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Bifurcation of Eigenvalues of Nonselfadjoint Differential Operators in Nonconservative Stability Problems

[+] Author Affiliations
Oleg N. Kirillov, Alexander P. Seyranian

M. V. Lomonosov Moscow State University, Moscow, Russia

Paper No. OMAE2002-28076, pp. 31-37; 7 pages
  • ASME 2002 21st International Conference on Offshore Mechanics and Arctic Engineering
  • 21st International Conference on Offshore Mechanics and Arctic Engineering, Volume 3
  • Oslo, Norway, June 23–28, 2002
  • Conference Sponsors: Ocean, Offshore, and Arctic Engineering Division
  • ISBN: 0-7918-3613-4 | eISBN: 0-7918-3599-5
  • Copyright © 2002 by ASME


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.

Copyright © 2002 by ASME



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