Solution of Eigenvalue Problems for Linear Hamiltonian Systems with a Nonlinear Dependence on the Spectral Parameterстатья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 11 апреля 2019 г.
Аннотация:A method to solve self-adjoint boundary value problems for the eigenvalues and eigenfunc-
tions of linear Hamiltonian systems with equations, coefficients, and boundary conditions nonlinearly
dependent on the spectral parameter is presented. The suggested approach is based on the iterative
Newton procedure with spectral correction. The fast convergence of the method is demonstrated, and
two-sided estimates of the eigenvalue sought are obtained. The results of the test application of the
outlined algorithm are presented for the problem of the transverse natural oscillations of nonhomoge-
neous rods with a density defect, using the Euler–Bernoulli, Rayleigh, and Timoshenko models.