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At least 253 records · Page 14

Nonlocal stability analysis of the MHD Kelvin-Helmholtz instability in a compressible plasma

A general stability analysis is given of the Kevin-Helmholtz instability, for the case of sheared MHD flow of finite thickness in a compressible plasma which allows for the arbitrary orientation of the magnetic field, velocity flow, and wave vector in the plane perpendicular to the velocity gradient. The stability problem is reduced to the solution of a single second-order differential equation including a gravitational term to represent the coupling between the Kelvin-Helmholtz mode and the interchange mode. Compressibility and a magnetic field component parallel to the flow are found to be stabilizing effects, with destabilization of only the fast magnetosonic mode in the transverse case, and the presence of both Alfven and slow magnetosonic components in the parallel case. Analysis results are used in a discussion of the stability of sheared plasma flow at the magnetopause boundary and in the solar wind.

Miura, A.↗

A vectorized algorithm for 3D dynamics of a tethered satellite

Equations of motion characterizing the three dimensional motion of a tethered satellite during the retrieval phase are studied. The mathematical model involves an arbitrary number of point masses connected by weightless cords. Motion occurs in a gravity gradient field. The formulation presented accounts for general functions describing support point motion, rate of tether retrieval, and arbitrary forces applied to the point masses. The matrix oriented program language MATLAB is used to produce an efficient vectorized formulation for computing natural frequencies and mode shapes for small oscillations about the static equilibrium configuration; and for integrating the nonlinear differential equations governing large amplitude motions. An example of time response pertaining to the skip rope effect is investigated.

Wilson, Howard B.↗

Nonlinear response of infinitely long circular cylindrical shells to subharmonic radial loads

The nonlinear response of infinitely long circular cylindrical shells (thin circular rings) in the presence of a two-to-one internal (autoparametric) resonance to a subharmonic excitation of order one-half of the higher mode is analyzed with the multiple-scale method. Four autonomous first-order ordinary differential equations are derived for the modulation of the amplitudes and phases of the interacting models. These modulation equations are used to determine the fixed points and their stability. The fixed points correspond to periodic oscillations of the shell, whereas the limit-cycle solutions of the modulation equations correspond to amplitude and phase-modulated oscillations of the shell. The force response curves exhibit saturation, jumps, and Hopf bifurcation. As excitation frequency changes, all limit cycles deform and lose stability through either pitchfork or cyclic-fold (saddle-node) bifurcations. Some of these saddle-node bifurcations cause a transition to chaos. The pitchfork bifurcations break the symmetry of the limit cycles.

Nayfeh, Ali H.↗

Buckling mode localization in elastic plates due to misplacement in the stiffener location

This paper deals with the buckling of the stiffened plate under uni-axial compression. The direct integration of the governing differential equation is performed and the exact solution to the problem is obtained. As examples, a square plate with single stiffener, and a stiffened three-span, continuous plate are investigated, with special attention given to the influence of stiffener misplacement on the buckling load and mode shape of the plate. It is found that a small misplacement of the stiffeners from the nominal configuration may change the buckling mode from a global one to a highly localized one.

Elishakoff, I.↗

Gas absorption/desorption temperature-differential engine

Continuously operating compressor system converts 90 percent of gas-turbine plant energy to electricity. Conventional plants work in batch mode, operating at 40 percent efficiency. Compressor uses metal hydride matrix on outside of rotating drum to generate working gas, hydrogen. Rolling valve seals allow continuous work. During operation, gas is absorbed, releasing heat, and desorbed with heat gain. System conserves nuclear and fossil fuels, reducing powerplant capital and operating costs.

Miller, C. G.↗

Investigation of Spiral Bevel Gear Condition Indicator Validation Via AC-29-2C Using Damage Progression Tests

This report documents the results of spiral bevel gear rig tests performed under a NASA Space Act Agreement with the Federal Aviation Administration (FAA) to support validation and demonstration of rotorcraft Health and Usage Monitoring Systems (HUMS) for maintenance credits via FAA Advisory Circular (AC) 29-2C, Section MG-15, Airworthiness Approval of Rotorcraft (HUMS) (Ref. 1). The overarching goal of this work was to determine a method to validate condition indicators in the lab that better represent their response to faults in the field. Using existing in-service helicopter HUMS flight data from faulted spiral bevel gears as a "Case Study," to better understand the differences between both systems, and the availability of the NASA Glenn Spiral Bevel Gear Fatigue Rig, a plan was put in place to design, fabricate and test comparable gear sets with comparable failure modes within the constraints of the test rig. The research objectives of the rig tests were to evaluate the capability of detecting gear surface pitting fatigue and other generated failure modes on spiral bevel gear teeth using gear condition indicators currently used in fielded HUMS. Nineteen final design gear sets were tested. Tables were generated for each test, summarizing the failure modes observed on the gear teeth for each test during each inspection interval and color coded based on damage mode per inspection photos. Gear condition indicators (CI) Figure of Merit 4 (FM4), Root Mean Square (RMS), +/- 1 Sideband Index (SI1) and +/- 3 Sideband Index (SI3) were plotted along with rig operational parameters. Statistical tables of the means and standard deviations were calculated within inspection intervals for each CI. As testing progressed, it became clear that certain condition indicators were more sensitive to a specific component and failure mode. These tests were clustered together for further analysis. Maintenance actions during testing were also documented. Correlation coefficients were calculated between each CI, component, damage state and torque. Results found test rig and gear design, type of fault and data acquisition can affect CI performance. Results found FM4, SI1 and SI3 can be used to detect macro pitting on two more gear or pinion teeth as long as it is detected prior to progressing to other components or transitioning to another failure mode. The sensitivity of RMS to system and operational conditions limit its reliability for systems that are not maintained at steady state. Failure modes that occurred due to scuffing or fretting were challenging to detect with current gear diagnostic tools, since the damage is distributed across all the gear and pinion teeth, smearing the impacting signatures typically used to differentiate between a healthy and damaged tooth contact. This is one of three final reports published on the results of this project. In the second report, damage modes experienced in the field will be mapped to the failure modes created in the test rig. The helicopter CI data will then be re-processed with the same analysis techniques applied to spiral bevel rig test data. In the third report, results from the rig and helicopter data analysis will be correlated. Observations, findings and lessons learned using sub-scale rig failure progression tests to validate helicopter gear condition indicators will be presented.

gears↗

Reusable Launch Vehicle Control In Multiple Time Scale Sliding Modes

A reusable launch vehicle control problem during ascent is addressed via multiple-time scaled continuous sliding mode control. The proposed sliding mode controller utilizes a two-loop structure and provides robust, de-coupled tracking of both orientation angle command profiles and angular rate command profiles in the presence of bounded external disturbances and plant uncertainties. Sliding mode control causes the angular rate and orientation angle tracking error dynamics to be constrained to linear, de-coupled, homogeneous, and vector valued differential equations with desired eigenvalues placement. Overall stability of a two-loop control system is addressed. An optimal control allocation algorithm is designed that allocates torque commands into end-effector deflection commands, which are executed by the actuators. The dual-time scale sliding mode controller was designed for the X-33 technology demonstration sub-orbital launch vehicle in the launch mode. Simulation results show that the designed controller provides robust, accurate, de-coupled tracking of the orientation angle command profiles in presence of external disturbances and vehicle inertia uncertainties. This is a significant advancement in performance over that achieved with linear, gain scheduled control systems currently being used for launch vehicles.

Shtessel, Yuri↗

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: Stationary modes

Spatially discrete difference approximations for hyperbolic initial-boundary-value problems (IBVPs) require numerical boundary conditions in addition to the analytical boundary conditions specified for the differential equations. Improper treatment of a numerical boundary condition can cause instability of the discrete IBVP even though the approximation is stable for the pure initial-value or Cauchy problem. In the discrete IBVP stability literature there exists a small class of discrete approximations called borderline cases. For nondissipative approximations, borderline cases are unstable according to the theory of the Gustafsson, Kreiss, and Sundstrom (GKS) but they may be Lax-Richtmyer stable or unstable in the L sub 2 norm on a finite domain. It is shown that borderline approximation can be characterized by the presence of a stationary mode for the finite-domain problem. A stationary mode has the property that it does not decay with time and a nontrivial stationary mode leads to algebraic growth of the solution norm with mesh refinement. An analytical condition is given which makes it easy to detect a stationary mode; several examples of numerical boundary conditions are investigated corresponding to borderline cases.

Warming, Robert F.↗

Solving nonlinear heat transfer constant area fin problems

Tables and graphs were compiled for solving nonlinear heat transfer constant area fin problems. The differential equation describing one-dimensional steady-state temperature distribution and heat flow under three modes of heat transfer with heat generation was investigated.

Source record↗

Testing of containers made of glass-fiber reinforced plastic with the aid of acoustic emission analysis

Acoustic emission analysis as a quasi-nondestructive test method makes it possible to differentiate clearly, in judging the total behavior of fiber-reinforced plastic composites, between critical failure modes (in the case of unidirectional composites fiber fractures) and non-critical failure modes (delamination processes or matrix fractures). A particular advantage is that, for varying pressure demands on the composites, the emitted acoustic pulses can be analyzed with regard to their amplitude distribution. In addition, definite indications as to how the damages occurred can be obtained from the time curves of the emitted acoustic pulses as well as from the particular frequency spectrum. Distinct analogies can be drawn between the various analytical methods with respect to whether the failure modes can be classified as critical or non-critical.

Wolitz, K.↗

Numerical study of baroclinic instability

The effect of a power law gravity field on baroclinic instability is examined with emphasis on the case of inverse fifth power gravity, since this is the power law produced when terrestrial gravity is simulated in spherical geometry by electrostatic means. Growth rates of unstable normal modes were obtained as a function of parameters of the problem by solving a second order differential equation numerically. Results are compared with those from an earlier study where gravity was a constant. The conclusion is that, over the range of parameter space explored here, there is no significant change in the character of theoretical regime diagrams if the vertically averaged gravity is used as a parameter.

Geisler, J. E.↗

Regular and Chaotic Quantum Dynamics of Two-Level Atoms in a Selfconsistent Radiation Field

Dynamics of two-level atoms interacting with their own radiation field in a single-mode high-quality resonator is considered. The dynamical system consists of two second-order differential equations, one for the atomic SU(2) dynamical-group parameter and another for the field strength. With the help of the maximal Lyapunov exponent for this set, we numerically investigate transitions from regularity to deterministic quantum chaos in such a simple model. Increasing the collective coupling constant b is identical with 8(pi)N(sub 0)(d(exp 2))/hw, we observed for initially unexcited atoms a usual sharp transition to chaos at b(sub c) approx. equal to 1. If we take the dimensionless individual Rabi frequency a = Omega/2w as a control parameter, then a sequence of order-to-chaos transitions has been observed starting with the critical value a(sub c) approx. equal to 0.25 at the same initial conditions.

Konkov, L. E.↗

Continuous and cyclic thermal exposure induced degradation in boron reinforced 6061 aluminum composites

Boron reinforced 6061 aluminum (B/Al) composite was continuously exposed at 728 K for up to 240 hours and cyclically exposed between 293 K and 728 K for up to 6000 three-minute cycles. Room temperature tensile strengths were measured and the specimens were metallographically examined. The data suggest that, in addition to AlB2 formation, magnesium in the matrix diffused to the reaction layer and formed (Al,Mg)B2. This formation could weaken the matrix and embrittle the reaction layer. Continuous exposure degraded the strength of the B/Al specimens about 28% in 240 hours. However, the fracture mode, one indicative of high strength interfaces, did not change. The strength degradation was attributed to crack initiation in the brittle reaction layer causing stress concentrations in the fibers. Cyclic exposure degraded the strength of the B/Al about 34% in 6000 cycles. The fracture mode of the cyclic exposure specimens showed transition toward a mode characteristic of low interfacial strength. The lower interfacial strengths were attributed to stress fields induced by differential thermal expansion. Cyclic exposure degraded the strength of the B/Al specimens more than continuous exposure for similar cumulative exposure times.

Olsen, G. C.↗

A static acoustic signature system for the analysis of dynamic flight information

The Army family of helicopters was analyzed to measure the polar octave band acoustic signature in various modes of flight. A static array of calibrated microphones was used to simultaneously acquire the signature and differential times required to mathematically position the aircraft in space. The signature was then reconstructed, mathematically normalized to a fixed radius around the aircraft.

Ramer, D. J.↗

Unstable current systems and plasma instabilities in astrophysics; Proceedings of the 107th Symposium, University of Maryland, College Park, August 8-11, 1983

Among the topics discussed are: magnetic field reconnection in cosmic plasmas; energy dissipation mechanisms in the solar corona; and the acceleration of runaway electrons and Joule heating in solar flares. Consideration is also given to: the nonlinear evolution of the resistive tearing mode; anomalous transport in current sheets; equilibrium and instability in extragalactic jets; and magnetic field reconnection in differentially rotating accretion disks. Among additional topics discussed are: the creation of high energy electron tails by lower hybrid waves and its connection with type-II and type-III bursts; beam current systems in solar flares; and the spatio-temporal features of microwave emissions of active regions and flares.

Kundu, M. R.↗

UNAERO: A package of FORTRAN subroutines for approximating unsteady aerodynamics in the time domain

This report serves as an instruction and maintenance manual for a collection of CDC CYBER FORTRAN IV subroutines for approximating the unsteady aerodynamic forces in the time domain. The result is a set of constant-coefficient first-order differential equations that approximate the dynamics of the vehicle. Provisions are included for adjusting the number of modes used for calculating the approximations so that an accurate approximation is generated. The number of data points at different values of reduced frequency can also be varied to adjust the accuracy of the approximation over the reduced-frequency range. The denominator coefficients of the approximation may be calculated by means of a gradient method or a least-squares approximation technique. Both the approximation methods use weights on the residual error. A new set of system equations, at a different dynamic pressure, can be generated without the approximations being recalculated.

Dunn, H. J.↗

Eye-Safe Lidar

Laser infrared radar (lidar) undergoing development harmless to human eyes, consists almost entirely of solid-state components, and offers high range resolution. Operates at wavelength of about 2 micrometers. If radiation from such device strikes eye, almost completely absorbed by cornea without causing damage, even if aimed directly at eye. Continuous-wave light from laser oscillator amplified and modulated for transmission from telescope. Small portion of output of oscillator fed to single-mode fiber coupler, where mixed with return pulses. Intended for remote Doppler measurements of winds and differential-absorption measurements of concentrations of gases in atmosphere.

Byer, Robert L.↗

A note concerning the onset of three dimensionality and time dependence in Goertler vortices

Recently Hall and Seddougui (1989) considered the secondary instability of large amplitude Goertler vortices in a growing boundary layer evolving into a three-dimensional flow with wavy vortex boundaries. They obtained a pair of coupled, linear ordinary differential equations for this instability which constituted an eigenproblem for the wavelength and frequency of this wavy mode. Investigations into the nonlinear version of this problem by Seddougui and Bassom have revealed several omissions in the numerical work of Hall and Seddougui. These issues are addressed in this note. In particular, it is found that many neutrally stable modes are possible. The properties of such modes are derived in a high wavenumber limit and it is shown that the combination of the results of Hall and Seddougui and the modifications made here lead to conclusions which are consistent with the available experimental observations.

Bassom, Andrew P.↗