Jimmy C. Ho

Investigation of Rotor Blade Structural Dynamics and Modeling Based on Measured Airloads

The work presented herein treats measured airloads from the UH-60A Airloads Program as prescribed external loads to calculate the resulting structural loads and motions of a rotor blade. Without the need to perform any aerodynamic computations, the coupled aeroelastic response problem is reduced to one involving only structural dynamics. The results, computed by RCAS and CAMRAD II, are compared against measured results and against each other for three representative test points. The results from the two codes mostly validate each other. Seven more test points, with responses computed by RCAS, to form thrust and airspeed sweeps are evaluated to better understand key issues. One such issue is an inability to consistently predict pushrod loads and torsion moments well, and this is found to be amplified at the two test points with the highest thrust coefficient. For these two test points, harmonic analysis reveals that the issue is due to excessive amounts of 5/rev response that stem from high levels of 5/rev pitching moment excitation. Another issue that concerns all test points is that the phase of the 1/rev blade flapping motion is not predicted well, which reflects the high sensitivity of this quantity that is developed due to having a first flap frequency of approximately 1/rev. Results also show that current force-velocity relationships, used in describing the lead-lag damper, are not satisfactory to consistently yield accurate inboard chordwise bending moment predictions. Overall, the investigation here, conducted with numerous test points, further confirms the methodology of prescribing measured airloads for assessing the structural dynamics capability of a computational tool.

Energy Transformation to Generalized Timoshenko Form for Nonuniform Beams

A, B, C, D = stiffness matrices of the second-order asymptotically correct beam theory a = characteristic length of the cross-sectional dimension ai = unit vectors of the reference coordinate system b = half-width of a beam with a rectangular cross section E = Young’s modulus F1 = internal axial force F2, F3 = internal shear forces k1 = initial twist k2, k3 = initial curvatures ‘ = characteristic wavelength of deformation along x1 M1 = internal torque M2,M3 = internal bending moments n = outward-directed unit normal vector R = characteristic radius of initial twist and curvatures R, S, T = submatrices of the generalized Timoshenko flexibility matrix t = thickness of a beam with a rectangular cross section U = sectional strain energy X, Y, G = submatrices of the generalized Timoshenko stiffness matrix x1 = beam axial coordinate x2, x3 = local, Cartesian, cross-sectional coordinates for the beam section

Energy Transformation to Generalized Timoshenko Form by the Variational Asymptotic Beam Sectional Analysis

The 2D beam cross-sectional analysis tool VABS finds stiffness constants for the generalized Timoshenko theory by an energy transformation from a 2-order asymptoticallycorrect strain energy. Two inconsistencies in the transformation used in previous versions are identified. These are resolved by re-deriving the energy transformation and formulating new solution procedures based on the revised transformation. An iterative method and a perturbation-based analytical solution are each presented to solve for the stiffness constants from the resulting equations. A comparison between results obtained from the new solutions and those from a previous version of VABS shows that this improved methodology sometimes changes the results measurably. As a form of validation and an internal consistency check, results obtained using curvilinear coordinate axes featuring twist for the 1D analysis of non-rotating, initially twisted, isotropic beams are shown to be equivalent to those obtained using Cartesian coordinates. Similarly, results obtained from a 1D analysis of rotating, initially twisted, isotropic beams using a set of piecewise Cartesian coordinates are shown to be equivalent to those from calculations using a global set of Cartesian coordinates.

Shear Stiffness of Homogeneous, Orthotropic, Prismatic Beams

Exact analytical expressions for shear stiffness constants are provided herein for homogeneous, orthotropic, prismatic beams with arbitrary cross-sectional shapes. The analytical expressions are extracted, without invoking any approximations, from exact solutions of the linear equations of three-dimensional elasticity for flexure. Owing to the elasticity solutions being in terms of a stress function for cross sections with arbitrary shapes, the shear stiffness constants are also provided in terms of the same stress function. For elliptical and rectangular cross sections, this stress function is known so that shear stiffness constants are provided in closed form. These closed-form expressions constitute a standard with which the accuracy of two-dimensional beam cross-sectional analyses to calculate shear stiffness in the presence of orthotropic materials may be assessed. The calculated shear stiffness constants, from two such cross-sectional analyses, are successfully validated in this manner.

Stiffness Constants of Homogeneous, Anisotropic, Prismatic Beams

This paper presents a complete set of analytical expressions for the stiffness constants of a generalized Euler–Bernoulli beam theory for homogeneous, anisotropic, prismatic beams with arbitrary cross-sectional shapes. These expressions are extracted from exact solutions of the linear equations of three-dimensional elasticity for the cases of loading by axial forces, torques, and bending moments about two orthogonal directions. Closed-form expressions are derived for the extensional stiffness and the extension-related coupling terms. Expressions for the remaining stiffness constants are derived in terms of the torsional stiffness: the expression of which is in terms of a function that needs to be obtained. The resulting expressions reveal both similarities and differences from its isotropic and orthotropic counterparts. For elliptical, anisotropic cross sections and rectangular, orthotropic cross sections, all stiffness constants are known in closed form. These closed-form expressions constitute a standar...