Eigenoscillations of the junction of an elastic body and thin rods

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Resumo

We study behaviour of eigenfrequencies of an anisotropic and homogeneous body with several thin cylindrical elastic rods whose exterior ends are clamped. We prove that, as rods thin, in the low-frequency range limits of normalized eigenvalues of the singularly perturbed elasticity problem imply eigenvalues of the family of systems of ordinary differential equations on rod’s axes with the Dirichlet and the Steklov boundary conditions at the outer and inner endpoints respectively while the systems are combined into a joint spectral problem by these the Steklov conditions. For an isotropic junction the limiting problem decouples into the Dirichlet problem for fourth order differential operators and the algebraic problem for a symmetric positive matrix of a size dependent on the number of clamped rods.

Sobre autores

S. Nazarov

Institute of Problems of Mechanical Science RAS

Autor responsável pela correspondência
Email: srgnazarov@yahoo.co.uk
St. Petersburg, Russia

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