Approximation of Functional-Algebraic Eigenvalue Problems

We propose a new symmetric variational functional-algebraic statement of the eigenvalueproblem in a Hilbert space with a linear dependence on the spectral parameter for a class ofmathematical models of thin-walled structures with an attached oscillator. The existence ofeigenvalues and eigenvectors is established. A new symmetric approximation of the problem ina finite-dimensional subspace with a linear dependence on the spectral parameter is constructed.Error estimates are obtained for the approximate eigenvalues and eigenvectors. The theoreticalresults are illustrated with an example of a structural mechanics problem.