Vibration analysis of twisted conical shells with tapered thickness

Considering twisted conical shells with tapered thickness, a numerical method for analyzing free vibration is developed, where an exact strain-displacement relationship of twisted conical shells is derived based on the shell theory, the equation of energy equilibrium for free vibration is formulated by the principle of virtual work, and the governing equation is obtained by the Rayleigh-Ritz procedure. The convergent property is investigated in view of the assumed displacement functions, and the comparison between the present and the available previous results for several typical conical shells is carried out in order to demonstrate the practicability and the accuracy. The effects of the tapered thickness in two directions, the twist angle, the subtended angle and the taper ratio of cross-section on the vibration behavior are discussed through the frequencies and corresponding mode shapes.