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A variationally consistent analytical beam model that describes the theory in a Timoshenko-Vlasov level is developed based on Reissner's mixed variational theorem. Starting from a shell theory, all the field-governing equations (equilibrium and continuity) and the boundary conditions of the shell wall are derived in closed form, and the mixed method enables finding the explicit forms of the reactive stresses and sectional warpings which are evaluated progressively depending on the level of beam model to be analyzed. The stress recovery part is incorporated in the post-stage of the analysis to compute the layer-wise distribution of stresses over the beam cross-section. The present analysis is validated against numerous benchmark examples available in the literature, including beams with multi-layered strip section, thin-walled anisotropic box sections with elastic couplings, and two-cell airfoil section. The comparison study demonstrates excellent correlations with the results from detailed three-dimensional finite element analysis and other up-to-date beam approaches. Also presented are symbolically expressed stiffness coefficients and the sectional warping modes of coupled composite beams to demonstrate the strength of the proposed beam model. [ABSTRACT FROM AUTHOR]

In this study, an assessment is made to quantify the influence of random material properties and fabrication/ manufacturing uncertainties on the aeroelastic response and hub vibratory loads of composite rotor blades. The random variables include lamina stiffness properties, ply thicknesses and fiber orientation angles of the laminate structures, and the elastic-axis offset from the aerodynamic center in the section of the blade. The stochastic behavior of the random variables obtained from previous experimental or analytical studies are used to evaluate the stochastic behavior of the cross-sectional stiffnesses of the blades. The uncertainties in the stiffness properties result in the dissimilarity of the rotor system, which brings extra non-[N.sub.b]/rev vibrations. It is observed that the probability histograms of [N.sub.b]/rev hub vibratory loads exhibit a normal distribution, whereas those of non-[N.sub.b]/rev hub loads show non-Gaussian-type distributions. Numerical results showing the effects of material and geometric uncertainties on the aeroelastic response and hub vibration behavior of composite rotor blades are illustrated and important conclusions are drawn based on the observations. DOI: 10.2514/1.44477

A mixed beam approach that combines both the stiffness and the flexibility formulation in a unified manner has been performed to model and analyze coupled composite blades with closed, multiple-celled cross sections. The analysis model includes the effects of elastic couplings, shell wall thickness, transverse shear deformation, torsion warping, and constrained warping. Reissner's semicomplementary energy functional is used to derive the beam force-displacement relations. The influence of the shell bending strain measures as well as the membrane strain measures are incorporated in the formulation. For completeness required in a rigorous beam theory, four separate continuity conditions are imposed on each cell of the closed, multicelled sections. The theory is validated against experimental test data, detailed finite element analysis results, and other analytical results found in the literature for coupled composite beams and blades with various cross sections. These include two-cell box beams with bending-torsion and/or extension-torsion couplings and bending-torsion coupled composite blades with two-cell airfoils. The correlation between the present theory and other methods is found to be good, dependent on the geometries and material distributions adopted in the blades. Numerical results showing the effects of including the shell bending strain measures are examined. The effects of inappropriate treatment of the direction of integration for two-celled composite beams are also investigated in the current framework of the analysis.

The shaft-fixed aeroelastic stability behavior of a soft-in-plane, composite hingeless rotor blade in hover and in forward flight has been investigated by using the finite element method in both space and time. The non-classical structural effects, such as anisotropy, transverse shear, and torsion warping, are incorporated in the structural formulation. Timoshenko-type shear correction coefficients, which take into account the bending-shear and extension-shear couplings, are introduced to consider the nonuniform distribution of shear across the section of the blade. The aerodynamic model in the current aeroelastic analysis is formulated to allow either quasi-steady or unsteady two-dimensional aerodynamics. The Leishman-Beddoes model based on an indicial response method is employed to consider the unsteady aerodynamic effects. The effects of compressibility and reversed flow are also incorporated. Finite element equations of motion undergoing moderately large displacements and rotations are derived using the Hamilton's principle. Numerical simulations are carried out to validate the current analysis with other literature. The influence of composite couplings, transverse shear deformation, and unsteady aerodynamics on the aeroelastic behavior of soft-in-plane helicopter blades is investigated. Numerical results illustrating a great potential to improve the aeroelastic stability are presented for a blade with positive tension-pitch coupling. The transverse shear deformation is seen to have a stabilizing effect on the lag mode stability for cases with elastic couplings. Overall, the transverse shear effects become larger at higher forward speeds. It is also seen that the lag mode stability is significantly influenced by the unsteady aerodynamic effects.

A refined structural model based on a mixed force and displacement method is proposed for the analysis of composite rotor blades with elastic couplings. The present formulation allows the modeling of either open-section or closed-section blades of arbitrary section shape, stacking sequence, and end restraint effects. The theory accounts for the effect of elastic couplings, shell wall thickness, section warping, warping restraint, and transverse shear deformations. A semicomplementary energy functional is used to derive, in a variationally consistent manner, the beam force--displacement relations. Bending and torsion related warpings and shear correction factors are obtained in closed form as part of the analysis. The resulting first-order shear deformation theory (Timoshenko) describes the beam kinematics in terms of the axial, flap and lag bending, flap and lag shear, twist, and torsion-warping deformations. The theory is validated against experimental data and other finite element results for graphite--epoxy composite beams of various cross sections such as I sections, box sections, and two-cell airfoils. Good correlation is achieved for all of the test examples. The influence of wall thickness and transverse shear on the static beam response is also investigated. Wall thickness effects are shown to become significant when the thickness-to-depth ratio of the beam reaches around 20%. The slenderness ratio has a significant effect on the transverse shear behavior of the beam, especially for beams with low slenderness ratios. It is also shown that the layup angle has a nonnegligible effect on the transverse shear behavior of the beam.

A refined one-dimensional beam formulation based on a mixed approach has been developed for structural dynamics analyses of rotating and nonrotating composite beams and blades of general section shape with open-or closed-section contours. The theory uses a mixed variational approach and accounts for the effects of elastic coupling, shell-wall thickness, warping, warping restraint, and transverse shear deformations. The analysis is validated against experimental data and other analytical results for composite cantilevered beams of various cross sections. Good correlation is achieved for all of the cases considered. The influence of wall thickness and transverse shear on the free vibration characteristics of composite beams with either bending-torsion or extension-torsion coupling is investigated. For a bending-torsion coupled beam, the influence of wall thickness becomes important when the thickness-to-depth ratio of the beam reaches about 30%. The frequency error in neglecting transverse shear flexibility is about 50% for a bending-torsion coupled composite box beam with a slenderness ratio of 5.