ON THE BUCKLING OF THIN ELASTIC SHELLS
The differential equations which must be solved to predict the buckling load are reviewed. The different possible physical interpretations of these equations are discussed.
ELASTIC BUCKLING↗
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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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Numerical determination of the transmissibility characteristics of a squeeze film damped forced vibration system
Numerical solutions of the governing equations of motion of a liquid squeeze film damped forced vibration system were carried out to examine the feasibility of using a liquid squeeze film to cushion and protect large structures, such as buildings, located in areas of high seismic activity. The mathematical model used was that for a single degree of freedom squeeze film damped spring mass system. The input disturbance was simulated by curve fitting actual seismic data with an eleventh order Lagranging polynomial technique. Only the normal component of the seismic input was considered. The nonlinear, nonhomogeneous governing differential equation of motion was solved numerically to determine the transmissibility over a wide range of physical parameters using a fourth-order Runge-Kutta technique. It is determined that a liquid squeeze film used as a damping agent in a spring-mass system can significantly reduce the response amplitude for a seismic input disturbance.
Sutton, M. A.↗
Sensitivity of model calculations to uncertain inputs, with an application to neutron star envelopes
A method is given for determining the sensitivity of certain types of calculations to the uncertainties in the input physics or model parameters; this method is applicable to problems that involve solutions to coupled, ordinary differential equations. In particular the sensitivity of calculations of the thermal structure of neutron star envelopes to uncertainties in the opacity and equation of state is examined. It is found that the uncertainties in the relationship between the surface and interior temperatures of a neutron star are due almost entirely to the imprecision in the values of the conductive opacity in the region where the ions form a liquid; here the conductive opacity is, for the most part, due to the scattering of electrons from ions.
Epstein, R. I.↗
Shape-memory properties in Ni-Ti sputter-deposited film
A Ni-Ti alloy, generically called nitinol, was prepared from sputtering targets of two different compositions on glass substrates using a dc magnetron source. The as-deposited films were amorphous in structure and did not exhibit a shape memory. The amorphous films were crystallized with a suitable annealing process, and the transformation properties were measured using differential scanning calorimetry. The annealed films demonstrated a strong shape-memory effect. Stress/strain measurements and physical manipulation were used to evaluate the shape recovery. These tests demonstrated sustained tensile stresses of up to 480 MPa in the high-temperature phase, and a characteristic plastic deformation in the low-temperature phase.
Busch, J. D.↗
Optimization of transistor design including large signal device/circuit interactions at extremely high frequencies (20-100+GHz)
Transistor design for extremely high frequency applications requires consideration of the interaction between the device and the circuit to which it is connected. Traditional analytical transistor models are to approximate at some of these frequencies and may not account for variations of dopants and semiconductor materials (especially some of the newer materials) within the device. Physically based models of device performance are required. These are based on coupled systems of partial differential equations and typically require 20 minutes of Cray computer time for a single AC operating point. A technique is presented to extract parameters from a few partial differential equation solutions for the device to create a nonlinear equivalent circuit model which runs in approximately 1 second of personal computer time. This nonlinear equivalent circuit model accurately replicates the contact current properties of the device as computed by the partial differential solver on which it is based. Using the nonlinear equivalent circuit model of the device, optimization of systems design can be performed based on device/circuit interactions.
Levy, Ralph↗
A Walsh Function Module Users' Manual
The solution of partial differential equations (PDEs) with Walsh functions offers new opportunities to simulate many challenging problems in mathematical physics. The approach was developed to better simulate hypersonic flows with shocks on unstructured grids. It is unique in that integrals and derivatives are computed using simple matrix multiplication of series representations of functions without the need for divided differences. The product of any two Walsh functions is another Walsh function - a feature that radically changes an algorithm for solving PDEs. A FORTRAN module for supporting Walsh function simulations is documented. A FORTRAN code is also documented with options for solving time-dependent problems: an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the usage of the Walsh function module including such features as operator overloading, Fast Walsh Transforms in multi-dimensions, and a Fast Walsh reciprocal.
Gnoffo, Peter A.↗
Calibration of a V-Cone for Low Mass Flows For Small Core Compressor Research
Advancements in core compressor technologies are necessary for next generation, high Overall Pressure Ratio (OPR) turbofan engines. High pressure compressors (HPCs) for future engines are being designed with exit corrected mass flow rates less than 2.25 kg/s (5 lbm/s). In order to accurately measure the performance of these advanced designs, high accuracy measurements are needed in test facilities. The W7 High Speed Multistage Axial Compressor Facility at NASA Glenn Research Center has been used to acquire data for advanced compressor designs. This facility utilizes an advanced differential pressure flow meter called a V-Cone. The facility has historically tested components with physical mass flow rates in the range of 27 to 45 kg/s (60 to 100 lbm/s). As such, when the V-Cone was calibrated prior to installation, the calibrations focused on higher mass flow rates, and uncertainties in that regime range from 0.5% to 0.85%. However, for low mass flow rates under 9 kg/s (20 lbm/s), expected in tests of advanced high OPR HPCs rear stages, the uncertainties of the V-Cone exceed 2.5%. To address this, using a method similar to that utilized by the National Institute of Standards and Technology, an array of Critical Flow Venturi Nozzles (CFVs) was installed in the W7 test section and used to calibrate the V-Cone in 0.5 kg/s (1 lbm/s) increments up to 10.5 kg/s (23 lbm/s). This effort details the measurements and uncertainties associated with this calibration which resulted in a final uncertainty of the V-Cone measurements under 1%.
Measurement Uncertainty↗
Novel Optical Diagnostic Techniques for Studying Particle Contact and Deposition Upon a Large Cylinder in a Sheared Suspension
The objectives of this research project were: 1) To study the fluid dynamics of sheared particle-liquid suspensions and the impact of differential particle-fluid inertia; 2) To develop new techniques for observing suspension particle contact and deposition upon solid surfaces. Dr. Yoda was supported by the NASA Office of Biological and Physical Research on a four-year grant from March 2000 through November 2004 for a ground-based study on the fluid dynamics of sheared particle-liquid suspensions and the impact of differential particle-fluid inertia on such flows. Such inertial effects can only be observed in reduced-gravity environments since they are overwhelmed by buoyancy effects on Earth. Moreover, these inertial effects will have a significant impact upon suspension flows in microgravity. Suspension dynamics are of importance in a wide variety of advanced life systems applications, including water reclamation and dust mitigation in confined habitats.
Rashidnia, Nasser↗
Generation of Surface Coordinates by Elliptic Partial Differential Equations
The problem of generating spatial coordinates by numerical methods through carefully selected mathematical models is of current interest both in mechanics and physics. The problem of generation of a desired system of coordinates in a given surface was considered, which essentially is an effort directed to the problem of grid generation in a two-dimensional non-Euclidean space. The mathematical model selected for this purpose is based on the formulae of Gauss for a surface. The proposed equations can be used to generate a new coordinate system from the data of an already given coordinate system in a surface. If the coefficients of the first and second fundamental forms have been given, then the proposed equations can be used to generate a surface satisfying the given data (surface fitting). The proposed equations can also be used to generate surfaces in the space between two arbitrary given surfaces, thus providing 3D grids in an Euclidean space.
Warsi, Z. U. A.↗
Variability of intensity ratios of H to He and He to ions with Z not smaller than 3 in solar energetic particle events
Data from the solid-state detector on Explorer 35 are applied to a study of two intensity ratios in the sub-MeV per nucleon specific kinetic energy range for several energetic particle events. It is found that the intensity ratios vary markedly from event to event, particularly during the time history of the individual events. This implies that the ratios have no simple relationship to 'solar abundances' in the usual sense of the term. The pattern of the variability of each ratio is established; the ratio of He to ions with Z not smaller than 3 starts with a low value and increases as the event proceeds. The H/He ratio exhibits a qualitatively similar time history with marked relative enhancement of He early in an event. Differential diffusion of the various ionic species with differing magnetic rigidities is seen to be the dominant physical cause for the variabilities observed.
Van Allen, J. A.↗
Non-Gaussian approach for parametric random vibration of non-linear structures
The dynamic response of a nonlinear, single degree of freedom structural system subjected to a physically white noise parametric excitation is investigated. The Ito stochastic calculus is employed to derive a general differential equation for the moments of the response coordinates. The differential equations of moments of any order are found to be coupled with higher order moments. A non-Gaussian closure scheme is developed to truncate the moment equations up to fourth order. The statistical of the stationary response are computed numerically and compared with analytical solutions predicted by a Gaussian closure scheme and the stochastic averaging method. It is found that the computed results exhibit the jump phenomenon which is typical of the characteristics of deterministic nonlinear systems. In addition, the numerical algorithm leads to multiple solutions all of which give positive mean squares. However, two of these solutions are found to violate the properties of high order moments. One solution preserves the moments properties and demonstrates that the system achieves a stationary response.
Ibrahim, R. A.↗
Three-dimensional grids as solutions of elliptic systems
An elliptic grid generation scheme is described which produces a curvilinear, boundary-fitted grid for highly swept wings with sharp leading edges. The three-dimensional integration domain is segmented in successive crossflow sections wherein the physical coordinates are transformed to computational coordinates by solving an elliptic set of two quasi-linear differential equations. Grid points are clustered in the vicinity of the wing surface, especially in the neighborhood of the leading edges. The formulation of the source terms in the equations governing the transformation contains adjustable parameters which are determined from limiting forms of the elliptic equations along the boundaries. The source terms are assigned to each grid point by interpolation of these parameters into the interior domain. The formulation does not depend on the boundary shape or on the distribution of the grid points along the boundaries. For the first time, the discretized governing equations have been solved using a fast AF1 iteration scheme.
Hartwich, P.-M.↗
Three-Axis Superconducting Gravity Gradiometer
Gravity gradients measured even on accelerating platforms. Three-axis superconducting gravity gradiometer based on flux quantization and Meissner effect in superconductors and employs superconducting quantum interference device as amplifier. Incorporates several magnetically levitated proof masses. Gradiometer design integrates accelerometers for operation in differential mode. Principal use in commercial instruments for measurement of Earth-gravity gradients in geo-physical surveying and exploration for oil.
Paik, Ho Jung↗
Continuous system modeling
A comprehensive and systematic introduction is presented for the concepts associated with 'modeling', involving the transition from a physical system down to an abstract description of that system in the form of a set of differential and/or difference equations, and basing its treatment of modeling on the mathematics of dynamical systems. Attention is given to the principles of passive electrical circuit modeling, planar mechanical systems modeling, hierarchical modular modeling of continuous systems, and bond-graph modeling. Also discussed are modeling in equilibrium thermodynamics, population dynamics, and system dynamics, inductive reasoning, artificial neural networks, and automated model synthesis.
Cellier, Francois E.↗
Combustion noise and combustion instabilities in propulsion systems
This paper is concerned with some aspects of non-linear behavior of unsteady motions in combustion chambers. The emphasis is on conditions under which organized oscillations having discrete frequencies may exist in the presence of random motions. In order to treat the two types of motions together, and particularly to investigate coupling between noise and combustion instabilities, the unsteady field is represented as a synthesis of acoustic modes having time-varying amplitudes. Each of the amplitudes are written as the sum of two parts, one associated with the random field and the remainder representing the organized oscillations. After spatial averaging, the general problem is reduced to solution of a set of second-order ordinary differential equations whose structure depends on the sorts of nonlinear processes accounted for. This formulation accommodates any physical process; in particular, terms are included to represent noise sources, although only limited modeling is discussed. Our results suggest that random sources of noise have only small effects on combustion instabilities and seem not to be a cause of unstable motions. However, the coupling between the two sorts of unsteady motions may be important as an essential process in a proposed scheme for noise control. It is now a familiar observation that many nonlinear deterministic systems are capable of exhibiting apparently random motions called 'chaos.' This is a particularly interesting possibility for systems which also executed non-deterministic random motions. In combustion chambers, a nonlinear deterministic system (acoustical motions) exists in the presence of noise produced by flow separation, turbulent motions, and energy released by combustion processes. The last part of the paper is directed to the matter of discovering whether or not chaotic motions exist in combustion systems. Analysis has not progressed sufficiently far to answer the question. We report here recent results of processing data taken in one combustor to determine the dimensions of any attractors in the motions. No evidence has been found for chaos in the strict sense, but the method seems to be an important means of investigating the nonlinear behavior of combustion systems.
F. E. C. Culick↗
Intercomparison of single-frequency methods for retrieving a vertical rain profile from airborne or spaceborne radar data
This paper briefly reviews several single-frequency rain profiling methods for an airborne or spaceborne radar. The authors describe the different methods from a unified point of view starting from the basic differential equation. This facilitates the comparisons between the methods and also provides a better understanding of the physical and mathematical basis of the methods. The application of several methods to airborne radar data taken during the Convective and Precipitation/Electrification Experiment is shown. Finally, the authors consider a hybrid method that provides a smooth transition between the Hitschfeld-Bordan method, which performs well at low attenuations, and the surface reference method, for which the relative error decreases with increasing path attenuation.
Iguchi, Toshio↗
Model-Reference Adaptive Control of Distributed Lagrangian Infinite-Dimensional Systems Using Hamilton’s Principle
This paper presents a Hamilton's principle for distributed control of infinite-dimensional systems modeled by a distributed form of the Euler-Lagrange method. The distributed systems are governed by a system of linear partial differential equations in space and time. A generalized potential energy expression is developed that can capture most physical systems including those systems that have no spatial distribution. The Hamilton's principle is applied to derive distributed feedback control methods without resorting to the standard weak-form discretization approach to convert an infinite-dimensional systems to a finite-dimensional systems. It can be shown by the principle of least action that the distributed control synthesized by the Hamilton's principle is a minimum-norm control. A model-reference adaptive control framework is developed for distributed Lagrangian systems in the presence of uncertainty. The theory is demonstrated by an application of adaptive flutter suppression control of a flexible aircraft wing.
Nguyen, Nhan T.↗
Analysis of embedded shock waves calculated by relaxation methods.
The requirements for uniqueness of the calculated jump conditions across embedded shock waves are investigated for type-dependent difference systems used in transonic flow studies. A mathematical analysis shows that sufficient conditions are (1) the equations should be differenced in conservative form and (2) a special difference operator should be used when switching from a hyperbolic to an elliptic operator. The latter results in a consistency condition on the integral equations, rather than the differential, at these points. Calculated jump conditions for several embedded and detached shock waves are analyzed in the physical and hodograph planes. Comparisons are made with previous results, a time-dependent calculation, and data.
Murman, E. M.↗