Engineering topics

Kvaternik, R. G.

Publications and source records attributed to Kvaternik, R. G..

At least 19 records

NASA NTRS1982

A formulation of rotor-airframe coupling for design analysis of vibrations of helicopter airframes

A linear formulation of rotor airframe coupling intended for vibration analysis in airframe structural design is presented. The airframe is represented by a finite element analysis model; the rotor is represented by a general set of linear differential equations with periodic coefficients; and the connections between the rotor and airframe are specified through general linear equations of constraint. Coupling equations are applied to the rotor and airframe equations to produce one set of linear differential equations governing vibrations of the combined rotor airframe system. These equations are solved by the harmonic balance method for the system steady state vibrations. A feature of the solution process is the representation of the airframe in terms of forced responses calculated at the rotor harmonics of interest. A method based on matrix partitioning is worked out for quick recalculations of vibrations in design studies when only relatively few airframe members are varied. All relations are presented in forms suitable for direct computer implementation.

Kvaternik, R. G.↗

NASA NTRS1981

Application of unsteady airfoil theory to rotary wings

A clarification is presented on recent work concerning the application of unsteady airfoil theory to rotary wings. The application of this theory may be seen as consisting of four steps: (1) the selection of an appropriate unsteady airfoil theory; (2) the resolution of that velocity which is the resultant of aerodynamic and dynamic velocities at a point on the elastic axis into radial, tangential and perpendicular components, and the angular velocity of a blade section about the deformed axis; (3) the expression of lift and pitching moments in terms of the three components; and (4) the derivation of explicit expressions for the components in terms of flight velocity, induced flow, rotor rotational speed, blade motion variables, etc.

Kaza, K. R. V.↗

NASA NTRS1980

Vibration modes and frequencies of structures

SUDAN, Substructuring in Direct Analysis, analyzes natural modes and frequencies of vibration of structural systems. Based on direct method of analysis that employs substructures methodology, program is used with structures that may be represented as equivalent system of beam, springs, and rigid bodies.

Durling, R. J.↗

NASA NTRS1979

Aeroelastic equations of motion of a Darrieus vertical-axis wind-turbine blade

The second-degree nonlinear aeroelastic equations of motion for a slender, flexible, nonuniform, Darrieus vertical-axis wind turbine blade which is undergoing combined flatwise bending, edgewise bending, torsion, and extension are developed using Hamilton's principle. The blade aerodynamic loading is obtained from strip theory based on a quasi-steady approximation of two-dimensional incompressible unsteady airfoil theory. The derivation of the equations has its basis in the geometric nonlinear theory of elasticity and the resulting equations are consistent with the small deformation approximation in which the elongations and shears are negligible compared to unity. These equations are suitable for studying vibrations, static and dynamic aeroelastic instabilities, and dynamic response. Several possible methods of solution of the equations, which have periodic coefficients, are discussed.

Kaza, K. R. V.↗

NASA NTRS1979

Examination of the flap-lag stability of rigid articulated rotor blades

Kaza, K. R. V.↗

NASA NTRS1979

Buckling of rotating beams

The stability of a beam subjected to compressive centrifugal forces arising from steady rotation about an axis which does not pass through the clamped end of the beam is analyzed to determine the critical rotational speeds for buckling in the inplane and out-of-plane directions. The differential equations of motion are solved numerically using an integrating matrix method in combination with an eigenanalysis to determine the eigenvalues from which stability is assessed. The results clarify several differences which have been identified in the literature relating to the proper behavior of the critical rotational speed for buckling as the radius of rotation of the clamped end of the beam is reduced.

White, W. F., Jr.↗

NASA NTRS1978

A user's guide to the SUDAN computer program for determining the vibration modes of structural systems

The use of the SUDAN computer program for analyzing structural systems for their natural modes and frequencies of vibration is described. SUDAN is intended for structures which can be represented as an equivalent system of beam, spring, and rigid-body substructures. User-written constraint equations are used to analytically join the mass and stiffness matrices of the substructures to form the mass and stiffness matrices of the complete structure from which all the frequencies and modes of the system are determined. The SUDAN program can treat the case in which both the mass and stiffness matrices of the coupled system may be singular simultaneously. A general description of the FORTRAN IV program is given, the computer hardware and software specifications are indicated, and the input required by the program is described.

Kvaternik, R. G.↗

NASA NTRS1978

Nonlinear flap-lag-axial equations of a rotating beam with arbitrary precone angle

In an attempt both to unify and extend the analytical basis of several aspects of the dynamic behavior of flexible rotating beams, the second-degree nonlinear equations of motion for the coupled flapwise bending, lagwise bending, and axial extension of an untwisted, torsionally rigid, nonuniform, rotating beam having an arbitrary angle of precone with the plane perpendicular to the axis of rotation are derived using Hamilton's principle. The derivation of the equations is based on the geometric nonlinear theory of elasticity and the resulting equations are consistent with the assumption that the strains are negligible compared to unity. No restrictions are imposed on the relative displacements or angular rotations of the cross sections of the beam other than those implied by the assumption of small strains. Illustrative numerical results, obtained by using an integrating matrix as the basis for the method of solution, are presented both for the purpose of validating the present method of solution and indicating the range of applicability of the equations of motion and the method of solution.

Kvaternik, R. G.↗

NASA NTRS1977

An experimental and analytical investigation of proprotor whirl flutter

The results of an experimental parametric investigation of whirl flutter are presented for a model consisting of a windmilling propeller-rotor, or proprotor, having blades with offset flapping hinges mounted on a rigid pylon with flexibility in pitch and yaw. The investigation was motivated by the need to establish a large data base from which to assess the predictability of whirl flutter for a proprotor since some question has been raised as to whether flutter in the forward whirl mode could be predicted with confidence. To provide the necessary data base, the parametric study included variation in the pylon pitch and yaw stiffnesses, flapping hinge offset, and blade kinematic pitch-flap coupling over a large range of advance ratios. Cases of forward whirl flutter and of backward whirl flutter are documented. Measured whirl flutter characteristics were shown to be in good agreement with predictions from two different linear stability analyses which employed simple, two dimensional, quasi-steady aerodynamics for the blade loading. On the basis of these results, it appears that proprotor whirl flutter, both forward and backward, can be predicted.

Kvaternik, R. G.↗

NASA NTRS1977

Nonlinear flap-lag axial equations of a rotating beam

It is possible to identify essentially four approaches by which analysts have established either the linear or nonlinear governing equations of motion for a particular problem related to the dynamics of rotating elastic bodies. The approaches include the effective applied load artifice in combination with a variational principle and the use of Newton's second law, written as D'Alembert's principle, applied to the deformed configuration. A third approach is a variational method in which nonlinear strain-displacement relations and a first-degree displacement field are used. The method introduced by Vigneron (1975) for deriving the linear flap-lag equations of a rotating beam constitutes the fourth approach. The reported investigation shows that all four approaches make use of the geometric nonlinear theory of elasticity. An alternative method for deriving the nonlinear coupled flap-lag-axial equations of motion is also discussed.

Kaza, K. R. V.↗

NASA NTRS1976

Nonlinear Curvature Expressions for Combined Flapwise Bending, Chordwise Bending, Torsion and Extension of Twisted Rotor Blades

The nonlinear curvature expressions for a twisted rotor blade or a beam undergoing transverse bending in two planes, torsion, and extension were developed. The curvature expressions were obtained using simple geometric considerations. The expressions were first developed in a general manner using the geometrical nonlinear theory of elasticity. These general nonlinear expressions were then systematically reduced to four levels of approximation by imposing various simplifying assumptions, and in each of these levels the second degree nonlinear expressions were given. The assumptions were carefully stated and their implications with respect to the nonlinear theory of elasticity as applied to beams were pointed out. The transformation matrices between the deformed and undeformed blade-fixed coordinates, which were needed in the development of the curvature expressions, were also given for three of the levels of approximation. The present curvature expressions and transformation matrices were compared with corresponding expressions existing in the literature.

Kvaternik, R. G.↗

NASA NTRS1976

Considerations for the application of finite element beam modeling to vibration analysis of flight vehicle structures

The manner of representing a flight vehicle structure as an assembly of beam, spring, and rigid-body components for vibration analysis is described. The development is couched in terms of a substructures methodology which is based on the finite-element stiffness method. The particular manner of employing beam, spring, and rigid-body components to model such items as wing structures, external stores, pylons supporting engines or external stores, and sprung masses associated with launch vehicle fuel slosh is described by means of several simple qualitative examples. A detailed numerical example consisting of a tilt-rotor VTOL aircraft is included to provide a unified illustration of the procedure for representing a structure as an equivalent system of beams, springs, and rigid bodies, the manner of forming the substructure mass and stiffness matrices, and the mechanics of writing the equations of constraint which enforce deflection compatibility at the junctions of the substructures. Since many structures, or selected components of structures, can be represented in this manner for vibration analysis, the modeling concepts described and their application in the numerical example shown should prove generally useful to the dynamicist.

Kvaternik, R. G.↗

NASA NTRS1976

A review of some tilt-rotor aeroelastic research at NASA-Langley

An overview of an experimental and analytical research program conducted within the Aeroelasticity Branch of the NASA Langley Research Center for studying the aeroelastic and dynamic characteristics of tilt-rotor VTOL aircraft is presented. Selected results from several joint NASA/contractor investigations of scaled models in the Langley transonic dynamics tunnel are shown and discussed with a view toward delineating various aspects of dynamic behavior peculiar to proprotor aircraft. Included are such items as proprotor/pylon stability, whirl flutter, gust response, and blade flapping. Theoretical predictions, based on analyses developed at Langley, are shown to be in agreement with the measured stability and response behavior.

Kvaternik, R. G.↗

NASA NTRS1976

A critical examination of the flap-lag dynamics of helicopter rotor blades in hover and in forward flight

A critical examination of flap-lag stability of a centrally hinged, spring-restrained rigid blade in both hover and forward flight is presented. Several differences in the equations of motion for blade flap-lag stability in the existing literature are identified. A rigorous and systematic development of these equations for a rigid articulated blade in forward flight shows the existence of some linear aerodynamic coupling terms associated with blade steady-state flapping and lagging in the perturbation equations. The differences identified are shown to be associated with the order in which the flap and lag transformations are taken in developing the equations of motion. The implications of these differences on stability are examined, and it is shown that the pitch-lag coupling terms associated with a flap-lag hinge transformation sequence have a marked influence on flap-lag stability. Some qualitative considerations on the role of the assumed transformation sequence in the development of the flap-lag equations for a hingeless elastic blade are also given. On the basis of these considerations, it is shown that aerodynamic coupling terms associated with blade steady-state flapping and lagging similar to those found for the rigid blade will also appear in the equations for the elastic blade.

Kaza, K. R. V.↗

NASA NTRS1975

Development and applications of two computational procedures for determining the vibration modes of structural systems

Two computational procedures for analyzing complex structural systems for their natural modes and frequencies of vibration are presented. Both procedures are based on a substructures methodology and both employ the finite-element stiffness method to model the constituent substructures. The first procedure is a direct method based on solving the eigenvalue problem associated with a finite-element representation of the complete structure. The second procedure is a component-mode synthesis scheme in which the vibration modes of the complete structure are synthesized from modes of substructures into which the structure is divided. The analytical basis of the methods contains a combination of features which enhance the generality of the procedures. The computational procedures exhibit a unique utilitarian character with respect to the versatility, computational convenience, and ease of computer implementation. The computational procedures were implemented in two special-purpose computer programs. The results of the application of these programs to several structural configurations are shown and comparisons are made with experiment.

Kvaternik, R. G.↗

NASA NTRS1974

Experimental and analytical studies in tilt-rotor aeroelasticity

An overview of an experimental and analytical research program underway for studying the aeroelastic and dynamic characteristics of tilt-rotor VTOL aircraft is presented. Selected results from several investigations of scaled models in the transonic dynamics tunnel, as well as some results from a test of a flight-worthy proprotor in the full-scale wind tunnel are shown and discussed with a view toward delineating various aspects of dynamic behavior peculiar to proprotor aircraft. Included are such items as proprotor/pylon stability, whirl flutter, gust response, and blade flapping. Theoretical predictions are shown to be in agreement with the measured stability and response behavior.

Kvaternik, R. G.↗

NASA NTRS1974

Experimental and analytical studies in tilt-rotor aeroelasticity

An overview of an experimental and analytical research program for studying the aeroelastic and dynamic characteristics of tilt-rotor VTOL aircraft is presented. Selected results from several investigations of scaled models in the Langley transonic dynamics tunnel as well as some results from a test of a flight-worthy prop rotor in the NASA Ames full-scale wind tunnel are shown and discussed with a view toward delineating various aspects of dynamic behavior peculiar to prop rotor aircraft. Included are such items as prop rotor pylon stability, whirl flutter, gust response, and blade flapping. Theoretical predictions, based on analyses developed at Langley, are shown to be in agreement with the measured stability and response behavior.

Kvaternik, R. G.↗

NASA NTRS1973

Studies in tilt-rotor VTOL aircraft aeroelasticity, volume 1

Aeroelastic and dynamic studies which complement and extend various aspects of technology applicable to tilt-rotor VTOL aircraft are discussed. Particular attention is given to proprotor/pylon whirl instability, a precession-type instability akin to propeller/nacelle whirl flutter. The blade flapping and pitch-change freedoms of a proprotor are shown to lead to a fundamentally different situation as regards the manner in which the precession-generated aerodynamic forces and moments act on the pylon and induce whirl flutter relative to that of a propeller. The implication of these forces and moments with regard to their capacity for instigating a whirl instability is examined, demonstrating why a proprotor can exhibit whirl flutter in either the backward or forward directions in contrast to a propeller which is found to always whirl in the backward direction. Analytical trend studies delineating the effect of several system design parameters on proprotor/pylon stability and response are shown.

Kvaternik, R. G.↗