Department of Mechanical Engineering

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Computational experiences which demonstrate the performance of two popular error estimators for finite-element approximations of the equations of plane linear elasticity are presented. The comparison involves element-residual and flux-projection error estimators for biquadratic elements. The numerical results indicate that element-residual estimates give reasonable predictions for the global energy-norm of the error for the types of meshes and solutions tested. From the results it is also clear that a popular class of flux-projection error estimators may lead to dangerous underestimation of the error for approximations obtained using biquadratic finite elements.

World University root node

American Society of Mechanical Engineers, Applied Mechanics Division, AMD

Recent computational experiences with residual and flux-projection error estimators

This paper presents a concise description of a structural dynamic model for composite rotor blades, with straight and swept tips, undergoing moderate deflections. The model can represent anisotropic totor blades, with arbitrary cross sections and is valid for the moderate amount of built-in twist encountered in helicopter rotor blades. The results illustrate the effects of composite ply orientation and tip sweep on the natural frequencies of composite blades. The paper also presents some interesting observations on the treatment of the axial degree of freedom, which plays an important role in the structural dynamic modeling of composite rotor blades.

American Society of Mechanical Engineers, Aerospace Division (Publication) AD

Structural dynamic model of composite rotor blades undergoing moderate deflections

This paper presents an analytical study of the aeroelastic behavior of composite rotor blades with straight and swept tips. The blade is modeled by beam type finite elements. A single finite element is used to model the swept tip. The nonlinear equations of motion for the finite element model are derived using Hamilton's principle and based on a moderate deflection theory and accounts for: arbitrary cross-sectional shape, pretwist, generally anisotropic material behavior, transverse shears and out-of-plane warping. Numerical results illustrating the effects of tip sweep, anhedral and composite ply orientation on blade aeroelastic behavior are presented. It is shown that composite ply orientation has a substantial effect on blade stability. At low thrust conditions, certain ply orientations can cause instability in the lag mode. The flap-torsion coupling associated with tip sweep can also induce aeroelastic instability in the blade. This instability can be removed by appropriate ply orientation in the composite construction.

Annual Forum Proceedings - American Helicopter Society

Aeroelastic behavior of composite rotor blades with swept tips

In the treatment of the structural dynamic problem of composite materials, two alternate types of formulations, based on the elastic modulus and compliance quantities, exist in the literature. The definitions of the various rigidities are observed to differ in these two approaches. Following these two types of formulation, the structural dynamic characteristics of a composite beam are analyzed. The results of the analysis are compared with those available in the literature. Based on the comparison, the influence of the warping function in defining the coupling terms in the modulus approach and also on the natural frequencies of the beam has been identified. It is found from the analysis that, in certain cases, the difference between the results of the two approaches is appreciable. These differences may be attributed to the constraints imposed on the deformation and flexibility of the beam by the choice of the description of the warping behaviour. Finally, the influence of material properties on the structural dynamic characteristics of the beam is studied for different composites for various angles of orthotropy. © 1990.

Journal of Sound and Vibration

Structural dynamic analysis of composite beams

The equations of motion for the coupled rotor/isolator/fuselage dynamical system are formulated for the prediction of vibrations in helicopters during forward flight. Using a combined Floquet theory/frequency-response technique, the equations are solved to predict the vibratory loads at the various locations of the helicopter. In addition, the influence of the isolator on the hub and blade loads is established. © 1989 American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Journal of Aircraft

Rotor/fuselage vibration isolation studies by a floquet-harmonic iteration technique

This paper addresses the problem of vibration prediction and vibration reduction in helicopters by means of active control methodologies. The nonlinear equations of a coupled rotor/flexible fuselage system have been derived using computer algebra, thus relegating this tedious task to the computer. In the solution procedure the trim state and vibratory response of the helicopter are obtained in a single pass by using a Harmonic Balance technique and simultaneously satisfying the trim and the vibratory response of the helicopter in all the rotor and fuselage degrees of freedom. Using this solution procedure, the influence of the fuselage flexibility on the vibratory response is studied. In addition it is shown that the conventional single frequency HHC is capable of reducing either the hub loads or only the fuselage vibrations but not both simultaneously. A new scheme called MHHC, having multiple higher harmonic pitch inputs was used to accomplish this task of simultaneously reducing both the vibratory hub loads and fuselage vibratory response. In addition, the uniqueness of this MHHC scheme is explained in detail.

Nonlinear coupled rotor-fuselage helicopter vibration studies with higher harmonic control

This paper presents a novel technique for formulating a high quality finite state unsteady aerodynamic model by applying Bode plot methods, used in control engineering. Indicial response functions for both fixed wing and rotary wing applications are obtained using these finite state unsteady aerodynamic models. It is shown that the rotary wing indicial response function has a fundamentally different characteristic when compared to fixed wing indicial response. The rotary wing indicial response function is oscillatory in nature while the fixed wing indicial response function is nonoscillatory. Furthermore it should be emphasized that this is the first that a rotary-wing indicial response function has been presented in the literature.

Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

NEW APPROACH TO FINITE STATE MODELLING OF UNSTEADY AERODYNAMICS.

A novel technique used in control engineering for formulating a high-quality, finite-state, unsteady aerodynamic model by applying Bode plot methods is presented. Indicial response functions for both fixed- and rotary-wing applications are obtained using these finite-state, unsteady aerodynamic models. It is shown that the rotary-wing indicial response function has a fundamentally different characteristics when compared to fixedwing indicial response. The rotary-wing indicial response function is oscillatory in nature, while the fixed-wing indicial response function is nonoscillatory. Furthermore, it should be emphasized that this is the first literary presentation of rotary-wing indicial response function. © 1986 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

AIAA Journal

New approach to finite-state modeling of unsteady aerodynamics

The aeromechanical stability of a helicopter in ground resonance was analyzed, using five different aerodynamic models in the coupled rotor/fuselage analysis. The sensitivity of the results to changes in aerodynamic modeling was examined. The theoretical results were compared with experimental data, and conclusions are drawn regarding the role of aerodynamic modeling on this aeromechanical stability problem. The aerodynamic model which provided the best overall correlation with the experimental data was identified.

Journal of the American Helicopter Society

INFLUENCE OF UNSTEADY AERODYNAMIC MODELS ON AEROMECHANICAL STABILITY IN GROUND RESONANCE.

Hybrid heavy lift airship (HHLA) is a proposed candidate vehicle aimed at providing heavy lift capability at low cost. This vehicle consists of a buoyant envelope attached to a supporting structure to which four rotor systems are attached. Nonlinear equations of motion capable of modeling the dynamics of this coupled multirotor/support-frame vehicle system have been developed. Using these equations, an aeromechanical stability analysis was performed in order to identify potential instabilities for this type of vehicle. The coupling between various blade, supporting structure, and rigid body modes is identified. Furthermore, the effects of changes in buoyancy ratio (buoyant lift/total weight) on the dynamic characteristics of the vehicle were studied. © 1985 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.