NORMAL-MODE PROPAGATION ON CONICAL SHELLS

This paper presents a theoretical study on waves on elastic shells of conical shape. The shell motions are formulated according to thin shell theory and the technique of multiple scales is used to derive solutions for shells with small vertex angles. Solutions are decomposed into angular harmonics in the circumferencial direction, each mode propagating along the shell axis. In contrast to waves on cylindrical shells, waves on conical shells experience amplitude and phase variations as a result of the changing shell radius. Discussed in detail is the case where waves propagate toward the apex of the shell. In this event, the decreasing radius causes different modes to be cut off at different locations where the waves also show strong dispersive behavior. Also, as a result of the shrinking radius, the wave amplitudes grow, the growth being limited by blowup at cutoff. The locations of cutoff for different modes are identified and the nature of the amplitude singularities at cutoff is examined in detail.