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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.

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

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