Extensional Vibrations and Waves in a Circular Disk and a Semi-Infinite Plate

[+] Author and Article Information
D. C. Gazis

Research Laboratories, General Motors Corporation, Warren, Mich.

R. D. Mindlin

Columbia University, New York, N. Y.

J. Appl. Mech 27(3), 541-547 (Sep 01, 1960) (7 pages) doi:10.1115/1.3644037 History: Received April 30, 1959; Online September 16, 2011


A set of approximate equations of extensional motion of elastic plates is solved for the case of axially symmetric vibrations of a circular disk and the results are compared with experiments performed by E. A. G. Shaw. Special attention is given to a new mode of vibration, discovered by Shaw, in which the deformation is predominantly at the edge of the disk. It is shown how this mode arises from the complex conjugate roots of the frequency equation of an infinite plate. The properties of the edge-mode are examined in detail in a study of the reflection of straight-crested extensional waves at the edge of a semi-infinite plate.

Copyright © 1960 by ASME
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