A finite element in elliptic coordinates with application to membrane vibration

A nine-node Lagrangian finite element is derived and implemented in elliptic coordinates. The element is used to formulate an analysis for the free vibration of an elliptical membrane. Frequencies and mode shapes are computed for vibration of both solid and annular elliptic membranes. The annular membrane is defined as a conformal ellipse. Both free and fixed interior boundary conditions are analyzed. Results for frequencies and mode shapes are presented in tabular and graphic format, respectively.