Vibrations of Conical Shells

A Rayleigh-Ritz procedure is used to determine the natural frequencies for a certain class of mode shapes of a thin conical shell built in on the edge with the smaller radius and either simply supported free on the other edge. Both bending and extensional energies are included in the analysis. The results show that, for a sufficiently large number of circumferential nodes, the natural frequency predicted by these analyses is very close to the inextensional natural frequency for the same number of circumferential nodes and simply supported at the edge with the smaller radius. The comparison with the inextensional theory predictions is consistent with what has already been found experimentally; i.e., boundary conditions for this type of shell are not as influential on the higher natural frequencies as the lower ones.