Mark V. Fulton

On a simplified strain energy function for geometrically nonlinear behaviour of anisotropic beams

Abstract An asymptotically exact methodology, based on geometrically nonlinear, three-dimensional elasticity, is presented for analysis of prismatic, nonhomogeneous, anisotropic beams. The analysis is subject only to the restrictions that the strain is small relative to unity and that the maximum dimension of the cross-section is small relative to a length parameter which is characteristic of the rapidity with which the deformation varies along the beam; thus, restrained warping effects are not considered. A two-dimensional function is derived which enables the determination of sectional elastic constants, as well as relations between the beam (i.e. one-dimensional) displacement and generalized strain measures and the three-dimensional displacement and strain fields. Since the three-dimensional foundation of the formulation allows for all possible deformations, the complex coupling phenomena associated with shear deformation are correctly accounted for. The final form of the strain energy contains only extensional, bending and torsional deformation measures—identical to the form of classical theory, but with stiffness constants that are numerically quite different from those of a purely classical theory. Indeed, the stiffnesses obtained from classical theory may, in certain extreme cases, be more than twice as stiff in bending as they should be. Stiffness constants which arise from these various models are used to predict beam deformation for different types of composite beams. Predictions from the present reduced stiffness model are essentially identical to those of more sophisticated models and agree very well with experimental data for large deformation.

Hover Testing of a Small-Scale Rotor with On-Blade Elevons

Abstract : A two-bladed, 7.5-ft diameter dynamic rotor model with 10% chord on-blade elevons driven by piezoceramic bimorph actuators was designed and tested in hover at tip speeds up to 298 ft/s. The elevon actuator succeeded in achieving deflections of plus or minus 5 deg at the nominal rotor speed of 760 RPM. Aeroelastic and structural dynamic response characteristics were evaluated over a wide rotor speed range using frequency sweep excitation of the elevon up to 100 Ha. The CIFER(registered) post processing method was very useful for determining frequency response magnitude, phase, and coherence of measured blade root flap bending and torsion moments to elevon input, as well as elevon response to actuator input voltage. Experimental results include actuator effectiveness, effects of low Reynolds number on elevon pitching moments, elevon reversal, and variation of flap bending mode responses with rotor speed and elevon excitation. The active rotor performed satisfactorily and the results provide an encouraging basis for future wind tunnel testing that will evaluate on-blade elevon effectiveness for reducing rotor blade vibratory loads.

Nonlinear Deformation of Composite Beams: Unification of Cross-Sectional and Elastic Analyses

A unified analysis is presented for predicting the deformation of anisotropic beams. Outlines of the derivations of both a linear, two-dimensional, cross-sectional analysis and a nonlinear, one-dimensional analysis are given from application of a general kinematical foundation, in which only small strain and small local rotation are assumed. The deformation may be arbitrary except that restrained warping effects are not treated. Predictions from the unified analysis agree quite well with published experimental results for both nonlinear static and linearized dynamic behavior about equilibrium.

Application of composite rotor blade stability analysis to extension-twist coupled blades

A finite element based stability analysis is developed for a hingeless, composite, isolated rotor in hover. It includes a mechanism for the inclusion of a complete 6 x 6 stiffness matrix, as well as the effects of rotary inertia. No restrictions are made on the magnitudes of the displacements and rotations if the magnitudes of the strains remain small compared to unity. The equilibrium position is obtained by an iterative solution of the complete nonlinear equations. The dynamic equations are linearized about this position, yielding and eigenproblem. The lift model is a two-dimensional, quasi-steady strip theory, with inflow taken from momentum theory. Initial results are given for the stability of extensiontwist coupled rotor blades.

Advancing State-of-the-Art Unsteady, Multidisciplinary Rotorcraft Simulations

To address the complex multidisciplinary nature of rotorcraft analysis, high-fidelity computational fluid and structural dynamics models have been developed to investigate a range of challenging rotorcraft issues. First, an advanced technology, active flap rotor (Boeing SMART) is investigated, and performance, aerodynamic and structural loads, vibration, noise prediction and flow physics mechanisms are shown. The rotor model includes complex and detailed flap and flap-gap modeling. Second, analyses on an advanced dynamics model (ADM) research configuration rotor investigate regressing lag mode (RLM) aero elastic instabilities. Tightly-coupled computational fluid dynamics (CFD)/computational structural dynamics (CSD) stability calculations show noticeable improvement over lower fidelity methods. Third, the state-of-the-art capability of CFD methods to directly predict low frequency in-plane noise on realistic lifting rotors is benchmarked for the first time. In all cases, comparisons are made between CFD/CSD, comprehensive analyses, and experimental data. Taken together, these works offer an important advancement in rotorcraft analysis capability for advanced technology rotor configurations under study for future Army rotorcraft, and highlight future needs in next-generation rotorcraft analysis software.