 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| A.A. Gavrikov, "Solution of Eigenvalue Problems for Linear Hamiltonian Systems with a Nonlinear Dependence on the Spectral Parameter," Mech. Solids. 53 (S2), 118-132 (2018) |
| Year |
2018 |
Volume |
53 |
Number |
S2 |
Pages |
118-132 |
| DOI |
10.3103/S0025654418050059 |
| Title |
Solution of Eigenvalue Problems for Linear Hamiltonian Systems with a Nonlinear Dependence on the Spectral Parameter |
| Author(s) |
A.A. Gavrikov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526 Russia, gavrikov@ipmnet.ru) |
| Abstract |
A method for solving self-adjoint eigenproblems for linear Hamiltonian systems with equation, coefficient, 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 nonhomogeneous rods with a density defect, using the Euler–Bernoulli, Rayleigh, and Timoshenko models. |
| Keywords |
Sturm–Liouville problem, linear Hamiltonian system, boundary value problem, eigenvalues, eigenfunctions, spectral correction |
| Received |
19 December 2017 |
| Link to Fulltext |
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