Representations for the high-frequency response of asuddenly loaded infinite plate are obtained from the modalform of the exact solution. The method of approach is presentedby treating a linearly elastic, homogeneous, isotropicplate subjected to a normal impulsive line load onone face.
An investigation of the branches of the governingRayleigh-Lamb frequency equation is given. These branchesare closely related to the modes of propagation, the sumof which is the modal solution. The relationship betweenthe high-frequency portions of the underlying frequencyspectra and the high-frequency response is brought out.
Series representations for the branches are used tofacilitate a summation over the branch (or mode) numbers.This results in convenient high-frequency representations,which exhibit all of the expected singular wave fronts inthe plate.
The method appears to be applicable to a broaderclass of problems than other methods which have been usedfor the high-frequency response of a plate.
