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At least 523 records · Page 29

All sources NASA NTRS DOE OSTI

NASA NTRS1974

Development of technology for fluid-structure interaction modeling of a 1/8-scale dynamic model of shuttle External Tank (ET). Volume i: Technical report

A NASTRAN analysis of the external tank (ET) substructure of the 1/8-scale space shuttle structural dynamics model is described. The NASTRAN hydroelastic procedures were used to form a model of the liquid oxygen portion of the ET. Large computer storage requirements and running times were required unless these procedures were modified. Several possibilities were demonstrated including the substitution of the real for the complex eigenvalue routine and the use of the OMIT capability to reduce the number of fluid coordinates. A NASTRAN model of the complete ET was formed and reduced to 252 degrees of freedom. A review of the eigenvector extracted, using the unsymmetrical inverse power method, indicated that the structural OMIT's resulted in unsatisfactory modal deflections. Modifications to the NASTRAN hydroelastic capability appeared necessary to generate a successful ET model. An approach is described which, by assuming incompressibility, reduces the fluid representation to a symmetric mass matrix which can be added to the structural mass. The problem is solved using faster and more efficient eigenvalue routines. Using this approach the ET NASTRAN model was analyzed for three separate weight conditions.

Bernstein, M.↗

NASA NTRS1975

Relaxation methods in fluid mechanics

The present work considers the iterative solution of a coupled set of difference equations and examines methods that carry successive approximates to a state that is invariant with further iteration and independent of the initial guess. Methods are studied with regard to their efficiency and economy of computer resources. The basic principles of classical relaxation are set forth, with attention confined to linear elliptic equations. This discussion involves the evaluation of the spectral radius that is the magnitude of the eigenvalue with largest modulus. The subject of relaxation is then related to the study of ordinary differential equations and hyperbolic partial differential equations. Problems that occur when linearly dependent eigenvectors appear in the relaxation matrix are discussed, leading to multiply connected eigenvalues in the Jordan canonical form. Finally, a brief survey of relaxation methods used in aerodynamics is given.

Lomax, H.↗

NASA NTRS1975

Degree of interdependence among atmospheric optical thicknesses in spectral bands between 0.36-2.4 micron

The degree of dependence among the atmospheric optical thicknesses that are measured in nonselective absorption bands is studied. The observations were made previously in many spectral bands within the range 0.36-2.4 micron from near sea level in two continents where urban and industrial pollutions were weak. The sample covariance matrices and corresponding eigenvalues and eigenvectors are computed. The two highest eigenvalues account for 90% of the total variance in 10 spectral bands within the range 0.4-1.6 micron. The linear regression of the optical thickness on the total precipitable water vapor is computed to determine the attenuation coefficient that is associated with water vapor. This coefficient shows a rapid power-law decrease with wavelength in the visible spectrum and indicates that numerous water particles of radius 0.03-0.06 micron cause the attenuation.

Fraser, R. S.↗

NASA NTRS1976

Free vibration analysis of spinning flexible space structures

Efficient computation of natural frequencies and associated free vibration modes of spinning flexible structures is required to accurately determine the nature of interaction between the flexible structure and the attitude control system, which is vital in relating control torques to attitude angles. While structural discretization is effected by the finite element method, the resulting eigenvalue problem is solved by a combined Sturm sequence and inverse iteration procedure that yields a few specified roots and associated vectors. An eigenvalue procedure, based on a simultaneous iteration technique, provides efficient computation of the first few roots and vectors; a modal synthesis procedure proves to be useful for eigenproblem solutions of unusual structures such as spacecraft.

Gupta, K. K.↗

NASA NTRS1976

Free vibration analysis of spinning flexible space structures

Gupta, K. K.↗

NASA NTRS1977

CAVE: A computer code for two-dimensional transient heating analysis of conceptual thermal protection systems for hypersonic vehicles

A digital computer code CAVE (Conduction Analysis Via Eigenvalues), which finds application in the analysis of two dimensional transient heating of hypersonic vehicles is described. The CAVE is written in FORTRAN 4 and is operational on both IBM 360-67 and CDC 6600 computers. The method of solution is a hybrid analytical numerical technique that is inherently stable permitting large time steps even with the best of conductors having the finest of mesh size. The aerodynamic heating boundary conditions are calculated by the code based on the input flight trajectory or can optionally be calculated external to the code and then entered as input data. The code computes the network conduction and convection links, as well as capacitance values, given basic geometrical and mesh sizes, for four generations (leading edges, cooled panels, X-24C structure and slabs). Input and output formats are presented and explained. Sample problems are included. A brief summary of the hybrid analytical-numerical technique, which utilizes eigenvalues (thermal frequencies) and eigenvectors (thermal mode vectors) is given along with aerodynamic heating equations that have been incorporated in the code and flow charts.

Rathjen, K. A.↗

NASA NTRS1978

Eigenvalue/eigenvector assignment using output feedback

The problem of eigenvalue assignment in a linear time-invariant system using output feedback is considered. New sufficient conditions are derived to assign an almost arbitrary set of minimum (n,m + r - 1) distinct eigenvalues where n, m, and r are the number of states, inputs, and outputs, respectively. These conditions precisely identify the class of systems where such an assignment is impossible. The synthesis technique also highlights the freedom in selection of closed-loop eigenvectors under output feedback. The utility of eigenvalue/eigenvector assignment in transient response shaping is illustrated by the design of a controller for the lateral dynamics of an aircraft.

Srinathkumar, S.↗

NASA NTRS1978

On the append and continue features in NASTRAN

The APPEND feature is described which is applicable in the case of real eigenvalue analysis. This feature permitted the addition of new eigenvalues and eigenvectors to those already computed in a previously checkpointed run without re-executing the entire problem. The next feature was the CONTINUE feature which was applicable in the case of transient analysis of coupled equations. This feature enabled the integration of coupled equations to be continued beyond the last output time for which the solution was obtained in a previously checkpointed run (without re-executing the entire problem). These two features are illustrated by suitable examples.

Pamidi, P. R.↗

NASA NTRS1978

A method of weighted residuals with trigonometric basis functions for sound transmission in circular ducts

The method of weighted residuals (MWR) in the form of a modified Galerkin method with trigonometric basis functions is used to compute the transmission of sound in an axisymmetric duct. The method is used to generate the axial wave number for uniform ducts. These are compared with exact solutions generated by a formal eigenvalue routine in the hard-wall case and a Runge-Kutta integration eigenvalue scheme in the soft-wall case. The method is applicable to both flow and no-flow cases.

Vo, P. T.↗

NASA NTRS1979

Linear state feedback, quadratic weights, and closed loop eigenstructures

Results are given on the relationships between closed loop eigenstructures, state feedback gain matrices of the linear state feedback problem, and quadratic weights of the linear quadratic regulator. Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used for the first time to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalues and the directional derivatives of closed loop eigenvectors (with respect to a scalar multiplying the feedback gain matrix or the quadratic control weight). An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, sufficient conditions to be in it are given, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties.

Thompson, P. M.↗

NASA NTRS1979

The application of finite element techniques to acoustic transmission in lined ducts with flow

The finite element method (FEM) is used to analyze the propagation of sound in two-dimensional nonuniform ducts carrying a compressible subsonic mean flow. Galerkin and residual least squares (RLS) methods with natural and forced boundary conditions are considered. The accuracy of FEM results for the eigenvalue and transmission problems is assessed by comparison with alternative numerical schemes for nonuniform ducts. The results presented and those from associated investigations indicate that modal coupling is a significant feature of the acoustic field, especially at high Mach numbers. A multimodal model therefore appears to be essential if any reliable conclusions are to be drawn in the context of turbofan inlet regions. Improvements to the eigenvalue scheme following the implementation of higher-order Hermitian elements indicate a similar modification for the transmission problem.

Astley, R. J.↗

NASA NTRS1978

A computer program to automatically generate state equations and macro-models

A computer program, PROSE, that produces nonlinear state equations from a simple topological description of an electrical or mechanical network is described. Unnecessary states are also automatically eliminated, so that a simplified terminal circuit model is obtained. The program also prints out the eigenvalues of a linearized system and the sensitivities of the eigenvalue of largest magnitude.

Garrett, S. J.↗

NASA NTRS1979

Design of robust state feedback controllers via eigenvalue/eigenvector assignment

A new method of selecting a multivariable state feedback controller is presented. The resulting controller simultaneously realizes arbitrary closed-loop eigenvalues, approximates specified modal behavior and achieves low eigensystem sensitivity with respect to plant parameter variations. The method characterizes a vector space slightly larger than the null space of the closed-loop system matrix and projects a desired modal matrix onto this space. Sensitivity of eigenvalues and eigenvectors is then minimized local to the desired modal matrix using a gradient search technique. A tutorial example to illustrate the design procedure is given.

Mielke, R. R.↗

NASA NTRS1979

Analysis of integral controls in linear quadratic regulator design

The application of linear optimal control to the design of systems with integral control action on specified outputs is considered. Using integral terms in a quadratic performance index, an asymptotic analysis is used to determine the effect of variable quadratic weights on the eigenvalues and eigenvectors of the closed loop system. It is shown that for small integral terms the placement of integrator poles and gain calculation can be effectively decoupled from placement of the primary system eigenvalues. This technique is applied to the design of integral controls for a STOL aircraft outer loop guidance system.

Slater, G. L.↗

NASA NTRS1980

Linear state feedback, quadratic weights, and closed loop eigenstructures

Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalue and the directional derivatives of closed loop eigenvectors. An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties. An algorithm is presented that can be used to select a feedback gain matrix for the linear state feedback problem which produces a specified asymptotic eigenstructure. Another algorithm is given to compute the asymptotic eigenstructure properties inherent in a given set of quadratic weights. Finally, it is shown that optimal root loci for nongeneric problems can be approximated by generic ones in the nonasymptotic region.

Thompson, P. M.↗

NASA NTRS1981

Acoustic transmission in non-uniform ducts with mean flow. I - The method of weighted residuals. II - The finite element method

The problem of acoustic transmission through nonuniform ducts containing a high-speed subsonic flow is studied by means of the method of weighted residuals in the form of a modified Galerkin method and a Galerkin formulation of the finite element method. The method of weighted residuals is shown to employ the basis functions generated from eigenvalue calculations for the case of no flow, and is verified by comparison with exact eigenvalue calculations in the uniform duct case and numerical solutions of the one-dimensional form of the equations in the nonuniform duct case. The finite element scheme based on both the Galerkin method and the residual least squares method and employing eight-noded isoparametric elements is presented and used to investigate multimodal propagation by the coupling of the solution in the duct nonuniform section to modal expansions in uniform sections. Comparison of the results of the two methods reveals them to be in substantial agreement, and predicts the importance of multimodal interactions at high Mach numbers.

Eversman, W.↗

NASA NTRS1981

Existence of axisymmetric modes of thin cylindrical shells with axial displacement restraint

A necessary and sufficient condition is derived for the existence of the axisymmetric mode of cylindrical shells with a radial displacement having one half wave along the axis and axial displacement restrained at both ends. The condition is purely geometric and consists of an upper bound on the mean radius of thickness ratio for a given fixed value of the length to mean radius ratio, above which the mode with one half wave in radial displacement along the axis ceases to exist. The proof is based on enforcing two basic lemmas concerned with the simplicity of the eigenvalues of the shell and the uniform ordering of these eigenvalues with the number of nodes of their corresponding radial displacement eigenfunctions.

El-Raheb, M.↗

NASA NTRS1981

Vibration and local instability of thermally stressed plates

The vibration and buckling of a double wedge square cantilever plate has been investigated. It is shown that the free vibration modes, which occur at Delta T ref = 0, transition into the buckled modes which occur at Delta T ref = Delta T ref-cr for the respective mode. Delta T ref-cr for a particular mode is defined as the magnitude of thermal load at which the frequency of the particular mode vanishes. The analysis yields the same number of buckling eigenvalues and buckling modes as there are vibration eigenvalues and vibration modes. Gradual application of the load in the analysis permits the change in each vibration frequency of interest and its associated mode to be followed up to the load at which the frequency of the mode becomes zero. This constitutes the limit of linear theory. As the load is increased, the thin edges of the plate begin to deform during vibration. This local deformation, which begins in the vibration mode, is shown to transition into the phenomena of local edge buckling at Delta T ref-cr for the mode.

Bailey, C. D.↗