Vibration and stability analysis of polar orthotropic uniform discs subjected to peripheral hydrostatic loading

Abstract

An analysis based upon the annular finite element method is carried out of the transverse vibration and stability of uniform polar orthotropic discs subjected to peripheral hydrostatic loading. Both the axi- and anti-symmetrical modes are considered for both clamped and simply supported at the outer peripheral radius. By separation of the flexural and geometric (membrane) components, the effect on both with respect to the degree of orthotropy is plotted and subsequently both components can be easily combined to produce the natural frequencies of the loaded disc. A simple relationship is derived to determine whether the lowest critical buckling mode is that containing zero nodal diameters and circles or some higher mode.