Fundamentals of Ultrasonic Nondestructive Evaluation by Lester W. Schmerr

Author:Lester W. Schmerr
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(9.40)

with (ρ, c p ) being the density and compressional wave speed of the solid in contact with the receiving transducer. Again, such a definition is useful only if it is possible to actually model this transfer function. This is possible since is proportional to the driving pressure, p 0, so we can rewrite the transfer function as

(9.41)

The non-dimensional wave field in the integral of Eq. (9.41) can in principle be calculated since it does not depend on knowing the actual pressure on the face of the transmitting transducer. This integral can be made even easier if we note that for a plane P-wave incident on a free surface at normal incidence, the total velocity at the free surface is just twice the velocity of the incident wave field, v inc (x, ω), calculated with the free surface absent, so if we make this assumption in the calculation of our transfer function we have

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