Modal Representations for the High-Frequency Response of Elastic Plates

Author: Randles, Philip Wayne

Year: 1969

Degree: Dissertation (Ph.D.)

Advisor: Miklowitz, Julius

Committee Member: Unknown, Unknown

Option: Applied Mechanics; Physics

DOI: 10.7907/F4BM-J980

Abstract

Representations for the high-frequency response of a suddenly loaded infinite plate are obtained from the modal form of the exact solution. The method of approach is presented by treating a linearly elastic, homogeneous, isotropic plate subjected to a normal impulsive line load on one face.

An investigation of the branches of the governing Rayleigh-Lamb frequency equation is given. These branches are closely related to the modes of propagation, the sum of which is the modal solution. The relationship between the high-frequency portions of the underlying frequency spectra and the high-frequency response is brought out.

Series representations for the branches are used to facilitate a summation over the branch (or mode) numbers. This results in convenient high-frequency representations, which exhibit all of the expected singular wave fronts in the plate.

The method appears to be applicable to a broader class of problems than other methods which have been used for the high-frequency response of a plate.

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