On the Flexural Motions of Plates at the Cut-Off Frequency

[+] Author and Article Information
C. C. Chao

Department of Aeronautics and Astronautics, Stanford University, Stanford, Calif.

Yih-Hsing Pao

Department of Engineering Mechanics, Cornell University, Ithaca, N. Y.

J. Appl. Mech 31(1), 22-24 (Mar 01, 1964) (3 pages) doi:10.1115/1.3629564 History: Received January 04, 1963; Online September 15, 2011


Mindlin’s equations of plates in flexural motion degenerate at the cut-off frequency of the lowest thickness shear mode. In this paper it is shown that, by introducing two displacement potentials, the original equations of motion can be transformed into one wave equation and one biharmonic equation. Based on these two equations, the reflection of a plane flexural wave at the free edge of a plate at this cut-off frequency is reexamined.

Copyright © 1964 by ASME
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