Out-of-plane Free Vibrations of Circular Strips With Variable Breadth

This paper deals with the out-of-plane free vibrations of circular strips with linearly varying breadth. In deriving the differential equations for such strips, the effects of the rotatory and torsional inertias and shear deformation are considered. The differential equations are numerically solved to calculate the natural frequencies and mode shapes. In the numerical examples, three end constraints, i.e. clamped–clamped, clamped-hinged and hinged–hinged ends, are considered. The five lowest frequency parameters and mode shapes are presented. The effects of the rotatory and torsional inertias, and shear parameter on the natural frequencies are evaluated. Parametric studies are carried out for the influence of following parameters of the strip on the natural frequencies: subtended angle, section ratio, thickness ratio, and slenderness ratio. Also presented are the experimental validations of the seven lowest predicted natural frequencies. The natural frequencies obtained by this study agree well with those by the finite element method for both the flexural and torsional modes.