Normalized influence of the decay length parameter

Again with the normalized coordinate of Eq. (9.3), the lengthwise displacement m( ) can be obtained by integration of the associated differential equa- 

To complete the anal3dical solution for the simplified case outlined in Remark 9.1, the remaining four equilibrium equations for shear and bending need to be considered. The external line loads contained therein are again provided by Eqs. (9.2), and the internal loads are supplied by the right one of Eqs. (8.4) in conjunction with Eq. (9.1). Further on, the beam shear angles are eliminated by virtue of Eq. (7.29). 

With the above substitutions, the equilibrium relations of Eqs. (8.36b) and (8.36d) as well as Eqs. (8.36c) and (8.36e) may be combined such that each resulting equation contains the axial derivative of one of the sought inclination angles of the cross-section. Integration in consideration of the clamped boundary conditions at one end, then yields 

To obtain a solution without the substantial restrictions dictated by insisting on an analytical approach, the finite element method will be utilized in this section. The diverse approaches to model various aspects of helicopter rotor blades without adaptive capabilities have been reviewed by Hodges [96] and Kunz [117]. 

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Fig. 9.1. Normalized influence of the decay length parameter A on the shape of the non-linear twist components r i(C) and r o( )-...

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