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At least 973 records · Page 54

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NASA NTRS1982

Equations of motion for a flexible spacecraft-lumped parameter idealization

The equations of motion for a flexible vehicle capable of arbitrary translational and rotational motions in inertial space accompanied by small elastic deformations are derived in an unabridged form. The vehicle is idealized as consisting of a single rigid body with an ensemble of mass particles interconnected by massless elastic structure. The internal elastic restoring forces are quantified in terms of a stiffness matrix. A transformation and truncation of elastic degrees of freedom is made in the interest of numerical integration efficiency. Deformation dependent terms are partitioned into a hierarchy of significance. The final set of motion equations are brought to a fully assembled first order form suitable for direct digital implementation. A FORTRAN program implementing the equations is given and its salient features described.

Storch, Joel↗

NASA NTRS1991

Improved finite-element methods for rotorcraft structures

An overview of the research directed at improving finite-element methods for rotorcraft airframes is presented. The development of a modification to the finite element method which eliminates interelement discontinuities is covered. The following subject areas are discussed: geometric entities, interelement continuity, dependent rotational degrees of freedom, and adaptive numerical integration. This new methodology is being implemented as an anisotropic, curvilinear, p-version, beam, shell, and brick finite element program.

Hinnant, Howard E.↗

NASA NTRS1990

Buoyancy-driven instabilities and the nonlinear breakup of a sheared magnetic layer

Motivated by problems concerning the storage and subsequent escape of the solar magnetic field, a study has been made of how a magnetic layer embedded in a convectively stable atmosphere evolves due to axisymmetric instabilities driven by magnetic buoyancy. The initial equilibrium consists of a toroidal field sheared by a weaker poloidal component. The linear stability problem is investigated for both ideal and resistive MHD, and the nonlinear evolution is followed by numerical integration of the equations of motion. In all cases, the instability is greatly affected by the distribution and strength of the poloidal field. In particular, both the horizontal and vertical scales of the motions are controlled by the location of the surface on which the poloidal field vanishes: the resonant surface. In the nonlinear regime, a resonant surface close to the interface between the magnetized and field-free fluid leads to the localization of the instability, so that only a fraction of the magnetic region is disrupted by the motions. By contrast, a deeply seated resonant surface leads to the complete disruption of the layer and to the formation of large, helical magnetic fragments whose identity is preserved for the entire simulation.

Cattaneo, Fausto↗

NASA NTRS1990

A perturbation method and some applications

For differential equations with one fast variable, a perturbation method is introduced that transforms a solution valid over only a short time interval to a new solution composed of averaged variables plus a periodic function of the averaged variables. The averaged variables are governed by a set of differential equations where the fast variable has been removed and thus can be numerically integrated quickly or solved directly. This method is applied to a perturbed harmonic oscillator with a cubic perturbation, van der Pol's equation, coorbital motion in the restricted three-body problem, and to nearly circular motion of a particle near one of the primaries in the restricted three-body problem.

Konopliv, Alex↗

NASA NTRS1990

Chaos in driven Alfven systems

The chaos in a one-dimensional system, which would be nonlinear stationary Alfven waves in the absence of an external driver, is characterized. The evolution equations are numerically integrated for the transverse wave magnetic field amplitude and phase using the derivative nonlinear Schroedinger equation (DNLS), including resistive wave damping and a long-wavelength monochromatic, circularly polarized driver. A Poincare map analysis shows that, for the nondissipative (Hamiltonian) case, the solutions near the phase space (soliton) separatrices of this system become chaotic as the driver amplitude increases, and 'strong' chaos appears when the driver amplitude is large. The dissipative system exhibits a wealth of dynamical behavior, including quasiperiodic orbits, period-doubling bifurcations leading to chaos, sudden transitions to chaos, and several types of strange attractors.

Hada, T.↗

NASA NTRS1990

Statistics of close approaches between asteroids and planets - Project Spaceguard

A data base of close approaches to the major planets has been generated via numerical integrations for a large number of planet-crossing asteroid orbits over the course of 200,000 yr; these data are then applied to such statistical theories as those of Kessler (1981) and Wetherill (1967). Attention is given to the orbits of the Toro-class asteroids, which violate the assumption of a lack of mean motion resonance locking between target planet and asteroid. A modified form of the Kessler theory is proposed which can address the problem of approaches between orbits that are either nearly coplanar or nearly tangent. A correlation analysis is used to test the assumption that the orbital elements of a planet-crossing orbit change solely due to close approaches.

Milani, A.↗

NASA NTRS1991

Nonlinear behavior of solar gravity modes driven by He-3 in the core. II - Numerical simulations

The nonlinear behavior of gravity-mode oscillations driven by He-3-destroying reactions in the solar core has been examined by numerically integrating equations describing a very simplified model. The results of a previous bifurcation analysis, which suggest that such oscillations are unlikely to attain amplitudes sufficient to trigger core convection, are verified. These results are extended to models whose nuclear reaction rates and thermal stratification represent the core somewhat more accurately. Nonlinear processes give rise to a preference for the oscillations to develop as standing waves rather than traveling waves, thus breaking the degeneracy between these two types of motion which exists in linearized theory. Study of the large-amplitude behavior of the oscillations is hindered by a tendency for the model to become thermally unstable.

Merryfield, William J.↗

NASA NTRS1991

Statistical-mechanical selection of the shapes of disk galaxies

A new method is proposed for selecting steady state shapes of disk galaxies as 'most probable states' of a large number of stars, given only the total energy and total angular momentum. A partial differential equation is derived for the mean gravitational potential; it is closely related to the 'sinh-Poisson' equation for the mean-field description of a line vortex system or electrostatic guiding-center plasma. A 'water bag' approximation to the distribution function for bound stars renders the equation analytically tractable, but accurate solution of it may require numerical integration, in view of its general nonlinearity.

Montgomery, David↗

NASA NTRS1991

Periodic response of multi-disk rotors with bearing clearances

The forced steady state response of a multi-disk rotor system involving a clearance at one of the bearings is determined by using a harmonic balance approach. The impedance method is applied to each of the harmonic steady state components in order to reduce the system to its displacement at the nonlinear bearing support. The results reveal the interrelated roles of the bearing clearance, mass eccentricity and side force in producing dangerous subharmonics. The significant effects of the strong nonlinearity of a bearing clearance are studied as related to the various system parameters. The results show that the approach developed in this study is computationally superior to numerical integration methods in analyzing multi-disk rotor systems with strong nonlinearity.

Kim, Y. B.↗

NASA NTRS1991

Variational finite element-tensor formulation for the large deflection random vibration of composite plates

A numerical integration routine is derived from a set of unified single step integration algorithms using a weighted satisfaction of the equilibrium equation governing the large deflection random response of laminated composite plates. The equilibrium equation is derived using a constant matrix large deflection finite-element formulation. In-plane inertia terms are considered in the formulation, however, rotary inertia terms are assumed negligible. Probability density, spectral density and autocorrelation functions of the maximum displacement and strain responses are presented for three acoustic excitation levels. Classical thin plate boundary conditions and pseudo white noise excitation are used in this investigation.

Robinson, Jay H.↗

NASA NTRS1989

Nonlinear mechanical behavior of thermoplastic matrix materials for advanced composites

Two recent theories of nonlinear mechanical response are quantitatively compared and related to experimental data. Computer techniques are formulated to handle the numerical integration and iterative procedures needed to solve the associated sets of coupled nonlinear differential equations. Problems encountered during these formulations are discussed and some open questions described. Bearing in mind these cautions, the consequences of changing parameters that appear in the formulations on the resulting engineering properties are discussed. Hence, engineering approaches to the analysis of thermoplastic matrix material can be suggested.

Arenz, R. J.↗

NASA NTRS1991

Near-critical spherical accretion by neutron stars - General relativistic treatment

Time-independent spherical accretion by a neutron star is studied using general relativistic radiation hydrodynamics. Numerical integrations of the flow equations are presented. These show that when the luminosity is sufficiently close to (but below) the Eddington limit, the flow velocity increases with decreasing radius far from the neutron star, reaches a maximum at an intermediate radius, and decreases at small radii. A large fraction of the binding energy of the flow is transferred to the radiation through scattering before the flow strikes the surface of the neutron star. Following Miller's treatment of accretion at luminosites near the Eddington limit (which neglected general relativistic effects), analytic approximations for the decelerating phase of the flow's velocity profile are derived. The dependence of the solutions on the variable Eddington factor prescription chosen to close the radiation moment equations is also examined.

Park, Myeong-Gu↗

NASA NTRS1991

Alfven shock trains

The Cohen-Kulsrud-Burgers equation (CKB) is used to consider the nonlinear evolution of resistive, quasi-parallel Alfven waves subject to a long-wavelength, plane-polarized, monochromatic instability. The instability saturates by nonlinear steepening, which proceeds until the periodic waveform develops an interior scale length comparable to the dissipation length; a fast or an intermediate shock then forms. The result is a periodic train of Alfven shocks of one or the other type. For propagation strictly parallel to the magnetic field, there will be two shocks per instability wavelength. Numerical integration of the time-dependent CKB equation shows that an initial, small-amplitude growing wave asymptotes to a stable, periodic stationary wave whose analytic solution specifies how the type of shock embedded in the shock train, and the amplitude and speed of the shock train, depend on the strength and phase of the instability. Waveforms observed upstream of the earth's bowshock and cometary shocks resemble those calculated here.

Malkov, M. A.↗

NASA NTRS1991

Exotic containers for capillary surfaces

This paper discusses 'exotic' rotationally symmetric containers that admit an entire continuum of distinct equilibrium capillary free surfaces. The paper extends earlier work to a larger class of parameters and clarifies and simplifies the governing differential equations, while expressing them in a parametric form appropriate for numerical integration. A unified presentation suitable for both zero and nonzero gravity is given. Solutions for the container shapes are depicted graphically along with members of the free-surface continuum, and comments are given concerning possible physical experiments.

Concus, Paul↗

NASA NTRS1991

Waves produced from a harmonic point source in a supersonic boundary layer

The disturbance wave pattern produced by a harmonic point source in a compressible flat-plate boundary layer is computed using linear stability theory and direct numerical integration approach. Receptivity coefficients are computed for the spectrum of spanwise modes generated at the source. The effect of boundary layer growth on the development of linear waves is determined by using the method of multiple scales. Results are presented for Mach numbers of 0, 2, 4.5, and 7. It is found that disturbances spread in wedge-shaped regions behind the source and the wedge angle decreases with Mach number. The lateral spreading angle for the instability waves turns out to be quite close to the angle found experimentally for turbulence lateral contamination.

Balakumar, P.↗

NASA NTRS1991

The effect of multi-periapse burns on planetary escape and capture

The use of multiple periapse burns to transfer between a planetocentric parking orbit and a hyperbolic trajectory with a high thrust propulsion system having constant, finite thrust is investigated. Such multiple burns offer propellant savings as a consequence of reduced velocity losses which accrue over the finite burn time of thrusting maneuvers. Velocity losses for an earth escape phase are calculated for an optimum steering program over a range of parameters that are typical of a Mars mission. These numerically integrated results are compared to velocity losses evaluated with a leading analytic approximation to establish boundaries within which the accuracy of the analytic approximation is adequate for preliminary mission planning purposes. Finally, results of the investigation are used to define typical benefits of the multi-periapse burn concept for Mars exploration missions.

Horsewood, Jerry L.↗

NASA NTRS1992

Faster Computation Of Far Fields Of Dish Antennas

Modified Zernike-polynomial approach reduces number of terms in numerical integration. Yields greater or equal accuracy with fewer terms in series expansion and fewer sampling points across aperture and, less computation. Method based on Jacobi-Bessel-expansion concept.

Jamnejad, Vahraz↗

NASA NTRS1992

Trajectory And Heating Of A Hypervelocity Projectile

Technical paper presents derivation of approximate, closed-form equation for relationship between velocity of projectile and density of atmosphere. Results of calculations based on approximate equation agree well with results from numerical integrations of exact equations of motion. Comparisons of results presented in series of graphs.

Tauber, Michael E.↗