Modal Representations for the High-Frequency Response of Elastic Plates

Citation

Randles, Philip Wayne (1969) Modal Representations for the High-Frequency Response of Elastic Plates. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/F4BM-J980. https://resolver.caltech.edu/CaltechTHESIS:06082017-101810031

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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