A SECTOR FOURIER p -ELEMENT APPLIED TO FREE VIBRATION ANALYSIS OF SECTORIAL PLATES

A sector Fourier p -element is presented and applied to free vibration analysis of sectorial plates. An important feature of this element is that it can describe the geometry of a sectorial plate exactly and is therefore suitable for this type of plate. The element is formulated in terms of a fixed number of cubic polynomial shape functions plus a variable number of trigonometric hierarchical shape functions. The cubic polynomial shape functions are used to describe the elementʹs nodal d.o.f. and the trigonometric hierarchical shape functions are used to give additional freedom to the edges and the interior of the element. Results are obtained for a number of sectorial plates with various boundary conditions and comparisons are made with exact and 16-d.o.f. sector finite element solutions. The results show that the solutions converge very quickly from above to the exact values as the number of trigonometric terms is increased and highly accurate values are obtained with the use of very few terms. The results also show that the sector Fourier p -element gives a much higher accuracy than the 16-d.o.f. sector finite element with far fewer system d.o.f.