An infinite class of periodic solutions of d super 2x/dt super 2 plus 2x super 3 equal p/t/.
Second order forced nonlinear oscillation differential equation with time-dependent term not even, having infinity of periodic solutions
PERIODIC FUNCTION↗
SEARCH · Engineering Papers
Results for “time-dependent”
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.
A statistical model of the formation of stars and interstellar clouds.
Oort model of stars and interstellar cloud formation and destruction mathematically formulated, obtaining time-dependent cloud-mass spectrum equations
STELLAR EVOLUTION↗
Effects of turbulence on vortex shedding from circular cylinders
Wind and water tunnel apparatus and techniques for free stream turbulent effects on time-dependent forces acting on circular cylinders
CIRCULAR CYLINDER↗
Transition probabilities for the forced harmonic oscillator.
Transition probabilities of nitrogen-nitrogen collision obtained with time-dependent wave functions of forced harmonic oscillator and by numerical methods
TRANSITION PROBABILITY↗
Accuracy of laser measurements improved by pulse autocorrelator electronic system
Pulse autocorrelator electronic system discriminates between the dispersion effect of a disturbed laser signal and background noise by detecting multipath arrivals of Gaussian-shaped signal pulses. The autocorrelation function is time-dependent and can be determined by integrating the product of a received pulse and its delayed replicas.
Campanella, S. J.↗
Computer program for analyzing battery performance data
Computer programs for processing and analyzing nickel-cadmium battery and time-dependent data
COMPUTER PROGRAM↗
Gaseous electronics
Measured time-dependent electron velocity in weakly ionized plasma compared with theoretical model using Boltzmann equation
ELECTRON ENERGY↗
Gaseous electronics
Electron-electron relaxation rates determined from time-dependent electron velocity distribution
VELOCITY DISTRIBUTION↗
An analysis of the ''laminar instability'' problem in gas-cooled nuclear reactor passages.
Instability of gas-cooled nuclear reactor passages in steady laminar flow studied by time-dependent analysis
LAMINAR FLOW↗
Small-signal current transients in insulators with traps.
Time-dependent current flow equations solved for insulator with traps if injected space charge produces negligible perturbation on external electric field
SPACE CHARGE↗
Program for calculating optimum dimensions of alpha radioisotope capsules exposed to varying stress and temperature
A method and computer program were developed for calculating the creep and optimizing the dimensions of capsules filled with alpha-emitting radioisotopes. The method solves an integral equation that was developed assuming linear accumulation of partial creep lives and relating life to time-dependent stress and temperature using the Larson-Miller parameter. The computer program, CAPSUL, is written in Fortran language for the IBM 360/75 computer. The program makes a least squares fit of the creep life function using conventional constant stress, constant temperature creep data. Dimensions of capsules having maximum thermal power per unit of weight, volume, or area are calculated for a given creep life and pressure-temperature history using a numerical Lagrange Multiplier formulation. The program also calculates the life to a prescribed strain for capsules of given dimensions and pressure-temperature history. The method has been used to analyze creep data for the alloys 304 stainless steel, Hastelloy N, Cb-1% Zr, FS-85, and T-222.
J. P. Nichols↗
Use of source distributions for evaluating theoretical aerodynamics of thin finite wings at supersonic speeds
A series of publications on the source-distribution methods for evaluating the aerodynamics of thin wings at supersonic speeds is summarized, extended, and unified. Included in the first part are the deviations of: (a) the linearized partial-differential equation for unsteady flow at a substantially constant Mach number. b) The source-distribution solution for the perturbation-velocity potential that satisfies the boundary conditions of tangential flow at the surface and in the plane of the wing; and (c) the integral equation for determining the strength and the location of sources to describe the interaction effects (as represented by upwash) of the bottom and top wing surfaces through the region between the finite wing boundary and the foremost Mach wave. The second part deals with steady-state thin-wing problems. The third part of the report approximates the integral equation for unsteady upwash and includes a solution of approximate equation. Expressions are then derived to evaluate the load distributions for time-dependent finite-wing motions.
Evvard, John C↗
Generalized indical forces on deforming rectangular wings in supersonic flight
A method is presented for determining the time-dependent flow over a rectangular wing moving with a supersonic forward speed and undergoing small vertical distortions expressible as polynomials involving spanwise and chordwise distances. The solution for the velocity potential is presented in a form analogous to that for steady supersonic flow having the familiar "reflected area" concept discovered by Evvard. Particular attention is paid to indicial-type motions and results are expressed in terms of generalized indicial forces. Numerical results for Mach numbers equal to 1.1 and 1.2 are given for polynomials of the first and fifth degree in the chordwise and spanwise directions, respectively, on a wing having an aspect ratio of 4.
Lomax, Harvard↗
Single-drop reactive extraction/extractive reaction with forced convective diffusion and interphase mass transfer
An algorithm has been developed for time-dependent forced convective diffusion-reaction having convection by a recirculating flow field within the drop that is hydrodynamically coupled at the interface with a convective external flow field that at infinity becomes a uniform free-streaming flow. The concentration field inside the droplet is likewise coupled with that outside by boundary conditions at the interface. A chemical reaction can take place either inside or outside the droplet, or reactions can take place in both phases. The algorithm has been implemented, and for comparison results are shown here for the case of no reaction in either phase and for the case of an external first order reaction, both for unsteady behavior. For pure interphase mass transfer, concentration isocontours, local and average Sherwood numbers, and average droplet concentrations have been obtained as a function of the physical properties and external flow field. For mass transfer enhanced by an external reaction, in addition to the above forms of results, we present the enhancement factor, with the results now also depending upon the (dimensionless) rate of reaction.
Kleinman, Leonid S.↗
A Comparison of Theory and Observation of the Echo I Satellite
Observations of the Echo I balloon satellite have been compared with a theory including the following perturbing effects: (1) solar radiation pressure; (2) lunar and solar gravitation; (3) second, third, and fourth harmonics of the earth's gravitational potential; and (4) atmospheric drag. With a set of orbital elements at the 26th day of the lifetime of the satellite, it was possible to match the observational data to 180 days with root mean square residuals as follows: Delta-a = 17.9 km, Delta-e = 0.0021, Delta-i = 0.0177 deg., Delta-omega = 1.1231 deg., Delta-Omega = 0.4821 deg., Delta-perigee height = 7.50 km. No differential correction has been applied as yet. Values of atmospheric density between 1500 and 930 km, assuming neutral drag effects only, have been inferred from the orbital data. The connection between solar activity and drag is also examined. As the Echo I perigee height continues to oscillate between 900 and 1500 km, more valuable orbital data will be obtained and atmospheric properties will be deduced. Further refinements in the mathematical model, especially in a time-dependent model atmosphere, should bring a substantial reduction in the residuals of the observations.
Bryant, R. W.↗
Theoretical Determination of Lifetime of Compressed Plates at Elevated Temperatures
A method for the theoretical determination of the lifetime of com- pressed plates at elevated temperatures is presented. In this approach, linearized equations are used throughout with the assumption that the plate material is a standard linear solid. The critical time (lifetime) is determined by reducing the time-dependent behavior to the time- independent response of purely elastic buckling. Theoretically predicted lifetimes of 2024-T3 (formerly 24S-T3) aluminum-alloy plates at 450 F are compared with experimental values obtained in previous work.
Herrmann, George↗
Correlation of Resonance Charge Exchange Cross-Section Data in the Low-Energy Range
During the course of a literature survey concerning resonance charge exchange, an unusual degree of agreement was noted between an extrapolation of the data reported by Kushnir, Palyukh, and Sena and the data reported by Ziegler. The data of Kushnir et al. are for ion-atom relative energies from 10 to 1000 ev, while the data of Ziegler are for a relative energy of about 1 ev. Extrapolation of the data of Kushnir et al. was made in accordance with Holstein's theory, 3 which is a combination of time-dependent perturbation methods and classical orbit theory. The results of this theory may be discussed in terms of a critical impact parameter b(sub c).
Sheldon, John W.↗
Battery Pack Shape Optimization using Transient Heat Conduction Coupled with Cell-Discharge Analysis
Battery electric systems exhibit significant time-dependence, especially when evaluated in the context of an aircraft mission profile with continually changing power demands. Additionally, when evaluating battery-powered aircraft concepts, it is important to accurately compute the temperature of the batteries and properly characterize the thermal response of the system. The temperature of the batteries has a significant impact on cell performance, in addition to safety considerations of maintaining battery temperatures below their operating limit. Because of these considerations, battery models for preliminary design and optimization of aircraft should include the capability to accurately compute the temperature distribution within the battery pack. Furthermore, battery pack designs should be as light-weight as possible to maximize the pack energy density, while also considering battery temperature limits. Here, we demonstrate a simultaneous trajectory and shape optimization of a battery pack concept, using a transient heat transfer finite element model coupled with a time-varying cell-discharge battery model to provide this capability. Including the transient finite element problem in the loop enables accurate temperatures that can be passed back to the cell discharge model, while the cell discharge model can supply the finite element model with time-varying heat boundary conditions to the finite element problem, further benefiting the fidelity of the thermal response of the batteries. We first demonstrate the coupling capability between the battery cell-discharge model and the transient finite-element heat transfer through an optimization which computes the optimal current profile for the battery pack while ensuring the battery temperatures remain below their operational limit. We then build on this optimization by adding shape optimization to the problem, which allows us to consider a composite objective function which also minimizes the mass of the battery pack, while also producing an optimal current discharge profile.
Optimization↗