The effect of wind bending deflection on the rolling moment due to sideslip
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AIRPLANES, BOMBING↗
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The calculation of modes and frequencies of a modified structure from those of the unmodified structure
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THEORIES - GALERKIN↗
A case study of analysis methods for large deflections of a cantilever beam
A load case study of geometric nonlinear large deflections of a cantilever beam is presented. The bending strain must remain elastic. Closed form solution and finite element methods of analysis are illustrated and compared for three common load cases. A nondimensional nomogram for each case is presented in the summary.
Craig, L. D.↗
Bending of a thin isotropic plate with a hole of general form, taking temperature stresses into account
Elastic equilibrium in isotropic plate in stationary thermal field, and bending due to temperature stresses
BENDING MOMENT↗
Nonlinear attitude control of elastic spacecraft-antenna system
An approach to large angle rotational maneuvers of a spacecraft-beam-tip body (an antenna or a reflector) configuration based on nonlinear invertibility and linear feedback stabilization is presented. A control law u sub d is derived to obtain independent decoupled control of attitude angles, lateral elastic deflections, slopes due to bending and angular deflection due to torsion at the tip of the beam using torquers and force actuators. For the stabilization of the elastic oscillations, a linear feedback control law, u sub s, is obtained based on a linearized model about the terminal state augmented with a servo-compensator. Simulation results obtained for single axis control, for simplicity, show that large slewing and elastic mode stabilization can be accomplished in spite of uncertainty in the system using the total control u = u sub d + u sub s.
Singh, S. N.↗
Robust nonlinear attitude control of flexible spacecraft
This paper presents an approach to large-angle rotational maneuvers of a spacecraft-beam-tip body configuration based on nonlinear invertibility and linear feedback stabilization. A control law u sub d is derived for the decoupled control of attitude angles, lateral elastic deflections, slopes due to bending and angular deflection due to torsion at the tip of the beam using torquers and force actuators. For the stabilization of the elastic modes, a linear feedback control law u sub s is obtained based on a linearized model augmented with a servocompensator. Simulation results are presented to show that large slewing and elastic mode stabilization can be accomplished.
Singh, Sahjendra N.↗
Hingeless helicopter rotor with improved stability
Improved stability was provided in a hingeless helicopter rotor by inclining the principal elastic flexural axes and coupling pitching of the rotor blade with the lead-lag bending of the blade. The primary elastic flex axes were inclined by constructing the blade of materials that display non-uniform stiffness, and the specification described various cross section distributions and the resulting inclined flex axes. Arrangements for varying the pitch of the rotor blade in a predetermined relationship with lead-lag bending of the blade, i.e., bending of the blade in a plane parallel to its plane of rotation were constructed.
Ormiston, R. A.↗
Calculation of exact vibration modes for plane grillages by the dynamic stiffness method
A dynamic stiffness method is developed for the calculation of the exact modal parameters for plane grillages which consist of straight and uniform beams with coincident elastic and inertial axes. Elementary bending-torsion beam theory is utilized, and bending translation is restricted to one direction. The exact bending-torsion dynamic stiffness matrix is obtained for a straight and uniform beam element with coincident elastic and inertial axes. The element stiffness matrices are assembled using the standard procedure of the static stiffness method to form the dynamic stiffness matrix of the complete grillage. The exact natural frequencies, mode shapes, and generalized masses of the grillage are then calculated by solving a nonlinear eigenvalue problem based on the dynamic stiffness matrix. The exact modal solutions for an example grillage are calculated and compared with the approximate solutions obtained by using the finite element method.
Hallauer, W. L., Jr.↗
Elastic properties and fracture strength of quasi-isotropic graphite/epoxy composites
A research program is described which was devised to determine experimentally the elastic properties in tension and bending of quasi-isotropic laminates made from high-modulus graphite fiber and epoxy. Four laminate configurations were investigated, and determinations were made of the tensile modulus, Poisson's ratio, bending stiffness, fracture strength, and fracture strain. The measured properties are compared with those predicted by laminate theory, reasons for scatter in the experimental data are discussed, and the effect of fiber misalignment on predicted elastic tensile properties is examined. The results strongly suggest that fiber misalignment in combination with variation in fiber volume content is responsible for the scatter in both elastic constants and fracture strength.
Sullivan, T. L.↗
Large-displacement structural durability analyses of simple bend specimen emulating rocket nozzle liners
Large-displacement elastic and elastic-plastic, finite-element stress-strain analyses of an oxygen-tree high-conductivity (OFHC) copper plate specimen were performed using an updated Lagrangian formulation. The plate specimen is intended for low-cost experiments that emulate the most important thermomechanical loading and failure modes of a more complex rocket nozzle. The plate, which is loaded in bending at 593 C, contains a centrally located and internally pressurized channel. The cyclic crack initiation lives were estimated using the results from the analyses and isothermal strain-controlled low-cycle fatigue data for OFHC copper. A comparison of the predicted and experimental cyclic lives showed that an elastic analysis predicts a longer cyclic life than that observed in experiments by a factor greater than 4. The results from elastic-plastic analysis for the plate bend specimen, however, predicted a cyclic life in close agreement with experiment, thus justifying the need for the more rigorous stress-strain analysis.
Arya, Vinod K.↗
Results of a parametric aeroelastic stability analysis of a generic X-wing aircraft
This paper discusses the trends in longitudinal dynamic aeroelastic stability of a generic x-wing aircraft model with design parameter variations. X-wing rotor blade sweep angle, ratio of blade mass to total vehicle mass, blade structural stiffness cross-coupling and vehicle center-of-gravity location were parameters considered. The typical instability encountered is body-freedom flutter involving a low frequency interaction of the first elastic mode and the aircraft short period mode. Parametric cases with the lowest static margin consistently demonstrated the highest flutter dynamic pressures. As mass ratio was increased, the flutter boundary decreased. The decrease was emphasized as center-of-gravity location was moved forward. As sweep angle varied, it was observed that the resulting increase in forward-swept blade bending amplitude relative to aft blade bending amplitude in the first elastic mode had a stabilizing effect on the flutter boundary. Finally, small amounts of stiffness cross-coupling in the aft blades increased flutter dynamic pressure.
Woods, Jessica A.↗
Results of a parametric aeroelastic stability analysis of a generic X-wing aircraft
This paper discusses the trend in longitudinal dynamic aeroelastic stability of a generic X-Wing aircraft model with design parameter variations. X-Wing rotor blade sweep angle, ratio of blade mass to total vehicle mass, blade structural stiffness cross-coupling and vehicle center-of-gravity location were parameters considered. The typical instability encountered is body-freedom flutter involving a low frequency interaction of the first elastic mode and the aircraft short period mode. Parametric cases with the lowest static margin consistently demonstrated the highest flutter dynamic pressures. As mass ratio was increased, the flutter boundary decreased. The decrease was emphasized as center-of-gravity location was moved forward. As sweep angle varied, it was observed that the resulting increase in forward-swept blade bending amplitude relative to aft blade bending amplitude in the first elastic mode had a stabilizing effect on the flutter boundary. Finally, small amounts of stiffness cross-coupling in the aft blades increased flutter dynamic pressure.
Woods, Jessica A.↗
Vibration response of geometrically nonlinear elastic beams to pulse and impact loading
The governing equations for the geometrically nonlinear deformation of elastic beams subjected to dynamic bending loads are developed and solved for various initial conditions. Of primary interest is the response to pulse loading and simulated impact. Both transient and several cycle solutions are generated for the free vibration response to pulse loading. The results obtained are compared to a first mode analysis approximation. A model is developed to simulate impact loading by the distribution of additional mass to the elastic system and subjecting it to a velocity pulse. The governing equations are solved using second order finite differences in space and time. The solutions obtained are in reasonable agreement with experimental results.
Liebowitz, H.↗
Tilt-rotor flutter control in cruise flight
Tilt-rotor flutter control under cruising operation is analyzed. The rotor model consists of a straight fixed wing, a pylon attached to the wingtip, and a three-blade rotor. The wing is cantilevered to the fuselage and is allowed to bend forward and upward. It also has a torsional degree of freedom about the elastic axis. Each rotor blade has two bending degrees of freedom. Feedback of wingtip velocity and acceleration to cyclic pitch is investigated for flutter control, using strip theory and linearized equations of motion. To determine the feedback gain, an eigenvalue analysis is performed. A second, independent, timewise calculation is conducted to evaluate the control law while employing more sophisticated aerodynamics. The effectiveness of flutter control by cyclic pitch change was confirmed.
Nasu, Ken-Ichi↗
Effect of Bending Stiffness of the Electroactive Polymer Element on the Performance of a Hybrid Actuator System (HYBAS)
An electroactive polymer (EAP)-ceramic hybrid actuation system (HYBAS) was developed recently at NASA Langley Research Center. This paper focuses on the effect of the bending stiffness of the EAP component on the performance of a HYBAS, in which the actuation of the EAP element can match the theoretical prediction at various length/thickness ratios for a constant elastic modulus of the EAP component. The effects on the bending stiffness of the elastic modulus and length/thickness ratio of the EAP component were studied. A critical bending stiffness to keep the actuation of the EAP element suitable for a rigid beam theory-based modeling was found for electron irradiated P(VDF-TrFE) copolymer. For example, the agreement of experimental data and theoretical modeling for a HYBAS with the length/thickness ratio of EAP element at 375 times is demonstrated. However, the beam based theoretical modeling becomes invalid (i.e., the profile of the HYBAS movement does not follow the prediction of theoretical modeling) when the bending stiffness is lower than a critical value.
Xu, Tian-Bing↗
Pyridoxine deficiency affects biomechanical properties of chick tibial bone
The mechanical integrity of bone is dependent on the bone matrix, which is believed to account for the plastic deformation of the tissue, and the mineral, which is believed to account for the elastic deformation. The validity of this model is shown in this study based on analysis of the bones of vitamin B6-deficient and vitamin B6-replete chick bones. In this model, when B6-deficient and control animals are compared, vitamin B6 deficiency has no effect on the mineral content or composition of cortical bone as measured by ash weight (63 +/- 6 vs. 58 +/- 3); mineral to matrix ratio of the FTIR spectra (4.2 +/- 0.6 vs. 4.5 +/- 0.2), line-broadening analyses of the X-ray diffraction 002 peak (beta 002 = 0.50 +/- 0.1 vs. 0.49 +/- 0.01), or other features of the infrared spectra. In contrast, collagen was significantly more extractable from vitamin B6-deficient chick bones (20 +/- 2% of total hydroxyproline extracted vs. 10 +/- 3% p < or = 0.001). The B6-deficient bones also contained an increased amount of the reducible cross-links DHLNL, dehydro-dihydroxylysinonorleucine, (1.03 +/- 0.07 vs. 0.84 +/- 0.13 p < or = 0.001); and a nonsignificant increase in HLNL, dehydro-hydroxylysinonorleucine, (0.51 +/- 0.03 vs. 0.43 +/- 0.03, p < or = 0.10). There were no significant changes in bone length, bone diameter, or area moment of inertia. In four-point bending, no significant changes in elastic modulus, stiffness, offset yield deflection, or fracture deflection were detected. However, fracture load in the B6-deficient animals was decreased from 203 +/- 35 MPa to 151 +/- 23 MPa, p < or = 0.01, and offset yield load was decreased from 165 +/- 9 MPa to 125 +/- 14 MPa, p < or = 0.05. Since earlier histomorphometric studies had demonstrated that the B6-deficient bones were osteopenic, these data suggest that although proper cortical bone mineralization occurred, the alterations of the collagen resulted in changes to bone mechanical performance.
Non-NASA Center↗
Pressures in Tumuli: A Study of Tumuli Formation
Tumuli form via localized inflation in surface lava flows. These domed features have widths of 10-20 m, lengths of 10-150 m, and heights of 1-9 m. The axial fracture exposes a brittle crust overlying a ductilely deformed layer. The total crustal thickness is typically less than lm. Tumuli are observed on both terrestrial and martian lava flow surfaces, and provide insight on the flow formation processes and rates. Past studies have estimated the inflation pressure using a bending model for a circular, thin elastic plate, assuming small deflection (Rossi and Gudmundson, 1996). This formulation results in unrealistic pressures for some tumuli. We thus examine alternative models, including those with different shapes, bending of the ductile crust, large deflection, plastic deformation, and thick plate bending. Using the thickness of the ductile crust in the equations for thin, circular plates reduces most pressures to reasonable values. Alternative plate shapes do not cause a significant reduction in inflation pressure. Although the large deflection equations should be applicable based on the plate thickness to tumuli height ratios, they give even less realistic pressures. Tumuli with unrealistic pressures appear to have exceeded the critical bending moment, and have relatively thick crusts, requiring thick plate bending models.
Hansen, James E.↗
Transverse shear stiffness of laminated anisotropic shells
Equations are derived for the transverse shear stiffness of laminated anisotropic shells. Without making assumptions for thickness distribution for either transverse shear stresses or strains, constitutive equations for the transverse shear deformation theory of anisotropic heterogeneous shells are found. The equations are based on Taylor series expansions about a generic point for stress resultants and couples, identically satisfying plate equilibrium equations. These equations are used to find statically correct expressions for in-surface stresses, transverse shear stresses, and the area density of transverse shear strain energy, in terms of transverse shear stress resultants and redundants. The application of Castigliano's theorem of least work minimizes shear strain energy with respect to the redundants. Examples are presented for several laminated walls. Good agreement is found between the results and those of exact three-dimensional elasticity solutions for the cylindrical bending of a plate.
Cohen, G. A.↗