A sector elliptic p-element applied to membrane vibrations

A new sector p-element is derived and implemented in elliptic coordinates. The element is applied to the free vibration analysis of annular elliptic membranes. The internal shape functions are derived from the shifted Legendre orthogonal polynomials. The stiffness and mass matrices may be integrated exactly using symbolic computing. One-quarter of the annular elliptic membrane is modeled as one element. The solution of the whole membrane is obtained from the solution of one-quarter with appropriate boundary conditions along the symmetry lines. The accuracy of the solution is improved simply by increasing the polynomial degree. Values for the natural frequencies of annular elliptic membranes are obtained and compared with published results. Comparisons show good agreement. New highly accurate values for the natural frequencies of annular elliptic membranes with different aspect ratios and boundary conditions are presented. A case of a sector annular elliptic membrane is also shown.