Vibratory behaviour of shallow conical shells by a global Ritz formulation

The development of a new approach based on the energy principle is presented to study the free vibration of shallow conical shells. In the numerical procedure, a set of orthogonally generated and kinematically oriented shape functions, which satisfies the geometric boundary conditions at the outset, is proposed to overcome the mathematical complexity in expressing the geometry and variable surface curvature of these shells. To establish the accuracy of this method, convergence and comparison studies have been carried out. In this study, the effects of various shell parameters on the fundamental and higher mode frequencies are investigated. It is found that monotonic increases in the fundamental nondimensional frequency parameter occurs when the cone vertex angle or base subtended angle is increased independently for the cantilever conical shell. The fundamental frequency parameter also becomes higher for the fully clamped conical shell with higher panel-length to cone-length (a/s) ratio. A set of first published vibration mode shapes is also presented. © 1994.