Effects of subtended and vertex angles on the vibration characteristics of conical shell panels: a conical coordinate approach

This paper presents a computational investigation on the effects of subtended and vertex angles on the free vibration characteristics of open conical shell panels. Unlike the conventional approximation using a rectangular or cylindrical co-ordinate system, this analysis adopts a natural conical co-ordinate system so that any approximation in geometry is eliminated. The strain and curvature components formulated in this orthogonal conical co-ordinate system have been employed to derive the strain and kinetic energy integrals. The energy functional is minimized in accordance with the Ritz procedure to arrive at a governing eigenvalue equation. Admissible shape functions compromising sets of two-dimensional orthogonal polynomials and a basic function are employed to account for the boundary constraints and to approximate the three-dimensional displacements of the conical shell. Comparison of natural frequency shows excellent agreement with the solution of finite element, finite strip and integral equation methods. The effects of subtended and vertex angles and other geometric parameters on vibration are investigated in a comprehensive parametric study. Selected vibration mode shapes are illustrated to enhance the physical understanding of vibration of such open conical shell panels