Bifurcation of Eigenvalues of Nonselfadjoint Differential Operators in Nonconservative Stability Problems

Kirillov, Oleg and Seyranian, Alexander (2002) Bifurcation of Eigenvalues of Nonselfadjoint Differential Operators in Nonconservative Stability Problems. In: 21st International Conference on Offshore Mechanics and Arctic Engineering, Volume 3. American Society of Mechanical Engineers, New York, pp. 31-37. ISBN 0-7918-3613-4

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Abstract

In the present paper eigenvalue problems for non-selfadjoint linear differential operators smoothly dependent on a vector of real parameters are considered. Bifurcation of eigenvalues along smooth curves in the parameter space is studied. The case of multipleeigen value with Keldysh chain of arbitrary length is considered. Explicit expressions describing bifurcation of eigen-values are found. The obtained formulae use eigenfunctions and associated functions of the adjoint eigenvalue problems as well as the derivatives of the differential operator taken at the initial point of the parameter space. These results are important for the stability theory, sensitivity analysis and structural optimization. As a mechanical application the extended Beck’s problem of stability of an elastic column under action of potential force and tangential follower force is considered and discussed in detail.

Item Type:	Book Section
Uncontrolled Keywords:	Stability, Bifurcation, Eigenvalues
Subjects:	H300 Mechanical Engineering
Department:	Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User:	Oleg Kirillov
Date Deposited:	06 Feb 2017 11:24
Last Modified:	12 Oct 2019 22:26
URI:	http://nrl.northumbria.ac.uk/id/eprint/29495

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