A theoretical study of waves on a conic shell

This paper reports some theoretical study on waves on an elastic shell of conic shape. The method of multiple scales is used to derive analytical solutions for the shell response to external driving. This response is analyzed in terms of helical waves whose amplitude and phase both vary with traveling distance due to the conic geometry. Of particular interest are waves traveling toward the apex of the shell. For these waves, the wave amplitude increases because of the decreasing shell radius, but this increase in amplitude is limited by the effects of caustics; these waves do not reach the apex. They are turned back at caustics with some phase shift. The effects of the conic geometry on the dispersive properties of the helical waves are discussed. [Work supported by ONR.]