ABSTRACT
The dynamic influence function of a shell describes the response of each point of the shell to a unit impulse applied at some other point. For simple structures, such as transversely vibrating beams, the influence function may be unidirectional. That is, the unit impulse is applied in the transverse direction and the response is in the transverse direction. Also for plates, where the in-plane response is uncoupled from the transverse response for small oscillations, a unidirectional dynamic influence function is applicable to the transverse vibration problem. However, in shell dynamics, coupling between the transverse response and the response in planes tangential to the shell surface has to be considered. Thus a unit impulse applied transversely at a point produces a response in two principal tangential directions as well as in the transverse direction at any point of the shell. The same is true for unit impulses applied tangentially to the shell in the two principal directions. Thus, to be complete, the dynamic influence function for the general shell case has to have nine components. It can be viewed as a field of response vectors due to unit impulse vectors applied at each point of the shell.
