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  • 1
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    Nonlinear flap-lag axial equations of a rotating beam (1977)
    In:  Other Sources
    Details
    Publication Date: 2011-08-17
    Description: 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.
    Keywords: MECHANICAL ENGINEERING
    Type: AIAA Journal; 15; June 197
    Format: text
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  • 2
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    A review of some tilt-rotor aeroelastic research at NASA-Langley (1976)
    In:  Other Sources
    Details
    Publication Date: 2011-08-16
    Description: 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.
    Keywords: AIRCRAFT DESIGN, TESTING AND PERFORMANCE
    Type: Journal of Aircraft; 13; May 1976
    Format: text
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  • 3
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    Examination of the flap-lag stability of rigid articulated rotor blades (1979)
    In:  Other Sources
    Details
    Publication Date: 2011-08-17
    Description: 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 whether or not the lag hinge flaps with the blade. The implications of these differences on stability are examined, and it is shown that the pitch-lag coupling terms associated with a hinge arrangement in which the lag hinge flaps with the blade have a marked influence on flap-lag stability, depending on the system parameters.
    Keywords: AIRCRAFT DESIGN, TESTING AND PERFORMANCE
    Type: Journal of Aircraft; 16; Dec. 197
    Format: text
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  • 4
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    Application of unsteady airfoil theory to rotary wings (1981)
    In:  Other Sources
    Details
    Publication Date: 2011-08-18
    Description: 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.
    Keywords: AERODYNAMICS
    Type: Journal of Aircraft; 18; July 198
    Format: text
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  • 5
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    Buckling of rotating beams (1979)
    In:  Other Sources
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    Publication Date: 2011-08-17
    Description: 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.
    Keywords: STRUCTURAL MECHANICS
    Type: International Journal of Mechanical Sciences; 21; 12, 1; 1979
    Format: text
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  • 6
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    Experimental and analytical studies in tilt-rotor aeroelasticity (1974)
    In:  CASI
    Details
    Publication Date: 2016-06-07
    Description: 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.
    Keywords: AERODYNAMICS
    Type: Its Rotorcraft Dyn.; p 171-184
    Format: application/pdf
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  • 7
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    A formulation of rotor-airframe coupling for design analysis of vibrations of helicopter airframes (1982)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: 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.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-RP-1089 , L-14243 , NAS 1.61:1089
    Format: application/pdf
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  • 8
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    Aeroelastic equations of motion of a Darrieus vertical-axis wind-turbine blade (1979)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: 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.
    Keywords: STRUCTURAL MECHANICS
    Type: NASA-TM-79295 , DOE/NASA/1028-79/25 , E-238
    Format: application/pdf
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  • 9
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    An experimental and analytical investigation of proprotor whirl flutter (1977)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: 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.
    Keywords: AERODYNAMICS
    Type: NASA-TP-1047 , L-11656
    Format: application/pdf
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  • 10
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    Studies in tilt rotor VTOL aircraft aeroelasticity, volume 2 (1973)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: Two methods for natural mode vibration analysis are discussed. The first consists of a direct approach based on a finite element representation of the complete structure as an entity. The mass and stiffness matrices for the complete structure are assembled by properly combining the mass and stiffness matrices of the individual elements into which the structure has been divided. The second approach is that of component mode synthesis. This method is based on the concept of synthesizing the natural modes of the complete structure from modes of conveniently difined substructures, or components, into which the structure has been partitioned. In this way the expedient of reducing the system degrees of freedom, and thus the size of the eigenvalue problem, can be introduced by partial modal synthesis.
    Keywords: AERODYNAMICS
    Type: NASA-TM-X-69496
    Format: application/pdf
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