Free Oscillations in an Elliptical Membrane and Mode Shapes

A study of the classical problem of the free oscillations in an elliptic membrane and its related mode shape is presented. The oscillating modes are characterized in an exact solution manner by Mathieu and modified Mathieu functions. Also some important characteristics of theses especial functions that related to oscillations of an elliptic membrane are presented. We emphasize the differences between the circular and elliptic membranes and discuss circular membrane as a special case of elliptical one. We have taken advantage of the modern computational tools to illustrate several vibrations modes patterns which appear in an elliptic membrane in perfect visual manner.

کلیدواژه ها:

Membrane ، Elliptic coordinate ، Mathieu ، Mode shape