Effects of subtended and vertex angles on the free vibration of open conical shell panels: A conical coordinate approach

The paper presents a computational investigation on the effects of subtende d and vertex angles on the free vibration characteristics of open conical s hell panels. Unlike the conventional approximation using a rectangular or c ylindrical co-ordinate system, this analysis adopts a natural conical co-or dinate system so that any approximation in geometry is eliminated. The stra in and curvature components formulated in this orthogonal conical co-ordina te system have been employed to derive the strain and kinetic energy integr als. The energy functional is minimized in accordance with the Ritz procedu re to arrive at a governing eigenvalue equation. Admissible shape functions comprising sets of two-dimensional orthogonal polynomials and a basic func tion are employed to account for the boundary constraints and to approximat e the three-dimensional displacements of the conical shell. Comparison of n atural frequencies shows excellent agreement with the solutions of finite e lement, finite strip and integral equation methods. The effects of subtende d and vertex angles and other geometric parameters on vibration are investi gated in a comprehensive parametric study. Selected vibration mode shapes a re illustrated to enhance the physical understanding of vibration of such o pen conical shell panels. (C) 1999 Academic Press.