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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Third-order resonance effects and the nonlinear stability of drop oscillations

The three-dimensional nonlinear oscillations of an isolated, inviscid drop with surface tension are studied by a multiple timescale analysis and pre-averaging applied to the variational principle for the appropriate Lagrangian. Amplitude equations are derived which describe the generic cubic resonance caused by the spatial degeneracy of the eigenfrequencies of the linear normal modes. This resonant coupling leads to the instability of the finite amplitude axisymmetric oscillations to small nonaxisymmetric perturbations, as is demonstrated here for the three- and four-lobed normal modes. Solutions to the interaction equations that describe finite amplitude, nonaxisymmetric traveling-wave solutions are also obtained and their stability is investigated. A nongeneric cubic resonance between the two-lobed and four-lobed oscillatory modes leads to quasi-periodic motions.

Natarajan, Ramesh↗
NASA NTRS1988

Oscillations of drops in zero gravity with weak viscous effects

Nonlinear oscillations and other motions of large axially symmetric liquid drops in zero gravity are studied numerically by a boundary-integral method. The effect of small viscosity is included in the computations by retaining first-order viscous terms in the normal stress boundary condition. This is accomplished by making use of a partial solution of the boundary-layer equations which describe the weak vortical surface layer. Small viscosity is found to have a relatively large effect on resonant mode coupling phenomena.

Lundgren, T. S.↗
NASA NTRS1985

Construction of approximate analytical solutions to a new class of non-linear oscillator equation

The principle of harmonic balance is invoked in the development of an approximate analytic model for a class of nonlinear oscillators typified by a mass attached to a stretched wire. By assuming that harmonic balance will hold, solutions are devised for a steady state limit cycle and/or limit point motion. A method of slowly varying amplitudes then allows derivation of approximate solutions by determining the form of the exact solutions and substituting into them the lowest order terms of their respective Fourier expansions. The latter technique is actually a generalization of the method proposed by Kryloff and Bogoliuboff (1943).

Mickens, R. E.↗
NASA NTRS1991

Stability and bifurcation analysis of oscillators with piecewise-linear characteristics - A general approach

A general approach is developed for determining the periodic solutions and their stability of nonlinear oscillators with piecewise-smooth characteristics. A modified harmonic balance/Fourier transform procedure is devised for the analysis. The procedure avoids certain numerical differentiation employed previously in determining the periodic solutions, therefore enhancing the reliability and efficiency of the method. Stability of the solutions is determined via perturbations of their state variables. The method is applied to a forced oscillator interacting with a stop of finite stiffness. Flip and fold bifurcations are found to occur. This led to the identification of parameter ranges in which chaotic response occurred.

Noah, S. T.↗
NASA NTRS1993

Nonlinear evolution of magnetic flux ropes. I - Low-beta limit

We study the nonlinear self-similar evolution of a cylindrical magnetic flux tube with two components of the magnetic field, axial and azimuthal. We restrict ourselves to the case of a plasma of low beta. Introducing a special class of configurations we call 'separable fields', we reduce the problem to an ordinary differential equation. Two cases are to be distinguished: (1) when the total field minimizes on the symmetry axis, the magnetic configuration inexorably collapses, and (2) when, on the other hand, the total field maximizes on the symmetry axis, the magnetic configuration behaves analogously to a nonlinear oscillator. Here we focus on the latter case. The effective potential of the motion contains two terms: a strong repulsive term and a weak restoring term associated with the pinch. We solve the nonlinear differential equation of motion numerically and find that the period of oscillations grows exponentially with the energy of the oscillator. Our treatment emphasizes the role of the force-free configuration as the lowest potential energy state about which the system oscillates.

Osherovich, V. A.↗
NASA NTRS1991

Limit cycle oscillation of a fluttering cantilever plate

A response of a cantilever plate in high supersonic flow to a disturbance is considered. The Rayleigh-Ritz method is used to solve the nonlinear oscillation of a fluttering plate. It is found that the length-to-width ratio for a cantilever plate has a great effect on flutter amplitude of the limit cycle. For small length-to-width ratio, the dominant chordwise modes are translation and rotation. It is suggested that higher bending modes must be included to obtain an accurate prediction of the flutter onset and limit cycle oscillation. For large length-to-width ratio, significant chordwise bending is apparent in the flutter motion, with the trailing edge area having the largest motion.

Dowell, Earl↗
NASA NTRS1993

Spectral response of a bilinear oscillator

An approximate analytical procedure is presented to estimate the response power spectral density of a randomly excited spring/mass/damper system having a bilinear spring. The approximate expression for the response spectrum is developed by representing the nonlinear oscillator as a linear system having a natural frequency that depends on the envelope of the random response. This approximate representation of the system leads to estimates of the response spectrum that agree extremely well with those obtained by direct numerical simulation of the governing equation.

Miles, R. N.↗
NASA NTRS1984

A finite element method for nonlinear forced vibrations of beams

Techniques for defining a finite element model (FEM) for analysis of nonlinear vibrations in beam structures subjected to harmonic excitation are presented. The resulting model covers longitudinal deformation and inertial effects. The nonlinear oscillations of a beam element under forced excitation are modeled by a harmonic force matrix based on first order approximations of the Jacobian elliptic forcing function. Harmonic force and nonlinear stiffness matrices are derived and the nonlinear forced responses of beams are calculated under various boundary conditions. The results of FEM computations for simply-supported and clamped beams show that midplane stretching caused by large deflections increases the nonlinearity. Axially-restrained beams experience only hardening nonlinearity, while axially-free beams have reduced nonlinearity in deformation and inertia and an increase in linearity due to large deflection.

Mei, C.↗
NASA NTRS1977

White-dwarf variability and the rotation of g-modes

The multiperiodic behavior clearly evident after Fourier analysis of many DA white-dwarf light curves is interpreted as arising from outbursts whose timing is regulated by the rotation and oscillation of the star. A model is proposed on the basis of three main assumptions: (1) a broad array of g-mode oscillations is taking place all the time in DA white-dwarf variables; (2) slow rotation permits most of the g-modes to couple and form a small group of nonlinear modes, each characterized by one of the indices of the spherical harmonic functions involved; and (3) the observed brightenings of the star are produced by upwelling of convection on a large horizontal scale when the antinodes of the nonlinear oscillation patterns periodically rotate into alignment and cause a temporary local enhancement of energy per unit volume. This model is used to match precisely almost every strong periodicity observed in the complex light curves of the DA white dwarfs G207-9, G38-29, G29-38, and HL Tau 76. If the model has been applied correctly, the results indicate that all four of these variables are rotating slowly with periods in the range from 250 to 500 sec.

Wolff, C. L.↗
NASA NTRS2009

Discharge Oscillations in a Permanent Magnet Cylindrical Hall-Effect Thruster

Measurements of the discharge current in a cylindrical Hall thruster are presented to quantify plasma oscillations and instabilities without introducing an intrusive probe into the plasma. The time-varying component of the discharge current is measured using a current monitor that possesses a wide frequency bandwidth and the signal is Fourier transformed to yield the frequency spectra present, allowing for the identification of plasma oscillations. The data show that the discharge current oscillations become generally greater in amplitude and complexity as the voltage is increased, and are reduced in severity with increasing flow rate. The breathing mode ionization instability is identified, with frequency as a function of discharge voltage not increasing with discharge voltage as has been observed in some traditional Hall thruster geometries, but instead following a scaling similar to a large-amplitude, nonlinear oscillation mode recently predicted in for annular Hall thrusters. A transition from lower amplitude oscillations to large relative fluctuations in the oscillating discharge current is observed at low flow rates and is suppressed as the mass flow rate is increased. A second set of peaks in the frequency spectra are observed at the highest propellant flow rate tested. Possible mechanisms that might give rise to these peaks include ionization instabilities and interactions between various oscillatory modes.

Polzin, K. A.↗
NASA NTRS1965

Variable frequency transistor inverters use multiple core transformers

Magnetic-coupled multivibrators containing two or more square-loop cores with multiple windings in a single transformer package, provide indirect frequency control and improved operational characteristics. This multivibrator can be used for power oscillators, nonlinear magnetic circuitry and telemetry circuits.

Source record↗
NASA NTRS1973

Plasma kinetic theory

Plasma kinetic theory is examined. Data cover nonlinear oscillations and plasma turbulence in uniform and nonuniform media.

Kaufman, A. N.↗