WAVE MOTION AND ENERGY-FLOW IN CYLINDRICAL-SHELLS

The vibrational energy flow that is associated with helical wave motion in a thin cylindrical shell is considered. Initially, a detailed analysis is presented in which the governing differential equations are solved exactly and the energy flows are calculated from the elastic forces in the shell. A more approximate technique is then presented which is based on a well known approximation to the dispersion relation. The latter approach leads to simple closed form expressions for the group velocity and the direction of the energy flow as a function of the helical wave angle. The method also leads to a graphical technique whereby the relationship between the energy flow direction and the helical wave angle may readily be visualized. It is found that the direction of the energy flow can differ significantly from the helical wave angle, and in certain cases a negative group velocity in the circumferential direction may arise. © 1994 Academic Press Limited.