Search NASA⌕ Search

SEARCH · Search NASA

Results for “structural equation model”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

Flutter Analysis for Turbomachinery Using Volterra Series

The objective of this paper is to describe an accurate and efficient reduced order modeling method for aeroelastic (AE) analysis and for determining the flutter boundary. Without losing accuracy, we develop a reduced order model based on the Volterra series to achieve significant savings in computational cost. The aerodynamic force is provided by a high-fidelity solution from the Reynolds-averaged Navier-Stokes (RANS) equations; the structural mode shapes are determined from the finite element analysis. The fluid-structure coupling is then modeled by the state-space formulation with the structural displacement as input and the aerodynamic force as output, which in turn acts as an external force to the aeroelastic displacement equation for providing the structural deformation. NASA's rotor 67 blade is used to study its aeroelastic characteristics under the designated operating condition. First, the CFD results are validated against measured data available for the steady state condition. Then, the accuracy of the developed reduced order model is compared with the full-order solutions. Finally the aeroelastic solutions of the blade are computed and a flutter boundary is identified, suggesting that the rotor, with the material property chosen for the study, is structurally stable at the operating condition, free of encountering flutter.

computational fluid dynamics↗
NASA NTRS1975

Stability of localized plasma model in two and three dimensions

Stability against catastrophic radial collapse is demonstrated for initially well-behaved, localized solutions in a class of two- and three-dimensional wave equations characterized by saturating nonlinearities, which model various electrostatic and electromagnetic 'caviton' structures in an asymptotically uniform plasma. This result contrasts sharply with mathematical predictions of equations with low-order nonlinearities. Discrete classes of possible quasistationary modes exhibit features comparable to atomic wave functions and differ qualitatively from one-dimensional structures.

Wilcox, J. Z.↗
NASA NTRS1987

Computational methods for vortex dominated compressible flows

The principal objectives were to: understand the mechanisms by which Euler equation computations model leading edge vortex flows; understand the vortical and shock wave structures that may exist for different wing shapes, angles of incidence, and Mach numbers; and compare calculations with experiments in order to ascertain the limitations and advantages of Euler equation models. The initial approach utilized the cell centered finite volume Jameson scheme. The final calculation utilized a cell vertex finite volume method on an unstructured grid. Both methods used Runge-Kutta four stage schemes for integrating the equations. The principal findings are briefly summarized.

Murman, Earll M.↗
NASA NTRS1987

Self-pulsing and bichromatic emission in homogeneously broadened bidirectional ring lasers

The effects of saturation-induced Bragg gratings on the mode structure and dynamics of bidirectional homogeneously broadened ring lasers are studied. The grating is viewed as a distributed feedback medium in a ring cavity and modes appropriate to such a structure are used. A Fourier decomposed rate equation model is developed to study the behavior of these modes above threshold. The difference in the properties of these solutions from the modes of an unfilled ring cavity lead to the possibility of bichromatic emission and both regular undamped and irregular damped self-pulsing.

Rabinovich, W. S.↗
NASA NTRS1994

Steepened structures in equatorial spread F. 2: Theory

This paper investigates the properties of a one-dimensional fluid model of plasma convection in the equatorial F region ionosphere. The model equations are similar in form to Burgers equation except for additional higher-order spatial derivatives. Like Burgers equation, solution to the model have the form of propagating, shocklike structures. Numerical simulations of the model closely resemble the steepened structures observed by sounding rocket plasma density probes within equatorial spread F. Simulated denstiy power spectra, like the spectra computed from in situ data, seem to possess power law forms with a break at wavelengths of about 100 m. The precise wavenumber of the spectral break is determined by the ambipolar diffusion coefficient. The model predicts that electric field fluctuations perpendicular to the direction of plasma steepening should be proportional to the plasma density fluctuations. Electric field fluctuations parallel to the steepening will be due primarily to the ambipolar field and have a Boltzmann relationship with density (square of the absolute value of delta E) approximately equal to (K(exp 2))(square of the absolute value of (delta n/n)). At wavelengths less than about 300 m, the ambipolar field should be the dominant component of the total field intensity.

Hysell, D. L↗
NASA NTRS1995

Nonlinear Stability of Supersonic Jets

This paper presents stability calculations made for a shock-free supersonic jet using the model based on parabolized stability equations. In this analysis the large-scale structures, which play a dominant role in the mixing as well as the noise radiated, are modeled as instability waves. This model takes into consideration non-parallel flow effects and also nonlinear interaction of the instability waves. The stability calculations have been performed for different frequencies and mode numbers over a range of jet operating temperatures. Comparisons are made, where appropriate, with the solutions to Rayleigh's equation (linear, inviscid analysis with the assumption of parallel flow). The comparison of the solutions obtained using the two approaches show very good agreement.

Bhat, T. R. S.↗
NASA NTRS1977

Continuum models for static and dynamic analysis of repetitive lattices

A simple, rational approach is presented for developing continuum models for large repetitive lattice structures subjected to static and dynamic loadings. The procedure involves introducing kinematic assumptions to reduce the dimensionality of the lattice, and equating the strain and kinetic energies of the continuum model to those of the original lattice structure. The proposed procedure is applied to obtain effective elastic and dynamic characteristics of continuum plate models for double-layered grids. Numerical results are presented of stress and free vibration problems for two double-layered grids. These problems demonstrate the high accuracy of the continuum plate models developed. Also, an assessment is made of different approximations to these models.

Noor, A. K.↗
NASA NTRS1980

A magnetohydrodynamic model for corotating interplanetary structures

A model is developed which treats interplanetary structures as a small-scale incompressible Alfvenic fluctuation superposed on a large-scale background flow, and uses the complete magnetohydrodynamic equations and the full energy equation to describe the interplanetary structures. For steady-state corotating structures the model assumes the background flow to be field aligned, and the nonlinear system is treated as being composed of two subsets: one dealing with the expansion of the solar wind in stream tubes, the other with the interaction between neighboring stream tubes. The expansion subset has a singularity at Parker's critical radius, and the interaction subset has a singularity at the Alfvenic point. Concerning the region where the flow velocity is super-Alfvenic, the characteristic equation is derived, and a general method of numerical solution for the three-dimensional problems based on the characteristics theory is discussed. In addition, a viscous WKB solution of the microscale system is presented.

Whang, Y. C.↗
NASA NTRS1987

Modeling and identification of SCOLE

Vector differential equations for distributed structures; discretization (in space) of distributed structures; and parameter identification for the Spacecraft Control Laboratory Experiment (SCOLE) are examined.

Meirovitch, L.↗
NASA NTRS1989

On finite element implementation and computational techniques for constitutive modeling of high temperature composites

The research work performed during the past year on finite element implementation and computational techniques pertaining to high temperature composites is outlined. In the present research, two main issues are addressed: efficient geometric modeling of composite structures and expedient numerical integration techniques dealing with constitutive rate equations. In the first issue, mixed finite elements for modeling laminated plates and shells were examined in terms of numerical accuracy, locking property and computational efficiency. Element applications include (currently available) linearly elastic analysis and future extension to material nonlinearity for damage predictions and large deformations. On the material level, various integration methods to integrate nonlinear constitutive rate equations for finite element implementation were studied. These include explicit, implicit and automatic subincrementing schemes. In all cases, examples are included to illustrate the numerical characteristics of various methods that were considered.

Saleeb, A. F.↗
NASA NTRS1979

The wave structures of the Eady model of baroclinic instability

By solving the linear quasi-geostrophic set of equations pertinent to the Eady model, the complex eigenvalues and the eigenfunctions are obtained. The propagation speed and the growth rate are computed. Quantitative information is provided about the wave structures for several unstable models, a marginally stable mode, and a stable mode. The peculiarities concerning the amplitude and the phase variations of the waves are noted as the wavenumber varies from the unstable region to the stable region. Physical interpretations of the interrelationships among the dynamical variables are given, with a view toward revealing important aspects of the energy transfer from the basic state to the growing waves.

Hyun, J. M.↗
NASA NTRS1989

Six-degree-of-freedom aircraft simulation with mixed-data structure using the applied dynamics simulation language, ADSIM

A realistic simulation of an aircraft in the flight using the AD 100 digital computer is presented. The implementation of three model features is specifically discussed: (1) a large aerodynamic data base (130,00 function values) which is evaluated using function interpolation to obtain the aerodynamic coefficients; (2) an option to trim the aircraft in longitudinal flight; and (3) a flight control system which includes a digital controller. Since the model includes a digital controller the simulation implements not only continuous time equations but also discrete time equations, thus the model has a mixed-data structure.

Savaglio, Clare↗
NASA NTRS1990

Application of symbolic computations to the constitutive modeling of structural materials

In applications involving elevated temperatures, the derivation of mathematical expressions (constitutive equations) describing the material behavior can be quite time consuming, involved and error-prone. Therefore intelligent application of symbolic systems to faciliate this tedious process can be of significant benefit. Presented here is a problem oriented, self contained symbolic expert system, named SDICE, which is capable of efficiently deriving potential based constitutive models in analytical form. This package, running under DOE MACSYMA, has the following features: (1) potential differentiation (chain rule), (2) tensor computations (utilizing index notation) including both algebraic and calculus; (3) efficient solution of sparse systems of equations; (4) automatic expression substitution and simplification; (5) back substitution of invariant and tensorial relations; (6) the ability to form the Jacobian and Hessian matrix; and (7) a relational data base. Limited aspects of invariant theory were also incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet pre-defined order and simplify expressions so as to limit expression growth. Results are displayed, when applicable, utilizing index notation. SDICE was designed to aid and complement the human constitutive model developer. A number of examples are utilized to illustrate the various features contained within SDICE. It is expected that this symbolic package can and will provide a significant incentive to the development of new constitutive theories.

Arnold, Steven M.↗
NASA NTRS1973

Singular perturbation equations for flexible satellites

The dynamic model of a flexible satellite with n generalized structural position coordinates requires the solution of a set of N coupled nonlinear ordinary or partial differential equations. For single composite body satellites, N is equal to (n + 3). For dual-spin systems, N is equal to (n + 9). These equations usually involve time derivatives up to the second order. For large values of n, linearization of the system has so far been the only practicable way of solution. The present study shows a method of avoiding this linearization by reducing the N equations to three or nine nonlinear, coupled, first-order ordinary differential equations involving only the angular velocities of the composite bodies. The solutions for these angular velocities lead to linear equations in the n generalized structural position coordinates, which can then be solved by known methods.

Huang, T. C.↗
NASA NTRS1983

Modeling of flexible structures for active control

If a flexible structure has a plane of symmetry, the equations of motion can be split into two uncoupled sets, one for symmetrical motions and one for anti-symmetric motions. If there are m controls, it is often convenient to assign the linear combinations of controls that enter into the m lowest frequency modes and new controls. As an example the feed-support structure of a spacecraft antenna is considered. It is modeled as a tetrahedron made up of flexible bars and connected to the spacecraft by six short flexible legs containing force actuators and displacement sensors. Due to the three-sided symmetry of this structure, both the symmetric and the anti-symmetric equations of motion can be decoupled into two subsystems. The resulting four subsystems are: (1) pitch/fore-aft motions with four degrees of freedom (DOF), two controls, and one output (the fore-aft motion of the feed); (2) vertical motions with three DOF, one control, and one output (the vertical motion of the feed); (3) roll/lateral motions with four DOF, two controls, and one output (the lateral motions of the feed); and (4) yaw motion with one DOF, one control, and no output (the feed does not move during yaw motion).

Bryson, A. E., Jr.↗
NASA NTRS1996

Nonlinear stability of supersonic jets

The stability calculations made for a shock-free supersonic jet using the model based on parabolized stability equations are presented. In this analysis the large scale structures, which play a dominant role in the mixing as well as the noise radiated, are modeled as instability waves. This model takes into consideration non-parallel flow effects and also nonlinear interaction of the instability waves. The stability calculations have been performed for different frequencies and mode numbers over a range of jet operating temperatures. Comparisons are made, where appropriate, with the solutions to Rayleigh's equation (linear, inviscid analysis with the assumption of parallel flow). The comparison of the solutions obtained using the two approaches show very good agreement.

Tiwari, S. N.↗