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At least 811 records · Page 45

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NASA NTRS1991

Unified nonlinear analysis for nonhomogeneous anisotropic beams with closed cross sections

A unified methodology for geometrically nonlinear analysis of nonhomogeneous, anisotropic beams is presented. A 2D cross-sectional analysis and a nonlinear 1D global deformation analysis are derived from the common framework of a 3D, geometrically nonlinear theory of elasticity. The only restrictions are that the strain and local rotation are small compared to unity and that warping displacements are small relative to the cross-sectional dimensions. It is concluded that the warping solutions can be affected by large deformation and that this could alter the incremental stiffnes of the section. It is shown that sectional constants derived from the published, linear analysis can be used in the present nonlinear, 1D analysis governing the global deformation of the beam, which is based on intrinsic equations for nonlinear beam behavior. Excellent correlation is obtained with published experimental results for both isotropic and anisotropic beams undergoing large deflections.

Atilgan, Ali R.↗

NASA NTRS1998

Vibrational Control of a Nonlinear Elastic Panel

The paper is concerned with the stabilization of the nonlinear panel oscillation by an active control. The control is actuated by a combination of additive and parametric vibrational forces. A general method of vibrational control is presented for stabilizing panel vibration satisfying a nonlinear beam equation. To obtain analytical results, a perturbation technique is used in the case of weak nonlinearity. Possible application to other types of problems is briefly discussed.

Chow, P. L.↗

DOE OSTI2022

Integrability technique for fluid flow induced deformation of a boundary hair

The deformation of a dense carpet of hair due to Stokes flow in a channel can be described by a nonlinear integrodifferential equation for the shape of a single hair, which possesses several solutions for a given choice of parameters. Although it was posed in a previous study and it bears a resemblance to the pendulum problem from mechanics, this equation has not been analytically solved until now. Despite the presence on an integral with a nonlinear functional dependence on the dependent variable, the system is integrable. We compare the analytically obtained solution to a finite-difference numerical approach, identify the physically realizable solution branch, and briefly study the solution structure through a conserved energylike quantity. Time-dependent fluid-structure interactions are a rich and complex subject to investigate, and we argue that the solution discussed herein can be used as a basis for understanding these systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1993

Computation of a controlled store separation from a cavity

Coupling of the Reynolds-averaged Navier-Stokes equations, rigid-body dynamics, and a pitch attitude control law is demonstrated in two- and three-dimensions. The application problem was the separation of a canard-controlled store from an open-flow rectangular cavity bay at a freestream Mach number of 1.2. The transient flowfield was computed using a diagonal scheme in an overset mesh framework, with the resultant aerodynamic loads used as the forcing functions in the nonlinear dynamics equations. The proportional and rate gyro sensitivities were computed a priori using pole placement techniques for the linearized dynamical equations. These fixed gain values were used in the controller for the nonlinear simulation. Reasonable comparison between the full and linearized equations for a perturbed two-dimensional missile was found. Also in two-dimensions, a controlled store was found to possess improved separation characteristics over a canard-fixed store. In three-dimensions, trajectory comparisons with wind-tunnel data for the canard-fixed case will be made. In addition, it will be determined if a canard-controlled store is an effective means of improving cavity store separation characteristics.

Atwood, Christopher A.↗

NASA NTRS1979

Evaluation of improved algorithms for nonlinear transient structural heat transfer

The paper presents the evaluation of algorithms having potential for reducing computer time to integrate large systems of equations governing nonlinear transient heat transfer in complex structures. A series of test problems is being developed to test two algorithms. The Shuttle Orbiter frame model having 190 nodes was the subject of an analytical/experimental study. Plans are to perform calculations for the complete wing model having about 4000 nodes as well as a regional (plug) model having about 200 nodes.

Adelman, H. M.↗

DOE OSTI2020

Self-compression of laser pulses in a discrete medium

Using the discrete nonlinear Schrödinger equation, we study the laser radiation self-action dynamics in a nanostructured waveguide system. It is shown that for a laser pulse energy exceeding the critical value, the nonlinear evolution of the wave field markedly differs from the corresponding process in a continuous medium. While the pulse propagates in a discrete medium, its length decreases to values comparable to the scale of the structure and the velocity decreases to zero. The system parameters are determined at which the wave field after the laser pulse termination begins to propagate in the opposite direction in a compressed form. The process of slowing down and stopping the pulse is accompanied by strong radiation losses, so that about a third of the energy of the initial field distribution remains in the final compressed state. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Alternative formulation of weak magnetohydrodynamic turbulence theory

In a recent paper, the weak turbulence theory for incompressible magnetohydrodynamics is formulated by employing the method customarily applied in the context of kinetic weak plasma turbulence theory. Such an approach simplified certain mathematical procedures including achieving the closure relationship. The formulation in the above-cited paper starts from the equations of incompressible magnetohydrodynamic (MHD) theory expressed via Elsasser variables. The derivation of nonlinear wave kinetic equation therein is obtained via a truncated solution at the second-order of iteration following the standard practice. In the present paper, the weak MHD turbulence theory is alternatively formulated by employing the pristine form of incompressible MHD equation rather than that expressed in terms of Elsasser fields. The perturbative expansion of the nonlinear momentum equation is carried out up to the third-order iteration rather than imposing the truncation at the second order. Furthermore, it is found that while the resulting wave kinetic equation is identical to that obtained in the previous paper cited above, the third-order nonlinear correction plays an essential role for properly calculating derived quantities such as the total and residual energies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1984

GCKP84--General Chemical Kinetics Code for Gas-Phase Flow and Batch Processes Including Heat Transfer Effects

A general chemical kinetics code is described for complex, homogeneous ideal gas reactions in any chemical system. The main features of the GCKP84 code are flexibility, convenience, and speed of computation for many different reaction conditions. The code, which replaces the GCKP code published previously, solves numerically the differential equations for complex reaction in a batch system or one dimensional inviscid flow. It also solves numerically the nonlinear algebraic equations describing the well stirred reactor. A new state of the art numerical integration method is used for greatly increased speed in handling systems of stiff differential equations. The theory and the computer program, including details of input preparation and a guide to using the code are given.

David A Bittker↗

NASA NTRS1989

Stationary nonlinear Alfven waves and solitons

Stationary solutions of the derivative nonlinear Schroedinger equation are discussed and classified by using a pseudopotential formulation. The solutions consist of a rich family of nonlinear Alfven waves and solitons with parallel and oblique propagation directions. Expressions for the envelope and the phase of nonlinear waves with periodic envelope modulation, and 'hyperbolic' and 'algebraic' solitons are given. The propagation angle for the slightly modulated elliptic, periodic waves and for oblique solitons is evaluated.

Hada, T.↗

NASA NTRS1990

Calculation of shocked one-dimensional flows on abruptly changing grids by mathematical programming

Cell-centered finite differences on cells of an arbitrarily spaced grid are presently used to discretize the steady-state inviscid and nearly inviscid Burgers' equations for steady-state shocked flow in a quasi-one-dimensional nozzle. The everdetermined system of nonlinear algebraic equations thus obtained is solved by a procedure which minimizes a weighted sum of the residuals' absolute values. Numerical solutions for both viscous and inviscid problems are accurate and nonoscillatory, on grids whose abrupt mesh lengths refinements are as great as a factor of 10,000.

Lavery, John E.↗

DOE OSTI2022

The principle of minimal power

This article is devoted to the memory of Yuri P Raizer, who passed away in 2021. He left a noticeable trace in gas discharge physics. The principle of minimal power (the state that requires minimal power is most probable) is thoroughly used in his books. Although the fundamental laws of physics do not imply this ad hoc principle, a detailed analysis of underlying phenomena can often reveal why nature prefers this path. Raizer illustrated this principle for plasma stratification, formation of electrode spots, discharge constriction, the shape of an arc channel, etc. We argue that the nonlinearity of equations describing gas discharges can often justify the realization of a plasma state maintained at minimal electric power. This nonlinearity appears because small groups of energetic electrons often control the ionization processes. The number of these electrons depends strongly on the ratio of the electric field to gas density, E/N. Under certain conditions, the ionization rate can also depend nonlinearly on electron density due to stepwise ionization and Coulomb collisions. Here, we use the principle of minimal power to illustrate some of Raizer's contributions to gas discharge physics from a single point of view. We demonstrate that nonlinearity of ionization processes in gas discharges can substantiate this principle for plasma stratification. However, striations of s, p, and r types in neon could exist with minimal or no ionization enhancement. This reminds us of Raizer's warning that applying the minimal power principle could lead to erroneous predictions, and a proper theory is required in each case to justify its use. 'The phenomenon of striations satisfies the principle of minimal power' – Yuri Raizer

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1977

The relative diffusion of strong magnetic fields and tenuous gases

General equations are given for treating the diffusion of a magnetic field in a fluid with electrical conductivity and a resistive diffusion coefficient. Consequences of nonnegligible gas motion are investigated by considering the one-dimensional problem where a tenuous isothermal gas with pressure expressed as a function of x-coordinate and time is enmeshed in a magnetic field in the y-direction. Approximate equations are obtained for the case of weak fluctuations in gas or field pressure, and the properties of a nonlinear diffusion equation are illustrated with the example of an initial thin slab of gas confined by a uniform field on either side. The advance of a gas front into a nonvanishing gas density is illustrated by using the progressive wave solution. Application of the results to the evolution of streamers and filaments observed in the solar corona is briefly discussed

Parker, E. N.↗

NASA NTRS1996

Computation of Static Shapes and Voltages for Micromachined Deformable Mirrors with Nonlinear Electrostatic Actuators

In modeling micromachined deformable mirrors with electrostatic actuators whose gap spacings are of the same order of magnitude as those of the surface deformations, it is necessary to use nonlinear models for the actuators. In this paper, we consider micromachined deformable mirrors modeled by a membrane or plate equation with nonlinear electrostatic actuator characteristics. Numerical methods for computing the mirror deformation due to given actuator voltages and the actuator voltages required for producing the desired deformations at the actuator locations are presented. The application of the proposed methods to circular deformable mirrors whose surfaces are modeled by elastic membranes is discussed in detail. Numerical results are obtained for a typical circular micromachined mirror with electrostatic actuators.

Wang, P. K. C.↗

NASA NTRS1999

An O(Nm(sup 2)) Plane Solver for the Compressible Navier-Stokes Equations

A hierarchical multigrid algorithm for efficient steady solutions to the two-dimensional compressible Navier-Stokes equations is developed and demonstrated. The algorithm applies multigrid in two ways: a Full Approximation Scheme (FAS) for a nonlinear residual equation and a Correction Scheme (CS) for a linearized defect correction implicit equation. Multigrid analyses which include the effect of boundary conditions in one direction are used to estimate the convergence rate of the algorithm for a model convection equation. Three alternating-line- implicit algorithms are compared in terms of efficiency. The analyses indicate that full multigrid efficiency is not attained in the general case; the number of cycles to attain convergence is dependent on the mesh density for high-frequency cross-stream variations. However, the dependence is reasonably small and fast convergence is eventually attained for any given frequency with either the FAS or the CS scheme alone. The paper summarizes numerical computations for which convergence has been attained to within truncation error in a few multigrid cycles for both inviscid and viscous ow simulations on highly stretched meshes.

Thomas, J. L.↗

NASA NTRS2006

Dynamic Theory of Relativistic Electrons Stochastic Heating by Whistler Mode Waves with Application to the Earth Magnetosphere

In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion by group symmetries of the problem were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. It is proved that the upper boundary of particle stochastic heating is conditioned by intrinsic property of the particle chaotic motion. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.

Khazanov, G. V.↗

NASA NTRS1996

Computation of Static Shapes and Voltages for Micromachined Deformable Mirrors with Nonlinear Electostatic Actuators

In modeling micromachined deformable mirrors with electrostatic actuators whose gap spacings are of the same order of magnitude as that of the surface deformations, it is neccessary to use nonlinear models for the actuators. In this paper, we consider micromachined deformable mirrors modeled by a membrane or plate equation with nonlinear electrostatic actuator characteristics.

deformations optical systems adaptive optical syst↗

NASA NTRS1993

A new class of exact, nonlinear solutions to the Grad-Shafranov equation

We have constructed a new class of exact, nonlinear solutions to the Grad-Shafranov equation, representing force-free magnetic fields with translational symmetry. These exact solutions are pertinent to the study of magnetic structures in the solar corona that are subjected to photospheric shearing motions.

Roumeliotis, George↗

NASA NTRS1980

Numerical solution of the Navier-Stokes equations for high Reynolds number incompressible turbulent flow

The full Navier-Stokes equations for incompressible turbulent flow must be solved to accurately represent all flow phenomena which occur in a high Reynolds number incompressible flow. A two layer algebraic eddy viscosity turbulence model is used to represent the Reynolds stress in the primitive variable formulation. The development of the boundary-fitted coordinate systems makes the numerical solution of these equations feasible for arbitrarily shaped bodies. The nondimensional time averaged Navier-Stokes equations, including the turbulence mode, are represented by finite difference approximations in the transformed plane. The resulting coupled system of nonlinear algebraic equations is solved using a point successive over relaxation iteration. The test case considered was a NACA 64A010 airfoil section at an angle of attack of two degrees and a Reynolds number of 2,000,000.

Thompson, D. S.↗