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

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.