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Applications of a novel curve-fitting technique are presented to efficiently predict the motion of the vortex filament, which is trailed from a rigid body such as wings and rotors. The governing equations of the motion, when a Lagrangian approach with the present curve-fitting method is applied, can be transformed into an easily solvable form of the system of nonlinear ordinary differential equations. The applicability of Bézier curves, B-spline, and Lagrange interpolating polynomials is investigated. Local Lagrange interpolating polynomials with a shift operator are proposed as the best selection for applications, since it provides superior system characteristics with minimum computing time, compared to other methods. In addition, the Gauss quadrature formula with local refinement strategy has been developed for an accurate prediction of the induced velocity computed with the line integration of the Biot–Savart law. Rotary-wing problems including a vortex ring problem are analyzed to show the efficiency, accuracy, and flexibility in the applications of the proposed method.

In this study, shear correction factor for thin-walled composite boxbeam is investigated with considering the anisotropic coupling effects in its laminated walls parallel to the external shear load. We first consider a generally orthotropic laminated beam whose cross section is rectangular. The beam does in-plane shear deformation by the applied shear force, so that there arises the effect of extension-shear coupling which does not arise in the conventionally studied out-of-plane shear deformation. The shear correction factor is defined by the energy considerations with taking into account the coupling effect. Then the procedures are extended to the case of laminated thin-walled boxbeam, where the coupling plays a significant role due to the geometric characteristics of boxbeam. The shear correction factors for the representative boxbeams which are the core structural components of modern composite helicopter rotor blade are presented with the change of their laminate sequences.

The aeroelastic stability of a composite hingeless rotor blade, idealized as a laminated thin-walled box-beam, has been investigated using a finite element formulation based on Hamilton’s principle. First-order shear deformation theory and quasi-steady aerodynamic theory have been employed for the analysis. In order to consider the sectional distribution of shear stresses for the box-beam in an effective manner, Timoshenko beam assumption has been made and the formula of shear correction factor of isotropic box section has been used to describe the motion. Three dimensional stress analysis of composite box-beam by using a detailed finite element analysis program has been performed to identify the distribution of shear of the box section and to correlate the results of shear correction factor of isotropic material with that of composite material. Free vibration tests of rotating composite box-beams have showed fairly good agreement between the current results and the experimental data. Transverse shear behavior on the aeroelastic stability has been studied for a specific box-beam configuration. The results displayed in this article have revealed that the transverse shear coupling has a significant role on the flutter boundary of the rotor, especially in case of anti-symmetric configuration.