Effects of initial twist and thickness variation on the vibration behaviour of shallow conical shells

Abstract

A thorough computational investigation is presented into the effects of initial twist and thickness variation on the vibratory characteristics of cantilevered pretwisted thin shallow conical shells with generally varying thickness. An energy approach with the Ritz minimization procedure is employed to arrive at a governing eigenvalue equation. The admissible pb-2shape functions which comprise sets of mathematically complete two-dimensional orthogonal polynomials and a basic function are introduced to account for the boundary constraints and to approximate the three-dimensional displacements of the conical shell. The effects of angle of twist, thickness variation and geometric parameters on the vibration response are presented in a comprehensive parametric study which provides useful new design data. Selected vibration mode shapes are also included to enhance the existing literature. It is found that an increase in the angle of twist does not necessarily increase the torsional stiffness. On the contrary, the fundamental frequencies is reduced in the present analysis. It is also observed that non-zero angle of twist and non-uniform chordwise thickness variation cause the absent of vibration mode symmetry.