Nonlinear vibration of beams
Nonlinear partial differential equations of two variables for vibratory motions of beam
PARTIAL DIFFERENTIAL EQUATION↗
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Results for “Nonlinear equations”
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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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↗
Generalization of the parameter plane method.
Generalization of parameter plane method for case when characteristic equation coefficients are nonlinear functions of system of adjustable parameters
NONLINEAR SYSTEM↗
Investigation to define the propagation characteristics of a finite amplitude acoustic pressure wave
A theoretical analysis of the propagation characteristics of a finite amplitude pressure wave is presented. The analysis attempts to study the contribution of entropy-producing regions to the mechanism of aerodynamic noise generation. It results in a nonlinear convective wave equation in terms of entropy and a thermodynamic 'J' function. A direct analogy between the derived governing equation and those used in classical literature is obtained. An idealization of the processes considered permits the uncoupling of the equations of motion with a consequent construction of an acoustic analogy treating shock wave emission of finite amplitude acoustic waves. An engineering approach is reflected in the concept of an extended plug nozzle whose function is to facilitate aerodynamic noise attenuation by modifying the entropy-producing regions.
Peter, A. C.↗
A study of fluid and structural behavior under low gravity conditions Final report
Rotational discrimination algorithm for nonlinear regression and equation solving
Law, V. J.↗
A multipoint method of third order
Multipoint algorithm applied to nonlinear Chandrasekar integral equation
Bosarge, W. E., Jr.↗
Determination of the flow field of an ideal axisymmetric impinging jet.
Axisymmetric jet impingement against solid plane from tube at finite distance, using nonlinear partial differential equation in finite difference form
Fisher, G. D.↗
General weak turbulence theory of resonant four-wave processes.
Nonlinear integrodifferential kinetic equation for weak turbulence of resonant four wave processes, considering spectral energy density
Davidson, R. C.↗
Non-linear theory of unstable plane Poiseuille flow.
Limit-cycle oscillations of unstable plane Poiseuille flow analyzed by nonlinear Navier- Stokes equations
Dowell, E. H.↗
Theory of radiative transfer in inhomogeneous atmospheres. IV - Application of the matrix perturbation method to a semi-infinite atmosphere
Polarized radiation transfer through inhomogeneous semiinfinite atmosphere by matrix perturbation method, giving nonlinear singular integral equation
Abhyankar, K. D.↗
Almost-periodic behavior of solutions of a nonlinear Volterra system
Almost periodic solutions of two nonlinear Volterra integral equations
Miller, R. K.↗
Joule heating and winds due to geomagnetic disturbances
Joule heating and winds in upper atmosphere due to geomagnetic disturbances at 140 km altitude, deriving set of nonlinear partial differential equations
Chang, S.-C.↗
Asymptotically almost periodic solutions of a nonlinear Volterra system
Nonlinear Volterra integral equation system solution using almost periodic forced oscillations
Miller, R. K.↗
A compilation of results pertaining to the behavior of phase locked loops
State-of-the art on phase locked loops PLL is reported by summarizing some specific results. Following a statement of the overall analysis and design objectives, results are presented in a format identifying working terminology, inherent assumptions, and references for each result. The use of PLL in tracking, synchronization, and demodulation is reemphasized, as well as the mathematical challenge involved in solving nonlinear stochastic differential equations.
Gleicher, N.↗
Design and testing of a magnetic suspension and damping system for a space telescope
The basic equations of motion are derived for a two dimensional, three degree of freedom simulation of a space telescope coupled to a spacecraft by means of a magnetic suspension and isolation system. The system consists of paramagnetic or ferromagnetic discs confined to the magnetic field between two Helmholtz coils. Damping is introduced by varying the magnetic field in proportion to a velocity signal derived from the telescope. The equations of motion are nonlinear, similar in behavior to the one-dimensional Van der Pol equation. The computer simulation was verified by testing a 264-kilogram air bearing platform which simulates the telescope in a frictionless environment. The simulation demonstrated effective isolation capabilities for disturbance frequencies above resonance. Damping in the system improved the response near resonance and prevented the build-up of large oscillatory amplitudes.
Ockman, N. J.↗
The thunderstorm forecasting system at the Kennedy Space Center.
One of the major problems concerning meteorologists at the Kennedy Space Center, Fla, involves the forecasting of thunderstorm activity and associated adverse weather phenomena. The purpose of the study is to outline some of the more successful diagnostic tools which have been developed to aid the forecaster. These involve a variety of statistical procedures including conditional probabilities, exposure-period probabilities, and systems of multiple-regression equations based on nonlinear predictors.
Charles J Neumann↗
Transient, compressible heat and mass transfer in porous media using the strongly implicit iteration procedure.
Coupled nonlinear partial differential equations describing heat and mass transfer in a porous matrix are solved in finite difference form with the aid of a new iterative technique (the strongly implicit procedure). Example numerical results demonstrate the characteristics of heat and mass transport in a porous matrix such as a charring ablator. It is emphasized that multidimensional flow must be considered when predicting the thermal response of a porous material subjected to nonuniform boundary conditions.
Curry, D. M.↗
Dynamic response of a plane-symmetrical exothermic reaction center.
?sger,An analysis of the dynamic behavior of an idealized, plane-symmetrical exothermic reaction center is presented. The conservation equations for the reaction center are combined and yield a single integral equation expressing a nonlinear transfer function of the system for which the input is provided by a given time profile of the heat released per unit mass while the output gives the pressure pulse it generates under the restriction of plane-symmetrical motion. The solution is governed by a Daumk]hler number. For a given form of the exothermic power pulse profile, the dynamic behavior of the system is completely specified in terms of only this Daumk]hler number and the heat of reaction per unit mass of the combustible medium. Specific solutions are worked out for a set of typical elementary power pulse profiles, and the practical significance of the results is illustrated by their application to the problem of transition to detonation in an explosive gas.
Meyer, J. W.↗