Calculation of eigenvalues of homogeneous problems of generalized eigenoscillation for the body of revolution using the finite element method

The generalized method of eigenoscillations generates the nonselfjoint homogeneous boundary value problems containing a spectral parameter in the boundary conditions. One of the ways for solving such problems is the variational technique. For the body of revolution such a technique is developed by Voitovich (1980) and described by Agranovich and Katsenelenbaum, Sivov, and Voitovich (see WILEY-VCH, Verlag, Berlin, 1999). Here the finite element method is used with a stationary functional of the method, which is applied to an investigation of resonators with impedance walls. The problem for the axially symmetrical harmonics of the closed resonator is considered and the main features of the method are described. The method is illustrated on a test problem for a resonator in the form of a finite circle cylinder with impedance side surfaces and metallic borders.