The formation of energy pass bands from periodically spaced point masses on a ribbed cylindrical shell

Abstract

An infinite cylindrical shell has bending energy that is able to propagate down the shell at all frequencies with little attenuation other than from material damping and the surrounding medium. In contrast, making the shell finite causes bending resonances to occur only at discrete frequencies. The addition of periodically spaced circumferential stiffeners causes the bending wave dispersion curves to be seen at additional axial modes, which is referred to as Brillouin folding. The stiffeners also cause energy stop bands to occur when the load is a single Fourier mode. In this presentation, periodically spaced point masses in the circumferential direction are added to a ribbed finite cylindrical shell and analyzed via the finite element method. It is seen that Brillouin folding occurs circumferentially. Also, energy pass bands are created in a certain pattern. Analysis of the axisymmetric version of this shell combined with information on the type of aperiodicity yields a prediction of the energy pass band behavior. This provides a qualitative approach toward understanding the motion of nonaxisymmetric shell structures. [Work supported by ONR.]