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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

Aeromechanical stability of helicopters with a bearingless main rotor. Part 1: Equations of motion

Equations of motion for a coupled rotor-body system were derived for the purpose of studying air and ground resonance characteristics of helicopters that have bearingless main rotors. For the fuselage, only four rigid body degrees of freedom are considered; longitudinal and lateral translations, pitch, and roll. The rotor is assumed to consist of three or more rigid blades. Each blade is joined to the hub by means of a flexible beam segment (flexbeam or strap). Pitch change is accomplished by twisting the flexbeam with the pitch-control system, the characteristics of which are variable. Thus, the analysis is capable of implicitly treating aeroelastic couplings generated by the flexbeam elastic deflections, the pitch-control system, and the angular offsets of the blade and flexbeam. The linearized equations are written in the nonrotating system retaining only the cyclic rotor modes; thus, they comprise a system of homogeneous ordinary differential equations with constant coefficients. All contributions to the linearized perturbation equations from inertia, gravity, quasi-steady aerodynamics, and the flexbeam equilibrium deflections are retained exactly.

Hodges, D. H.↗
NASA NTRS1986

Prediction of blade stresses due to gust loading

An analysis is developed for investigating the response of a rotor-fuselage system in a three-dimensional gust field wherein the gust velocity conponents can have arbitrary variation in space and time. Each rotor blade undergoes flap bending, lag bending and torsional deflections. The blades are divided into beam elements and each element consists of fifteen nodal degrees of freedom. Quasi-steady strip theory is used to obtain the aerodynamic loads. Unsteady aerodynamic effects are introduced through dynamic inflow modeling. Dynamic stall and reverse flow effects are also included. The fuselage is allowed five degrees of freedom: vertical, longitudinal, lateral, pitch and roll motions. The gust response equations are linearized about the vehicle trim state and the blade steady-state deflected position, and then solved by time integration. The blade bending moments, which determine blade stresses, are evaluated using the force summation technique. Systematic studies are made to identify the importance of several parameters including dynamic stall, forward speed, lag stiffness, gust profile, gust penetration rate and gust velocity direction.

Bir, Gunjit↗
NASA NTRS1991

Thermal stresses and deflections of cross-ply laminated plates using refined plate theories

Exact analytical solutions of refined plate theories are developed to study the thermal stresses and deflections of cross-ply rectangular plates. The state-space approach in conjunction with the Levy method is used to solve exactly the governing equations of the theories under various boundary conditions. Numerical results of the higher-order theory of Reddy for thermal stresses and deflections are compared with those obtained using the classical and first-order plate theories.

Khdeir, A. A.↗
NASA NTRS1993

Method and apparatus for measuring the strain developed in a coated surface

A method and apparatus are provided for determining the strain developed in a coated surface. A beam with a coating on a surface thereof is mounted as a cantilever and a force is applied to the free end of the beam to cause deflection of the beam until the coating on the beam fails. The strain in the beam, and hence in the coating at the point of failure, is determined based on the dimensions of the beam, the point along the beam where failure of the coating occurs and the amount of deflection of the beam, and this determination is made independently of the temperature of the beam and the material from which the beam is made. The determination is made based on the equation E= 1.5hdx/l(exp 3), where E is strain, h is the beam thickness, d is the beam deflection, x is the distance from the free end of the beam to the point where failure of the coating occurred, and l is the length of the beam.

Smith, Sheldon M.↗
NASA NTRS1974

Estimation of material properties of a nonlinearly elastic bar

A method of determining certain characteristic flexural rigidities and elastic properties of nonlinearly elastic materials is presented. An estimation method utilizing perturbation methods and a least squares fitting technique is used to solve the nonlinear differential equation derived from the moment curvature relation, subject to boundary values representing deflections of the bar at discrete points. Deflection data from numerical simulations of a nonlinearly elastic, prismatic bar are used to demonstrate the estimation method. Numerical experiments relating the accuracy of the identification to the number and accuracy of the boundary values are presented. Conclusions based on the numerical experiments are included.

Baker, B. E.↗
NASA NTRS1975

Prediction of unsteady aerodynamic loadings caused by leading edge and trailing edge control surface motions in subsonic compressible flow: Computer program description

A digital computer program has been developed to calculate unsteady loadings caused by motions of lifting surfaces with leading edge or trailing edge controls based on the subsonic kernel function approach. The pressure singularities at hinge line and side edges have been extracted analytically as a preliminary step to solving the integral equation by collocation. The program calculates generalized aerodynamic forces for user supplied deflection modes. Optional intermediate output includes pressure at an array of points, and sectional generalized forces. From one to six controls on the half span can be accommodated.

Redman, M. C.↗
NASA NTRS1979

Reduction of computer usage costs in predicting unsteady aerodynamic loadings caused by control surface motions: Computer program description

A digital computer program was developed to calculate unsteady loadings caused by motions of lifting surfaces with leading edge and trailing edge controls based on the subsonic kernel function approach. The pressure singularities at hinge line and side edges were extracted analytically as a preliminary step to solving the integral equation of collocation. The program calculates generalized aerodynamic forces for user supplied deflection modes. Optional intermediate output includes pressure at an array of points, and sectional generalized forces. From one to six controls on the half span can be accomodated.

Petrarca, J. R.↗
NASA NTRS1986

Vibro-acoustics for Space Station applications

An analytical procedure has been developed to study noise generation in a double wall and single wall cylindrical shell due to mechanical point loads. The objective of this study is to develop theoretical procedures for parametetric evaluation of noise generation andd noise transmission for the habitability modules of the proposed Space Station operation. The solutions of the governing acoustic-structural equations are obtained utilizing modal decomposition. The numerical results include modal frequencies, deflection response spectral densities and interior noise sound pressure levels.

Vaicaitis, R.↗
NASA NTRS1986

On mixed and displacement finite element models of a refined shear deformation theory for laminated anisotropic plates

An improved plate theory that accounts for the transverse shear deformation is presented, and mixed and displacement finite element models of the theory are developed. The theory is based on an assumed displacement field in which the inplane displacements are expanded in terms of the thickness coordinate up to the cubic term and the transverse deflection is assumed to be independent of the thickness coordinate. The governing equations of motion for the theory are derived from the Hamilton's principle. The theory eliminates the need for shear correction factors because the transverse shear stresses are represented parabolically. A mixed finite element model that uses independent approximations of the displacements and moments, and a displacement model that uses only displacements as degrees of freedom are developed. A comparison of the numerical results for bending with the exact solutions of the new theory and the three-dimensional elasticity theory shows that the present theory (and hence the finite element models) is more accurate than other plate-theories of the same order.

Reddy, J. N.↗
NASA NTRS1952

A Miniature Electrical Pressure Gage Utilizing a Stretched Flat Diagram

A variable-air-gap, inductance-type, electrical pressure gage is described that is basically 7/16 inch in diameter and 1/4 inch in thickness. The gage was designed to measure accurately pressures fluctuating at high frequencies and has proved to be a value as a general-purpose electrical gage for aeronautical work where small size and minimum response to acceleration forces are important factors. Design equations and curves are presented which can be used to predict the deflections and fundamental natural frequencies of stretched flat diaphragms.

INSTRUMENTS, LABORATORY↗
NASA NTRS1993

Proposed framework for thermomechanical life modeling of metal matrix composites

The framework of a mechanics of materials model is proposed for thermomechanical fatigue (TMF) life prediction of unidirectional, continuous-fiber metal matrix composites (MMC's). Axially loaded MMC test samples are analyzed as structural components whose fatigue lives are governed by local stress-strain conditions resulting from combined interactions of the matrix, interfacial layer, and fiber constituents. The metallic matrix is identified as the vehicle for tracking fatigue crack initiation and propagation. The proposed framework has three major elements. First, TMF flow and failure characteristics of in situ matrix material are approximated from tests of unreinforced matrix material, and matrix TMF life prediction equations are numerically calibrated. The macrocrack initiation fatigue life of the matrix material is divided into microcrack initiation and microcrack propagation phases. Second, the influencing factors created by the presence of fibers and interfaces are analyzed, characterized, and documented in equation form. Some of the influences act on the microcrack initiation portion of the matrix fatigue life, others on the microcrack propagation life, while some affect both. Influencing factors include coefficient of thermal expansion mismatch strains, residual (mean) stresses, multiaxial stress states, off-axis fibers, internal stress concentrations, multiple initiation sites, nonuniform fiber spacing, fiber debonding, interfacial layers and cracking, fractured fibers, fiber deflections of crack fronts, fiber bridging of matrix cracks, and internal oxidation along internal interfaces. Equations exist for some, but not all, of the currently identified influencing factors. The third element is the inclusion of overriding influences such as maximum tensile strain limits of brittle fibers that could cause local fractures and ensuing catastrophic failure of surrounding matrix material. Some experimental data exist for assessing the plausibility of the proposed framework.

Halford, Gary R.↗
NASA NTRS2015

Acceleration and Velocity Sensing from Measured Strain

A simple approach for computing acceleration and velocity of a structure from the strain is proposed in this study. First, deflection and slope of the structure are computed from the strain using a two-step theory. Frequencies of the structure are computed from the time histories of strain using a parameter estimation technique together with an autoregressive moving average model. From deflection, slope, and frequencies of the structure, acceleration and velocity of the structure can be obtained using the proposed approach. Simple harmonic motion is assumed for the acceleration computations, and the central difference equation with a linear autoregressive model is used for the computations of velocity. A cantilevered rectangular wing model is used to validate the simple approach. Quality of the computed deflection, acceleration, and velocity values are independent of the number of fibers. The central difference equation with a linear autoregressive model proposed in this study follows the target response with reasonable accuracy. Therefore, the handicap of the backward difference equation, phase shift, is successfully overcome.

shape sensing↗
NASA NTRS1976

Higher-order effects of initial deformation on the vibrations of crystal plates

A system of plate equations for the thickness-shear and flexural vibrations superposed on large initial deflection due to bending is derived; in the stress-strain relations, the terms associated with the fourth-order elastic stiffness coefficients are retained. An explicit formula for the change in the fundamental cut-off thickness shear frequency is obtained, and the effects of the terms associated with the fourth-order constants appear to be significant for large gradients of the rotation angles.

Markenscoff, X.↗
NASA NTRS1984

Error analysis and correction of discrete solutions from finite element codes

Many structures are an assembly of individual shell components. Therefore, results for stresses and deflections from finite element solutions for each shell component should agree with the equations of shell theory. This paper examines the problem of applying shell theory to the error analysis and the correction of finite element results. The general approach to error analysis and correction is discussed first. Relaxation methods are suggested as one approach to correcting finite element results for all or parts of shell structures. Next, the problem of error analysis of plate structures is examined in more detail. The method of successive approximations is adapted to take discrete finite element solutions and to generate continuous approximate solutions for postbuckled plates. Preliminary numerical results are included.

Thurston, G. A.↗
NASA NTRS1994

Coupling equivalent plate and finite element formulations in multiple-method structural analyses

A coupled multiple-method analysis procedure for use late in conceptual design or early in preliminary design of aircraft structures is described. Using this method, aircraft wing structures are represented with equivalent plate models, and structural details such as engine/pylon structure, landing gear, or a 'stick' model of a fuselage are represented with beam finite element models. These two analysis methods are implemented in an integrated multiple-method formulation that involves the assembly and solution of a combined set of linear equations. The corresponding solution vector contains coefficients of the polynomials that describe the deflection of the wing and also the components of translations and rotations at the joints of the beam members. Two alternative approaches for coupling the methods are investigated; one using transition finite elements and the other using Lagrange multipliers. The coupled formulation is applied to the static analysis and vibration analysis of a conceptual design model of a fighter aircraft. The results from the coupled method are compared with corresponding results from an analysis in which the entire model is composed of finite elements.

VIBRATION ANALYSIS↗
NASA NTRS2000

Polar Plate Theory for Orthogonal Anisotropy

Laminated fiber-reinforced (or filamentary) composites are used today for their high strength-to-weight and stiffness-to-weight ratios. However, because of the anisotropic behavior of composites, determining the response on a macroscopic scale is challenging. This is particularly evident in the evaluation of the governing differential equations of a circular disk with the fibers of the lamina oriented with rectilinear orthogonality. This includes any situation involving a composite plate of circular geometry in which out-of-plane displacements due to load are desired, such as fastener pull through loading of a composite plate. Current analysis techniques use numerical methods with rectilinear coordinate systems to solve problems with circular geometry. These analyses over predict plate stiffness by 20% and underpredict failure by 70%. Consequently, there is a need to transform classical composite plate theory to a polar coordinate system. In order to better analyze structures with circular geometries the classical composite plate equations are transformed into the plate equations for a rectilinearly anisotropic composite in polar coordinates. A composite plate is typically a laminate of fibers in rectilinear directions. Subsequent to the lay-tip the necessary geometry is cut out of a rectangular plate. In a similar manner, the derivation of the plate equation starts with the fundamental definitions of strain, displacement and curvature and incorporates the material property angular dependence into the equilibrium equations for a differential polar element. In the transformed state, the stiffness coefficients are no longer constant, adding to the complexity of the governing differential equations. This paper discusses the new derivation and evaluation of the plate equations for a circular composite disk with orthogonal rectilinear anisotropy. The resultant new three partial differential equations, which describe the circular anisotropic plate, can be used to evaluate out-of-plane displacements for given load conditions in design of composite Structures. Without the formation of these unique plate equations, design of such structures is not a precise engineering accomplishment due to the lack of precise design tools. Such structures are over designed to compensate and costly tests need to be performed after production to validate safety. Though impossible to present the mathematical solution within the limits of this paper, the application of the newly derived plate equation in its orthotropic form for a balanced symmetric laminate compared favorably with test results and surpassed the results of standard numerical methods. Within the limitations of the problem foundation the predictive model provides a mechanism for establishing out-of-plane deflection levels for a circular composite plate. Future work in this area should include incorporating the circular composite plate equations in Finite Element Models. The new anisotropic polar plate equations call be utilized as a design tool so that the design more accurately meets the requirements, thus taking full advantage of the weight savings of composites. These accomplishments have not previously been presented to the engineering community nor ever proposed to the IAF. Should the proposed paper be accepted for presentation, attendance is assured.

Bailey, Michelle D.↗
NASA NTRS1930

Pressure element of constant logarithmic stiffness for temperature compensated altimeter

The usual type of altimeter contains a pressure element, the deflections of which are approximately proportional to pressure changes. An evenly divided altitude scale is secured by using a mechanism between the pressure element and pointer which gives the required motion of the pointer. A temperature-compensated altimeter was constructed at the Bureau of Standards for the Bureau of Aeronautics of the Navy Department which contained a manually operated device for controlling the multiplication of the mechanism to the extent necessary for temperature compensation. The introduction of this device made it difficult to adjust the multiplying mechanism to fit an evenly divided altitude scale. To meet this difficulty a pressure element was designed and constructed which gave deflections which were proportional to altitude; that is, to the logarithm of the pressure. The element consisted of a metal bellows of the sylphon type coupled to an internal helical spring which was designed so as to have a variable number of active coils. This report presents a description of and laboratory data relating to the special pressure element for the altimeter. In addition equations which apply generally to springs and pressure elements of constant logarithmic stiffness are developed, including the deflection and the spacing between the coils in terms of the constants of the helical spring and pressure elements. (author)

Brombacher, W G↗
NASA NTRS1994

Effect of Reynolds number and turbulence on airfoil aerodynamics at -90-degree incidence

A method has been developed for calculating the viscous flow about airfoils with and without deflected flaps at -90 deg incidence. This method provides for the solution of the unsteady incompressible Navier-Stokes equations by means of an implicit technique. The solution is calculated on a body-fitted computational mesh using a staggered-grid method. The vorticity is defined at the node points, and the velocity components are defined at the mesh-cell sides. The staggered-grid orientation provides for accurate representation of vorticity at the node points and the continuity equation at the mesh-cell centers. The method provides for the noniterative solution of the flowfield and satisfies the continuity equation to machine zero at each time step. The method is evaluated in terms of its stability to predict two-dimensional flow about an airfoil at -90-deg incidence for varying Reynolds number and laminar/turbulent models. The variations of the average loading and surface pressure distribution due to flap deflection, Reynolds number, and laminar or turbulent flow are presented and compared with experimental results. The comparisom indicate that the calculated drag and drag reduction caused by flap deflection and the calculated average surface pressure are in excellent agreement with the measured results at a similar Reynolds number.

Stremel, Paul M.↗