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At least 667 records · Page 37
All sourcesNASA NTRSDOE OSTI
NASA NTRS2015

Toward a Nonlinear Acoustic Analogy: Turbulence as a Source of Sound and Nonlinear Propagation

An acoustic analogy is proposed that directly includes nonlinear propagation effects. We examine the Lighthill acoustic analogy and replace the Green's function of the wave equation with numerical solutions of the generalized Burgers' equation. This is justified mathematically by using similar arguments that are the basis of the solution of the Lighthill acoustic analogy. This approach is superior to alternatives because propagation is accounted for directly from the source to the far-field observer instead of from an arbitrary intermediate point. Validation of a numerical solver for the generalized Burgers' equation is performed by comparing solutions with the Blackstock bridging function and measurement data. Most importantly, the mathematical relationship between the Navier-Stokes equations, the acoustic analogy that describes the source, and canonical nonlinear propagation equations is shown. Example predictions are presented for nonlinear propagation of jet mixing noise at the sideline angle.

Miller, Steven A. E.↗
NASA NTRS1966

Nonlinear theory of elastic directed surfaces.

Nonlinear theory for deformation of elastic directed surface, assuming existence of strain energy function and postulating virtual work governing mechanical behavior

ELASTIC DEFORMATION↗
NASA NTRS1984

Regions of attraction and ultimate boundedness for linear quadratic regulators with nonlinearities

The closed-loop stability of multivariable linear time-invariant systems controlled by optimal linear quadratic (LQ) regulators is investigated for the case when the feedback loops have nonlinearities N(sigma) that violate the standard stability condition, sigma N(sigma) or = 0.5 sigma(2). The violations of the condition are assumed to occur either (1) for values of sigma away from the origin (sigma = 0) or (2) for values of sigma in a neighborhood of the origin. It is proved that there exists a region of attraction for case (1) and a region of ultimate boundedness for case (2), and estimates are obtained for these regions. The results provide methods for selecting the performance function parameters to design LQ regulators with better tolerance to nonlinearities. The results are demonstrated by application to the problem of attitude and vibration control of a large, flexible space antenna in the presence of actuator nonlinearities.

Joshi, S. M.↗
NASA NTRS1973

Theoretical and experimental investigation of the nonlinear behavior of angleplied boron/aluminum composites

Specimens from angleplied laminates of boron/aluminum composites were tested and the results analyzed. The specimens consisted of eight-ply symmetric layups and were loaded in tension at various angles to the 0 deg-ply direction. Stress-strain curves to specimen fracture were obtained. The analysis was performed using linear composite mechanics which includes residual stresses and a combined stress yield function. The results obtained indicate that angleplied boron/aluminum laminates exhibit a nonlinear stress-strain behavior to fracture. The residual stresses affect the initial and yield laminate properties. Linear composite mechanics is inadequate to predict the mechanical behavior of boron/aluminum angleplied laminates.

Chamis, C. C.↗
NASA NTRS1973

Theoretical and experimental investigation of the nonlinear behavior of angleplied boron/aluminum composites.

Specimens from angleplied laminates of boron/aluminum composites were tested and the results analyzed. The specimens consisted of eight-ply symmetric layups and were loaded in tension at various angles to the 0-deg-ply direction. Stress-strain curves to specimen fracture were obtained. The analysis was performed using linear composite mechanics which includes residual stresses and a combined stress yield function. The results obtained indicate that angleplied boron/aluminum laminates exhibit a nonlinear stress-strain behavior to fracture. The residual stresses affect the initial and 'yield' laminate properties.

Chamis, C. C.↗
NASA NTRS1987

Multiple-mode large deflection random response of beams with nonlinear damping subjected to acoustic excitation

Multiple-mode nonlinear analysis is carried out for beams subjected to acoustic excitation. Effects of both nonlinear damping and large-deflection are included in the analysis in an attempt to explain the experimental phenomena of aircraft panels excited at high sound pressure levels; that is the broadening of the strain response peaks and the increase of modal frequency. An amplitude dependent nonlinear damping model is used in the anlaysis to study the effects and interactions of multiple modes, nonlinear stiffness and nonlinear damping on the random response of beams. Mean square maximum deflection, mean square maximum strain, and spectral density function of maximum strain for simple supported and clamped beams are obtained. It is shown analytically that nonlinear damping contributes significantly to the broadening of the response peak and to the mean square deflection and strain.

Prasad, C. B.↗
NASA NTRS1992

Failure of the method of slowly varying amplitude and phase for non-linear, singular oscillators

It is shown that the method of slowly varying amplitude and phase yields erroneous results in the study of the mathematical properties of nonlinear singular oscillator systems. The analytical solution is described in which the phase function is constant and for which a special limiting behavior exists when the wavelength is zero. The previous method based on the condition of boundedness cannot be satisfied for nonlinear singular characteristics, and the erroneous designation of the expansion parameter is identified.

Mickens, R. E.↗
NASA NTRS1970

Construction of Liapunov functions

Liapunov functions construction through conversion of differential equation with polynomial nonlinearities into auxiliary exact differential equation using algorithm

Chen, C.-S.↗
NASA NTRS1973

Dynamics of electromechanical flow structures.

Free-surface gravity flows and capillary wicking provide examples of flow structures with fluid partially ducted at free surfaces by external forces. Wall-less electromechanical flow structures are developed which have a similar nature, but with polarization forces providing the orientation at free surfaces. Like their mechanical counterparts, these have the ability to ingest liquid or expel vapor through their walls. The structures consist of electrodes running in the flow direction z with slowly varying cross sections in a plane transverse to the flow. A formulation is given of the long-wave nonlinear (principal mode) dynamics, with use made of energy functions to represent a broad class of possible mechanical and electrical structure geometries.

Jones, T. B., Jr.↗
NASA NTRS1974

Creep response of the lunar crust in mare regions from an analysis of crater deformation

The settling trends of 318 lunar mare craters are compared with predictions of numerical finite-element models in order to determine the creep response of the upper lunar mare crust. No settling is evident in craters smaller than 5 km in diameter. Settling rates of larger craters increase as function of crater size in a manner suggesting a nonlinear lunar creep response corresponding to the power law epsilon = 8.3 x 10 to the minus 34th sigma squared where epsilon is the strain rate and sigma is the differential stress. However, the observed nonlinearity is probably an apparent nonlinearity resulting from the temperature-induced viscosity decrease with depth due to a lunar crustal temperature gradient of 3 C/km and a creep activation energy of 20 kcal/mole. It is concluded that creep in the lunar medium is essentially Newtonian, and that the effective viscosity of the upper lunar mare is (1.6 plus or minus 0.3) x 10 to the 25th poise.

Kunze, A. W. G.↗
NASA NTRS1977

Liquid jet impingement normal to a disk in zero gravity

The free surface shapes of circular liquid jets impinging normal to sharp-edged disks in zero gravity are determined. Zero gravity drop tower experiments yielded three distinct flow patterns that were classified in terms of the relative effects of surface tension and inertial forces. An order of magnitude analysis was conducted that indicated regions where viscous forces were not significant in the computation of free surface shapes. The free surface analysis was simplified by transforming the governing potential flow equations and boundary conditions into the inverse plane, where the stream function and velocity potential became the coordinates. The resulting nonlinear equations were solved by standard finite difference methods, and comparisons were made with the experimental data for the inertia dominated regime.

Labus, T. L.↗
NASA NTRS1981

Influence of combined visual and vestibular cues on human perception and control of horizontal rotation

Measurements are made of manual control performance in the closed-loop task of nulling perceived self-rotation velocity about an earth-vertical axis. Self-velocity estimation is modeled as a function of the simultaneous presentation of vestibular and peripheral visual field motion cues. Based on measured low-frequency operator behavior in three visual field environments, a parallel channel linear model is proposed which has separate visual and vestibular pathways summing in a complementary manner. A dual-input describing function analysis supports the complementary model; vestibular cues dominate sensation at higher frequencies. The describing function model is extended by the proposal of a nonlinear cue conflict model, in which cue weighting depends on the level of agreement between visual and vestibular cues.

Zacharias, G. L.↗
NASA NTRS1988

Flexible spacecraft maneuver - Inverse attitude control and modal stabilization

A control law is presented for three-axis rotational maneuvers of a spacecraft (orbiter)-beam-tip body (antenna or a reflector) configuration based on nonlinear inversion and modal velocity feedback. Using invertibility and functional reproducibility results, a decoupling attitude control law is presented such that, in the closed-loop system, the attitude angles of the spacecraft are independently controlled using the control moments acting on the space vehicle. This controller asymptotically decouples the flexible dynamics from the rigid one and also allows the decomposition of the elastic dynamics into two subsystems representing the transverse deflections of the beam in two orthogonal planes. These low-order subsystems are used for derivation of a modal velocity feedback stabilizer using the force and moment actuators at the end body. Simulation results are presented to show that, in the closed-loop system, attitude control and elastic mode stabilization are accomplished in spite of the parameter uncertainty and disturbance torque input in the system.

Singh, Sahjendra N.↗
NASA NTRS1989

Variable-Metric Algorithm For Constrained Optimization

Variable Metric Algorithm for Constrained Optimization (VMACO) is nonlinear computer program developed to calculate least value of function of n variables subject to general constraints, both equality and inequality. First set of constraints equality and remaining constraints inequalities. Program utilizes iterative method in seeking optimal solution. Written in ANSI Standard FORTRAN 77.

Frick, James D.↗