A sector Fourier p-element for free vibration analysis of sectorial membranes

A sector Fourier p-element for free vibration analysis of sectorial membranes is presented. A major feature of this element is that it can describe the geometry of a sectorial membrane exactly and is therefore suitable to use for this type of membrane. The element transverse displacement is described by a fixed number of linear polynomial shape functions plus a variable number of trigonometric shape functions. The polynomial shape functions are used to describe the element’s nodal displacements and the trigonometric shape functions are used to provide additional freedom to the edges and the interior of the element. Different numbers of trigonometric terms are allowed in radial and circumferential directions. Results are obtained for a number of simply supported sectorial membranes and comparisons are made with exact and sector linear finite element solutions. The results clearly show that the solutions converge rapidly from above to the exact values as the number of trigonometric terms is increased and highly accurate values are obtained with the use of a very few terms. The results also show that the sector Fourier p-element produces a much higher accuracy than the sector linear finite element with fewer system degrees of freedom.