Transient Wave Propagation in Elastic Plates with Cylindrical Boundaries, Studied with the Aid of Multi-integral Transforms

Author: Scott, Richard Anthony

Year: 1964

Degree: Dissertation (Ph.D.)

Advisor: Miklowitz, Julius

Committee Member: Unknown, Unknown

Option: Engineering

DOI: 10.7907/G7HA-F836

Abstract

Some mixed time dependent boundary value problems for isotropic elastic plates with circular cylindrical boundaries are studied using the linear equations of elasticity. A multi-integral transform approach is employed, necessitating the introduction of extended Hankel transforms, and formal solutions are obtained with the aid of residue theory. Some properties of the Rayleigh-Lamb frequency equation, pertinent to the inversion processes, are derived. The problem of a free infinite plate with a circular cylindrical cavity subjected to a step normal displacement is studied in detail and numerical information for the far-field, showing the effect of the cavity radius on the displacements, is obtained using stationary phase techniques.

The generation of transient elastic waves in free isotropic infinite elastic plates by time dependent body forces is also treated and the results for a radial body force, with step time-dependence, are compared with the corresponding platecavity results. Good agreement between the two is found in the far-field.

Similar problems for a free, transversely isotropic, semi-infinite plate (slab) are also studied and some numerical information for the farfield is obtained using the head of the pulse method. Stationary phase solutions for an isotropic slab subjected to a step edge displacement are obtained and compared with the corresponding plate-cavity results. It is found that at a fixed station the plate cavity solutions approach those for the slab, as the cavity radius goes to zero. A comparison between the head of the pulse and stationary pulse results for the isotropic slab is also made and some discrepancies between the two are found.

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