The problem treated is that of an infinite free plate with a circular cylindrical cavity subjected to a step normal displacement. The linear equations of elasticity are employed and the formal solution is obtained using a multi-integral transform technique, necessitating the introduction of extended Hankel transforms, and residue theory. Some properties of the Rayleigh-Lamb frequency equation, pertinent to the inversion process, are derived. Numerical information for the far field, showing the effect of the hole radius on the displacements, is obtained using the stationary phase method and, in the case of the radial displacement, the solution is compared with the corresponding slab solution. The results show that at a given station the plate-cavity solution approaches that for the slab, as the hole radius decreases. The head of the pulse and stationary-phase approximations to the corresponding horizontal slab displacement are also compared, and some discrepancies between the two are found in the vicinity of the wave-front arrival time.
Transient Compressional Waves in an Infinite Elastic Plate With a Circular Cylindrical Cavity
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Scott, R. A., and Miklowitz, J. (December 1, 1964). "Transient Compressional Waves in an Infinite Elastic Plate With a Circular Cylindrical Cavity." ASME. J. Appl. Mech. December 1964; 31(4): 627–634. https://doi.org/10.1115/1.3629724
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