Abstract
Eigenvalue problem of ordinary differential equations is considered. We present the definition of the Green functions and reduce some eigenvalue problems to homogeneous Fredholm integral equation with the Green function as kernel. A solution algorithm is suggested by the use of which numerical solutions are given for some vibration problems of circular plates subjected to constant radial in plane load and for the vibratory behavior of beams loaded by an axially force.
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Notes
- 1.
The line of thought in section Eigenvalue problems of ordinary differential equations is based mainly on the book [1] by Lothar Collatz (1910–1990).
- 2.
George Green (1793–1841).
- 3.
Józef Höené-Wroński (1776–1853).
- 4.
Eric Ivar Fredholm (1866–1927).
- 5.
James Mercer (1883–1932).
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Szeidl, G., Kiss, L. (2020). Eigenvalue Problems of Ordinary Differential Equations. In: Mechanical Vibrations. Foundations of Engineering Mechanics. Springer, Cham. https://doi.org/10.1007/978-3-030-45074-8_8
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DOI: https://doi.org/10.1007/978-3-030-45074-8_8
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