Free and random vibrations of shells of revolution with interior supports

A new analytical method based on the wave propagation scheme has been developed for the dynamic analysis of axially symmetric shells with arbitrary boundary conditions and interior supports. In this approach, a shell structure is considered as a waveguide and the response to external excitations is treated as a superposition of wave motions. To segregate the effect of the interior supports, the waveguide is first divided into several sub-waveguides. Upon analyzing these sub-waveguides separately, a composition scheme is adopted to relate them by connecting the wave components according to the continuity conditions for the state variables at each interior supports. Closed form solutions for free and random vibration are derived. The proposed method is presented in a general fashion and numerical examples are given to illustrate the application of the theory.