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Differential Eigenvalue Problems with Particular Reference to Rotor Blade Bending

Published online by Cambridge University Press:  07 June 2016

M. Wadsworth  and
E. Wilde
M. Wadsworth
Affiliation:
The University, Salford
E. Wilde
Affiliation:
The University, Salford
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Summary

A differential equation which contains an eigenvalue is considered as a pair of simultaneous differential equations by augmenting the main equation with the equation λ′=0. This ensures the constancy of the eigenvalue λ. The differential eigenvalue problem is thus reduced to a pair of simultaneous non-linear differential equations with two-point boundary conditions. An iterative method for the solution of the two-point boundary value problem is described.

To demonstrate the method, the normal modes and frequencies in flapping of a helicopter rotor blade are calculated. In the case considered the stiffness and mass/(unit length) of the blade have points of discontinuity. The method may also be applied when the blade parameters are given in the form of experimental data.

Information

Type
Research Article
Information
Aeronautical Quarterly , Volume 19 , Issue 2 , May 1968 , pp. 192 - 204
Copyright
Copyright © Royal Aeronautical Society. 1968

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References

1. Fox, L. The numerical solution of two-point boundary problems in ordinary differential equations. Oxford University Press, 1957.Google Scholar
2. Haselgrove, C. B. The solution of non-linear equations and of differential equations with two-point boundary conditions. Computer Journal, Vol. 4, p. 255, 1962.CrossRefGoogle Scholar
3. Fox, L. Numerical solution of ordinary and partial differential equations. Pergamon, 1962.Google Scholar
4. Osborne, M. R. A note on finite difference methods for solving the eigenvalue problems of second-order differential equations. Mathematics of Computation, Vol. 16, p. 338, 1962.Google Scholar
5. Osborne, M. R. and Michelson, S. The numerical solution of eigenvalue problems in which the eigenvalue parameters appear non-linearly, with an application to differential equations. Computer Journal, Vol. 7, p. 66, 1964.Google Scholar
6. Osborne, M. R. A new method for the solution of eigenvalue problems. Computer Journal, Vol. 7, p. 228, 1964.Google Scholar