Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Programming, Linear”

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 1,045 records · Page 58

A symbolic framework to obtain mid-fidelity models of flexible multibody systems with application to horizontal-axis wind turbines

Abstract. The article presents a symbolic framework (also called computer algebra program) that is used to obtain, in symbolic mathematical form, the linear and nonlinear equations of motion of a mid-fidelity multibody system including rigid and flexible bodies. Our approach is based on Kane's method and a nonlinear shape function representation for flexible bodies. The shape function approach does not represent the state of the art for flexible multibody dynamics but is an effective trade-off to obtain mid-fidelity models with few degrees of freedom, taking advantage of the separation of space and time. The method yields compact symbolic equations of motion with implicit account of the constraints. The general and automatic framework facilitates the creation and manipulation of models with various levels of complexity by adding or removing degrees of freedom. The symbolic treatment allows for analytical gradients and linearized equations of motion. The linear and nonlinear equations can be exported to Python code or dedicated software. There are multiple applications, such as time domain simulation, stability analyses, frequency domain analyses, advanced controller design, state observers, and digital twins. In this article, we describe the method we used to systematically generate the equations of motion of multibody systems and present the implementation of the framework using the Python package SymPy. We apply the framework to generate illustrative land-based and offshore wind turbine models. We compare our results with OpenFAST simulations and discuss the advantages and limitations of the method. The Python implementation is provided as an open-source project.

Branlard, Emmanuel (ORCID:0000000277506128)↗

Generalized Newton-Raphson trajectory optimization-generator 1

Computer program constructs a sequence of optimal solutions to dynamically-approximate linear equations. Specification of the number and type of subarcs in the optimal solution allows simultaneous satisfaction of all switching criteria.

Cope, D. D.↗

Television camera as a scientific instrument

Rigorous calibration program, coupled with a sophisticated data-processing program that introduced compensation for system response to correct photometry, geometric linearity, and resolution, converted a television camera to a quantitative measuring instrument. The output data are in the forms of both numeric printout records and photographs.

Smokler, M. I.↗

Vibration computer programs E13101, E13102, E13104, and E13112 and application to the NERVA program. Project 187: Methodology documentation

Programs for the analyses of the free or forced, undamped vibrations of one or two elastically-coupled lumped parameter teams are presented. Bearing nonlinearities, casing and rotor distributed mass and elasticity, rotor imbalance, forcing functions, gyroscopic moments, rotary inertia, and shear and flexural deformations are all included in the system dynamics analysis. All bearings have nonlinear load displacement characteristics, the solution is achieved by iteration. Rotor imbalances allowed by such considerations as pilot tolerances and runouts as well as bearing clearances (allowing concail or cylindrical whirl) determine the forcing function magnitudes. The computer programs first obtain a solution wherein the bearings are treated as linear springs of given spring rates. Then, based upon the computed bearing reactions, new spring rates are predicted and another solution of the modified system is made. The iteration is continued until the changes to bearing spring rates and bearing reactions become negligibly small.

Mironenko, G.↗

Finite element solution algorithm for incompressible fluid dynamics

A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the transient motion of a viscous incompressible fluid, i.e., hydrodynamics. Dependent variable transformation renders the differential equation description uniformly elliptic. The finite element algorithm is established using the Galerkin criterion on a local basis within the Method of Weighted Residuals. It is unconstrained with respect to system linearity, computational mesh uniformity or solution domain closure regularity. The finite element matrices are established using a linear 'natural coordinate function' description. Computational solutions using the COMOC computer program illustrate the various features of the algorithm including recirculating flows.

Baker, A. J.↗

A user oriented microcomputer facility for designing linear quadratic Gaussian feedback compensators

A laboratory design facility for digital microprocessor implementation of linear-quadratic-Gaussian feedback compensators is described. Outputs from user interactive programs for solving infinite time horizon LQ regulator and Kalman filter problems were conditioned for implementation on the laboratory microcomputer system. The software consisted of two parts: an offline high-level program for solving the LQ Ricatti equations and generating associated feedback and filter gains and a cross compiler/macro assembler which generates object code for the target microprocessor system. A PDP 11/70 with a UNIX operating system was used for all high level program and data management, and the target microprocessor system is an Intel MDS (8080-based processor). Application to the control of a two dimensional inverted pendulum is presented and issues in expanding the design/prototyping system to other target machine architectures are discussed.

Houpt, P. K.↗

An Automated Technique for Estimating Daily Precipitation over the State of Virginia

Digital IR and visible imagery obtained from a geostationary satellite located over the equator at 75 deg west latitude were provided by NASA and used to obtain a linear relationship between cloud top temperature and hourly precipitation. Two computer programs written in FORTRAN were used. The first program computes the satellite estimate field from the hourly digital IR imagery. The second program computes the final estimate for the entire state area by comparing five preliminary estimates of 24 hour precipitation with control raingage readings and determining which of the five methods gives the best estimate for the day. The final estimate is then produced by incorporating control gage readings into the winning method. In presenting reliable precipitation estimates for every cell in Virginia in near real time on a daily on going basis, the techniques require on the order of 125 to 150 daily gage readings by dependable, highly motivated observers distributed as uniformly as feasible across the state.

Follansbee, W. A.↗

Thermal capabilities and graphical output of PAFEC

The program for automatic finite element calculations (PAFEC) developed for the computation of heat transfer in structures is discussed. The passive and interactive graphics capabilities of the PAFEC system are presented and future developments are outlined. This finite element system is shown to have significant thermal capabilities in support of its general structures. The program offers the following types of analysis: interactive graphics; user defined program control steps; steady state, transient heat transfer; boundary element methods; linear static, stress and displacements; modes and frequencies calculations; direct dynamic time intergration; frequency response analysis; elastohydrodynamic lubrication; large deflection analysis, buckling; creep and plasticity analysis; and substructures analysis.

Akin, J. E.↗

Experimental verification of a computational procedure for the design of TWT-refocuser-MDC systems

A comparison of analytical and experimental results is presented for a high performance dual-mode helix TWT, equipped with multistage depressed collectors (MDC), and operated over conditions ranging from saturation to the linear regime. The computations are carried out with advanced multidimensional computer programs which model the electron beam as a series of disks or rings of charge and follow their trajectories from the RF input of the TWT, through the slow-wave structure, through the refocusing system, to their points of impact in the depressed collector. TWT performance, collector efficiency, and collector current distribution are computed and compared with measurements. Very good agreement is obtained between computed and measured TWT performance and collector efficiencies. The analytical techniques were subsequently applied to the design of a smaller MDC of nearly equal efficiency.

Dayton, J. A., Jr.↗

Geometric and Material Nonlinear Structural Analysis

GAMNAS (Geometric and Material Nonlinear Analysis of Structures) is twodimensional finite-element stress-analysis program supporting fracturemechanics studies of debonding and delamination. GAMNAS options include linear, geometricnonlinear, material-nonlinear, and combined geometric- and material-nonlinear analysis.

Whitcomb, J. D.↗

Minimum weight design of helicopter rotor blades with frequency constraints

The minimum weight design of helicopter rotor blades subject to constraints on fundamental coupled flap-lag natural frequencies has been studied in this paper. A constraint has also been imposed on the minimum value of the blade autorotational inertia to ensure that the blade has sufficient inertia to autorotate in case of an engine failure. The program CAMRAD has been used for the blade modal analysis and the program CONMIN has been used for the optimization. In addition, a linear approximation analysis involving Taylor series expansion has been used to reduce the analysis effort. The procedure contains a sensitivity analysis which consists of analytical derivatives of the objective function and the autorotational inertia constraint and central finite difference derivatives of the frequency constraints. Optimum designs have been obtained for blades in vacuum with both rectangular and tapered box beam structures. Design variables include taper ratio, nonstructural segment weights and box beam dimensions. The paper shows that even when starting with an acceptable baseline design, a significant amount of weight reduction is possible while satisfying all the constraints for blades with rectangular and tapered box beams.

Chattopadhyay, Aditi↗

Measurement of birefringence for optical recording disk substrates

The birefringence of bare and coated substrates for magneto-optical recording is experimentally investigated using ellipsometry at the wavelengths of 632.8 nm and 780 nm. The rotation and ellipticity of the polarization state of the reflected or transmitted light is measured for different incident angles and different orientations of the incident linear polarization. The measured data is then fitted by a computer program which solves the Maxwell equations for the plane-wave propagation in a multilayer structure and minimizes the error between the measured and calculated data by adjusting the unknown parameters of the multilayer. This approach enables us to determine orientations of the three principal axes in the substrate and the corresponding refractive indices. A special feature of our ellipsometers is that a glass hemisphere is placed in contact with the substrate, which eliminates the refraction of the incident light and enables a maximum propagation angle of 70 degrees (with respect to the normal) in the substrate. This increases the sensitivity of the measurement. Certain anomalies were observed, which we believe are associated with the presence of grooves on these substrates.

Fu, Hong↗

The X-33 Flight Test Challenge

Low cost access to space has eluded present launch system technologies. Our objective is to reduce the cost of putting a payload into space from $10,000 per pound to $1000 per pound. In July 1996, a cooperative agreement was initiated between the Lockheed Martin Skunk Works and NASA to help accomplish this goal. The X-33 is the first step in the process to make low cost space access a reality. The X-33 is a suborbital, hypersonic lifting body, proof of concept of a reusable launch vehicle. The X-33 flight test program will validate technologies such as a metallic thermal protection system, Linear Aerospike Engines, use of tanks and struts as fundamental structural elements, as well as quick turnaround time. Flight testing will begin in July 2000, with launches originating from Edwards Air Force Base and initial landings at Michael Army Airfield in Utah. Data collected from these flight tests will aid in the decision to build an economically viable single stage to orbit reusable launch vehicle. This paper will explore the technical challenges facing the X-33 Flight Test Team.

Borden, David↗

X-56A MUTT: Aeroservoelastic Modeling

For the NASA X-56a Program, Armstrong Flight Research Center has been developing a set of linear states space models that integrate the flight dynamics and structural dynamics. These high order models are needed for the control design, control evaluation, and test input design. The current focus has been on developing stiff wing models to validate the current modeling approach. The extension of the modeling approach to the flexible wings requires only a change in the structural model. Individual subsystems models (actuators, inertial properties, etc.) have been validated by component level ground tests. Closed loop simulation of maneuvers designed to validate the flight dynamics of these models correlates very well flight test data. The open loop structural dynamics are also shown to correlate well to the flight test data.

Modeling↗

An exploratory study of finite difference grids for transonic unsteady aerodynamics

Unsteady aerodynamic forces are calculated by the XTRAN2L finite difference program which solves the complete two dimensional unsteady transonic small perturbation equation. The unsteady forces are obtained using a pulse transfer function technique which assumes the flow field behaves in a locally linear fashion about a mean condition. Forces are calculated for a linear flat plate using the default grids from the LTRAN2-NLR, LTRAN2-HI, and XTRAN3S programs. The forces are compared to the exact theoretical values for flat plate, and grid generated boundary and internal numerical reflections are observed to cause significant errors in the unsteady airloads. Grids are presented that alleviate the reflections while reducing computational time up to fifty-three percent and program size up to twenty-eight percent. Forces are presented for a six percent thick parabolic arc airfoil which demonstrate that the transform technique may be successfully applied to nonlinear transonic flows.

Seidel, D. A.↗

AV-8B system identification results from full scale development flight test program

The results presented in this paper demonstrate a methodology for identification of a non-linear model of the AV-88 V/STOL aircraft from flight test data. Conventional aerodynamics, thrust-induced aerodynamic effects and propulsion model correction factors are identified for hover, transitional and low-speed wingborne flight conditions. A special model formulation is adopted which is continuous at zero airspeed. The identified model is validated by prediction of flight test measurements, and by comparison with wind-tunnel results.

Anderson, L. C.↗