coefficient, which must be a positive number. The coefficient α (which is usually dependent on the frequency ω ) has units as reciprocals of length but the units are often expressed as nepers per length. A neper is a natural logarithmic unit corresponding to a reduction in amplitude of e –1 times the initial value. The attenuation coefficient can also be expressed in terms of decibels per length as follows: (108) Equation 107 may also be written as follows: (109) where k* = k + j α . (110) The complex wave number k* can be used to represent a wave propagating through a lossy medium. Because the wave number is inversely proportional to the square root of the elastic modulus ( k E –0.5 ), then the lossy medium may also be modeled by replacing the elastic modulus E with a complex modulus E *: The terms α and η are related by the following expression: (111) The complex wave number approach, as exemplified in Eq. 109, has been used to study the effects of losses encountered in the propagation of waves generated by step forces in plastics. 123 The analytical technique compared well to the experimental results.
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  • Fall '19
  • Nondestructive testing, Acoustic Emission, Acoustic Emission Testing

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