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Green's function for vibration problems of an elliptical membrane

Kukla S.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2011

Vol. 10, nr 2

129-134

The aim of the paper is to derive the Green's function of the Helmholtz operator in an elliptical region. The function is found in the form of a double series of Mathieu functions, which are obtained as a solution to the associated boundary problem. The Dirichlet condition on the boundary ellipse is assumed. The eigenvalues are the roots of characteristic equations, which are derived from the boundary condition. To construct Green's function depending on time, the orthogonality condition of the eigenfunctions in the elliptical region was used.