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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Aeroelastic behavior of low aspect ratio metal and composite blades

The aeroelastic stability of titanium and composite blades of low aspect ratio is examined over a range of design parameters, using a Rayleigh-Ritz formulation. The blade modes include a plate-type mode to account for chordwise bending. Chordwise flexibility is found to have a significant effect on the unstalled supersonic flutter of low aspect ratio blades, and also on the stability of tip sections of shrouded fan blades. For blades with a thickness of less than approximately four percent of chord, the chordwise, second bending, and first torsion branches are all unstable at moderately high supersonic Mach numbers. For composite blades, the important structural coupling between bending and torsion cannot be modeled properly unless chordwise bending is accounted for. Typically, aft fiber sweep produces beneficial bending-torsion coupling that is stabilizing, whereas forward fiber sweep has the opposite effect. By using crossed-ply laminate configurations, critical aeroelastic modes can be stabilized.

White, J. F., III↗
NASA NTRS1991

Thermal buckling and postbuckling of symmetrically laminated composite plates

The thermal buckling and postbuckling response of symmetrically laminated composite plates are discussed. Using variational methods in conjunction with a Rayleigh-Ritz formulation, thermal buckling and postbuckling are investigated for two laminates, a (+/- 45/0/90) and a (+/- 45/02), under two different simple support conditions, fixed and sliding. These laminates are subjected to the condition of a uniform temperature change. The effects of the principal material axis not being aligned with the edges of the plate, referred to here as material axis skewing, are also investigated. Although differences between buckling temperatures for the two support conditions were small, support conditions can have a large influence on thermal postbuckling response. In general, plates with fixed simple supports deflect more than plates with sliding simple supports. In addition, support conditions can influence modal interaction. Skewing of the material axis decreases the buckling temperatures of both laminates and, like fixed support conditions, causes increased postbuckling deflections. Skewing also influences modal interaction.

Meyers, C. A.↗
NASA NTRS1992

Thermally-induced, geometrically nonlinear response of symmetrically laminated composite plates

This paper discusses the thermally-induced geometrically nonlinear response of symmetrically laminated composite plates. The plate response is due to a temperature increase that is uniform in the plane of the plate but has a slight gradient through the thickness. The case of a completely uniform temperature increase but with an initial out-of-plane imperfection in the plate is also considered. Because they are closely allied problems, thermal buckling and postbuckling are discussed. Using variational methods in conjunction with a Rayleigh-Ritz formulation, these responses are investigated for two laminates, a (+/- 45/0/90)s and a (+/- 45/02)s, under two different simple support conditions.

Meyers, C. A.↗
NASA NTRS1991

Thermal buckling of symmetrically laminated composite plates

This paper discusses an investigation into the thermal buckling of symmetrically laminated composite plates. In this study thermal buckling is investigated for laminates under two different simple support conditions, fixed and sliding. These laminates are subjected to the conditions of a uniform temperature change, and a temperature change varying linearly along the length of the plate. The effects of the principal material axes not being aligned with the edges of the plate are also investigated. The buckling response is studied using variational methods, specifically the Trefftz criterion. A Rayleigh-Ritz formulation is used to obtain numerical results from the formulations for the prebuckling response and the buckling response.

Meyers, C. A.↗
NASA NTRS1993

Vibration analysis of heated anisotropic plates with free edge conditions

Tabular and plotted results are presented (as a function of lamination angle and temperature) for the first two vibration frequencies and mode shapes of a heated, single-layer Boron/epoxy laminate. A Ritz formulation is used to determine the thermally induced in-plane forces and the out-of-plane vibration frequencies. This approach is formulated in terms of the out-of-plane displacement and the in-plane stress function; both the displacement and the stress function are expressed as simple algebraic polynomials modified to satisfy the essential boundary conditions. Heating is applied as a steady-state temperature distribution; material properties are considered to be temperature-dependent. To establish the correctness and effectiveness of the method, the in-plane forces are compared with Fourier series analytical results.

Locke, James E.↗
NASA NTRS1989

On modelling the residual strength of impact damaged, compression loaded laminates

A methodology is presented to predict the residual compression strength of impact damaged composite laminates by considering the competing failure modes of local delamination buckling and compression failure. The minimum delamination buckling load and the location of the first local region to buckle are determined by a Rayleigh-Ritz analysis. The Rayleigh-Ritz analysis is formulated to account for the multiple delamination locations, Poisson's ratio mismatch between sublaminates and possible bending-stretching coupling behavior of the delaminated regions. The compression failure load is determined by a modified maximum strain criterion applied in the delaminated region. The minimum delamination buckling and compression failure loads may be compared to the global buckling load to predict initial failure. For non-catastrophic failures, failure sequences are predicted in an iterative manner. Analytical predictions for sequential failure modes and loads are shown to correlate well with experimental results. A comparative evaluation of various delamination buckling models and their accuracy in predicting experimental results is also presented.

Davidson, B. D.↗
NASA NTRS1991

Periodic trim solutions with HP-version finite elements in time

Finite Element in Time has been proven to be a powerful alternative solving strategy for the rotor craft trim problem. Additionally, Finite Element Method in Time has been developed in various versions like time-marching framework, Galerkin framework, Rayleigh-Ritz framework, and mixed formulation. Recently, this method was applied to the rotorcraft trim problem to obtain linearized solutions. The rotorcraft trim problem consists of trying to find a period solution for period-coefficient, differential equations subject to side constraints where certain force and momentum balance equations are forced to be equal to zero. There are free (or trim) parameters that are chosen to meet these side constraints. This project aims at expanding the application, in terms of the rotorcraft trim problem, from a linearized solution to nonlinear solution.

Source record↗
NASA NTRS1995

Analytic Sensitivity and Approximation of Skin Buckling Constraints in Wing-Shape Synthesis

Explicit expressions for terms of the stiffness and geometric stiffness matrices are derived for the buckling analysis of trapezoidal fiber composite wing skin panels. The formulation is based on Ritz analysis using simple polynomials, and leads to explicit expressions for the analytic sensitivities of the stiffness and geometric stiffness matrices with respect to layer thickness, fiber directions, and panel shape. Integration with wing box analysis using either the equivalent plate approach or the finite element method, makes it possible to obtain sensitivities of panel buckling constraints with respect to wing planform shape or locations of internal ribs and spars. The analytic sensitivities are used to construct approximations of panel buckling constraints for integrated wing/panel design synthesis.

Livne, Eli↗
NASA NTRS1988

A Rayleigh-Ritz approach to structural parameter identification

This paper is concerned with the identification of parameter distributions in large space structures. The formulation is based on a Rayleigh-Ritz type approach working with the actual displacement at a given number of points in the structure. The parameter distributions are expanded in terms of known admissible functions multiplied by unknown coefficients, and the identification process reduces to the determination of these coefficients. The procedure uses a perturbation approach, beginning with a postulated set of parameters and iterating to the actual values in an incremental fashion.

Meirovitch, L.↗
NASA NTRS1997

Wing Weight Optimization Under Aeroelastic Loads Subject to Stress Constraints

A minimum weight optimization of the wing under aeroelastic loads subject to stress constraints is carried out. The loads for the optimization are based on aeroelastic trim. The design variables are the thickness of the wing skins and planform variables. The composite plate structural model incorporates first-order shear deformation theory, the wing deflections are expressed using Chebyshev polynomials and a Rayleigh-Ritz procedure is adopted for the structural formulation. The aerodynamic pressures provided by the aerodynamic code at a discrete number of grid points is represented as a bilinear distribution on the composite plate code to solve for the deflections and stresses in the wing. The lifting-surface aerodynamic code FAST is presently being used to generate the pressure distribution over the wing. The envisioned ENSAERO/Plate is an aeroelastic analysis code which combines ENSAERO version 3.0 (for analysis of wing-body configurations) with the composite plate code.

Kapania, Rakesh K.↗
NASA NTRS1976

Response of space shuttle insulation panels to acoustic noise pressure

The response of reusable space shuttle insulation panels to random acoustic pressure fields are studied. The basic analytical approach in formulating the governing equations of motion uses a Rayleigh-Ritz technique. The input pressure field is modeled as a stationary Gaussian random process for which the cross-spectral density function is known empirically from experimental measurements. The response calculations are performed in both frequency and time domain.

Vaicaitis, R.↗
NASA NTRS1993

Hybrid equations of motion for flexible multibody systems using quasi-coordinates

A variety of engineering systems, such as automobiles, aircraft, rotorcraft, robots, spacecraft, etc., can be modeled as flexible multibody systems. The individual flexible bodies are in general characterized by distributed parameters. In most earlier investigations they were approximated by some spatial discretization procedure, such as the classical Rayleigh-Ritz method or the finite element method. This paper presents a mathematical formulation for distributed-parameter multibody systems consisting of a set of hybrid (ordinary and partial) differential equations of motion in terms of quasi-coordinates. Moreover, the equations for the elastic motions include rotatory inertia and shear deformation effects. The hybrid set is cast in state form, thus making it suitable for control design.

Meirovitch, L.↗
NASA NTRS1985

Spline-based Rayleigh-Ritz methods for the approximation of the natural modes of vibration for flexible beams with tip bodies

Rayleigh-Ritz methods for the approximation of the natural modes for a class of vibration problems involving flexible beams with tip bodies using subspaces of piecewise polynomial spline functions are developed. An abstract operator theoretic formulation of the eigenvalue problem is derived and spectral properties investigated. The existing theory for spline-based Rayleigh-Ritz methods applied to elliptic differential operators and the approximation properties of interpolatory splines are useed to argue convergence and establish rates of convergence. An example and numerical results are discussed.

Rosen, I. G.↗
NASA NTRS1986

Spline-based Rayleigh-Ritz methods for the approximation of the natural modes of vibration for flexible beams with tip bodies

Rayleigh-Ritz methods for the approximation of the natural modes for a class of vibration problems involving flexible beams with tip bodies using subspaces of piecewise polynomial spline functions are developed. An abstract operator-theoretic formulation of the eigenvalue problem is derived and spectral properties investigated. The existing theory for spline-based Rayleigh-Ritz methods applied to elliptic differential operators and the approximation properties of interpolatory splines are used to argue convergence and establish rates of convergence. An example and numerical results are discussed.

Rosen, I. G.↗
NASA NTRS1977

Modal characteristics of crossed rectangular waveguides

An integral-eigenvalue problem is formulated for a crossed rectangular waveguide and solved numerically by applying the Ritz-Galerkin method. Theoretical formulas for determining cutoff frequencies and modal-field expressions are obtained for the specific case of a symmetrical rectangular waveguide, cutoff frequencies are calculated numerically, and the results are verified by comparison with available experimental data. The modal fields are expressed in terms of Fourier series for both TE and TM modes. It is found that the bandwidth can be increased to a maximum of 38% when the waveguide dimensions are properly selected and that the numerical results are in agreement with those computed by the method of partial regions. Some practical applications of the modal-field equations are briefly noted.

Lin, F.-L. C.↗
NASA NTRS2014

In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part I: Linear Theory

Conical shell theory and piston theory aerodynamics are used to study the aeroelastic stability of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). Structural models of the TPS consist of single or multiple orthotropic conical shell systems resting on several circumferential linear elastic supports. The shells in each model may have pinned (simply-supported) or elastically-supported edges. The Lagrangian is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the equations of motion. The natural modes of vibration and aeroelastic stability boundaries are found by calculating the eigenvalues and eigenvectors of a large coefficient matrix. When the in-flight configuration of the TPS is approximated as a single shell without elastic supports, asymmetric flutter in many circumferential waves is observed. When the elastic supports are included, the shell flutters symmetrically in zero circumferential waves. Structural damping is found to be important in this case. Aeroelastic models that consider the individual TPS layers as separate shells tend to flutter asymmetrically at high dynamic pressures relative to the single shell models. Several parameter studies also examine the effects of tension, orthotropicity, and elastic support stiffness.

Goldman, Benjamin D.↗
NASA NTRS2015

In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part II: Nonlinear Theory and Extended Aerodynamics

Conical shell theory and a supersonic potential flow aerodynamic theory are used to study the nonlinear pressure buckling and aeroelastic limit cycle behavior of the thermal protection system for NASA's Hypersonic Inflatable Aerodynamic Decelerator. The structural model of the thermal protection system consists of an orthotropic conical shell of the Donnell type, resting on several circumferential elastic supports. Classical Piston Theory is used initially for the aerodynamic pressure, but was found to be insufficient at low supersonic Mach numbers. Transform methods are applied to the convected wave equation for potential flow, and a time-dependent aerodynamic pressure correction factor is obtained. The Lagrangian of the shell system is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the governing differential-algebraic equations of motion. Aeroelastic limit cycle oscillations and buckling deformations are calculated in the time domain using a Runge-Kutta method in MATLAB. Three conical shell geometries were considered in the present analysis: a 3-meter diameter 70 deg. cone, a 3.7-meter 70 deg. cone, and a 6-meter diameter 70 deg. cone. The 6-meter configuration was loaded statically and the results were compared with an experimental load test of a 6-meter HIAD. Though agreement between theoretical and experimental strains was poor, the circumferential wrinkling phenomena observed during the experiments was captured by the theory and axial deformations were qualitatively similar in shape. With Piston Theory aerodynamics, the nonlinear flutter dynamic pressures of the 3-meter configuration were in agreement with the values calculated using linear theory, and the limit cycle amplitudes were generally on the order of the shell thickness. The effect of axial tension was studied for this configuration, and increasing tension was found to decrease the limit cycle amplitudes when the circumferential elastic supports were neglected, but resulted in more complex behavior when the supports were included. The nominal flutter dynamic pressure of the 3.7-meter configuration was significantly lower than that of the 3-meter, and it was found that two sets of natural modes coalesce to flutter modes near the same dynamic pressure. This resulted in a significant drop in the limit cycle frequencies at higher dynamic pressures, where the flutter mode with the lower frequency becomes more critical. Pre-buckling pressure loads and the aerodynamic pressure correction factor were studied for all geometries, and these effects resulted in significantly lower flutter boundaries compared with Piston Theory alone. The maximum dynamic pressure predicted by aerodynamic simulations of a proposed 3.7-meter HIAD vehicle was still lower than any of the calculated flutter dynamic pressures, suggesting that aeroelastic effects for this vehicle are of little concern.

Goldman, Benjamin D.↗
NASA NTRS1997

Improvements in Block-Krylov Ritz Vectors and the Boundary Flexibility Method of Component Synthesis

A method of dynamic substructuring is presented which utilizes a set of static Ritz vectors as a replacement for normal eigenvectors in component mode synthesis. This set of Ritz vectors is generated in a recurrence relationship, proposed by Wilson, which has the form of a block-Krylov subspace. The initial seed to the recurrence algorithm is based upon the boundary flexibility vectors of the component. Improvements have been made in the formulation of the initial seed to the Krylov sequence, through the use of block-filtering. A method to shift the Krylov sequence to create Ritz vectors that will represent the dynamic behavior of the component at target frequencies, the target frequency being determined by the applied forcing functions, has been developed. A method to terminate the Krylov sequence has also been developed. Various orthonormalization schemes have been developed and evaluated, including the Cholesky/QR method. Several auxiliary theorems and proofs which illustrate issues in component mode synthesis and loss of orthogonality in the Krylov sequence have also been presented. The resulting methodology is applicable to both fixed and free- interface boundary components, and results in a general component model appropriate for any type of dynamic analysis. The accuracy is found to be comparable to that of component synthesis based upon normal modes, using fewer generalized coordinates. In addition, the block-Krylov recurrence algorithm is a series of static solutions and so requires significantly less computation than solving the normal eigenspace problem. The requirement for less vectors to form the component, coupled with the lower computational expense of calculating these Ritz vectors, combine to create a method more efficient than traditional component mode synthesis.

Carney, Kelly Scott↗