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NASA NTRS1985

Oscillations of a compound drop system undergoing rotation

A compound liquid-drop system is comprised of three immiscible concentric fluids: a core fluid of density p(i) surrounded by a shell of density p(s) which is embedded in a medium of density p(o). In this analysis, the fluids are incompressible and inviscid. The effect of rotation upon the modes of oscillation of a compound drop is investigated. Rotation rate is considered as a small perturbation of the normal modes of the compound drop, thus introducing the effects of a Coriolis force and a centrifugal distortion.

Lyell, M. J.↗

NASA NTRS1996

Observational Consequences of Galactic Oscillations

The normal mode oscillations of galaxies we reported recently are large enough to produce observational consequences. The two lowest order modes were both very strong and long lived: the fundamental is a "breathing" mode in which the entire galaxy expands and contracts homologously, while the second radial mode is spherically symmetrical and has one radial node. A sheet of neutral hydrogen in an oscillating galaxy partakes of the general oscillations, and the resulting velocity fields would normally be interpreted in terms of warps or oval distortions. More interestingly, the second radial mode might be a dynamical driver for bulges in early-type spiral galaxies. If bulges result from a dynamical process within the galaxy, there might be other observable properties driven by the same dynamical process. The hole often reported in neutral hydrogen in early type spiral galaxies is one such candidate. It has sometimes been reported to be about the same size as the bulge. We will discuss evidence from velocity fields concerning the fundamental mode and from the coincidence of bulge and HI hole sizes as evidence for the second mode.

Miller, R. H.↗

NASA NTRS1990

Resonant decay of global MHD modes at 'thick' interfaces

A global surface mode can exist on a 'surface' which is not a true discontinuity, but without sufficient dissipation it is not a normal mode and it decays in time via resonance absorption. The decay rate can be calculated analytically when the 'surface' is thin. The goal of this paper is to numerically estimate the decay rate when the surface is not thin. A cold plasma in a uniform magnetic field is considered in which density varies linearly across the 'surface'. In this linearized calculation, the global surface mode is driven in steady state by an antenna located in one of the uniform regions external to the surface. The frequency is a free parameter, and resonance curves are computed numerically without approximations. The widths of the resonance curves are used to estimate the free decay times of undriven surface modes, via the uncertainty principle. When applied to the active solar corona, the decay rates are large enough to account for the coronal heating, but it should be kept in mind that the role of nonlinearity in resonance absorption is still undetermined.

Hollweg, Joseph V.↗

NASA NTRS1977

Mathematical and computational studies of the stability of axisymmetric annular capillary free surfaces

Of principal interest is the stability of a perfectly wetting liquid in an inverted, vertical, right circular-cylindrical container having a concave spheroidal bottom. The mathematical conditions that the contained liquid be in stable static equilibrium are derived, including those for the limiting case of zero contact angle. Based on these results, a computational investigation is carried out for a particular container that is used for the storage of liquid fuels in NASA Centaur space vehicles, for which the axial ratio of the container bottom is 0.724. It is found that for perfectly wetting liquids the qualitative nature of the onset of instability changes at a critical liquid volume, which for the Centaur fuel tank corresponds to a mean fill level of approximately 0.503 times the tank's radius. Small-amplitude periodic sloshing modes for this tank were calculated; oscillation frequencies or growth rates are given for several Bond numbers and liquid volumes, for normal modes having up to six angular nodes.

Albright, N.↗

NASA NTRS1985

Computational modes and the Machenauer N.L.N.M.I. of the GLAS 4th order model

An attempt was made to use the GLAS global 4th order shallow water equations to perform a Machenhauer nonlinear normal mode initialization (NLNMI) for the external vertical mode. A new algorithm was defined for identifying and filtering out computational modes which affect the convergence of the Machenhauer iterative procedure. The computational modes and zonal waves were linearly initialized and gravitational modes were nonlinearly initialized. The Machenhauer NLNMI was insensitive to the absence of high zonal wave numbers. The effects of the Machenhauer scheme were evaluated by performing 24 hr integrations with nondissipative and dissipative explicit time integration models. The NLNMI was found to be inferior to the Rasch (1984) pseudo-secant technique for obtaining convergence when the time scales of nonlinear forcing were much smaller than the time scales expected from the natural frequency of the mode.

Navon, I. M.↗

NASA NTRS2012

Nonlinear Reduced-Order Simulation Using An Experimentally Guided Modal Basis

A procedure is developed for using nonlinear experimental response data to guide the modal basis selection in a nonlinear reduced-order simulation. The procedure entails using nonlinear acceleration response data to first identify proper orthogonal modes. Special consideration is given to cases in which some of the desired response data is unavailable. Bases consisting of linear normal modes are then selected to best represent the experimentally determined transverse proper orthogonal modes and either experimentally determined inplane proper orthogonal modes or the special case of numerically computed in-plane companions. The bases are subsequently used in nonlinear modal reduction and dynamic response simulations. The experimental data used in this work is simulated to allow some practical considerations, such as the availability of in-plane response data and non-idealized test conditions, to be explored. Comparisons of the nonlinear reduced-order simulations are made with the surrogate experimental data to demonstrate the effectiveness of the approach.

Rizzi, Stephen A.↗

NASA NTRS1980

Theoretical studies of solar oscillations

Possible sources for the excitation of the solar 5 minute oscillations were investigated and a linear non-adiabatic stability code was applied to a preliminary study of the solar g-modes with periods near 160 minutes. Although no definitive conclusions concerning the excitation of these modes were reached, the excitation of the 5 minute oscillations by turbulent stresses in the convection zone remains a viable possibility. Theoretical calculations do not offer much support for the identification of the 160 minute global solar oscillation (reported by several independent observers) as a solar g-mode. A significant advance was made in attempting to reconcile mixing-length theory with the results of the calculations of linearly unstable normal modes. Calculations show that in a convective envelope prepared according to mixing length theory, the only linearly unstable modes are those which correspond to the turbulent eddies which are the basic element of the heuristic mixing length theory.

Goldreich, P.↗

NASA NTRS1994

Growing 'Alfvenic' modes in the upstream region of Saturn

Recent studies of low-frequency electromagnetic waves upstream of the Saturn bow shock have shown that these waves, in contrast to those at Earth, are observed not in one, but in at least two, distinct frequency bands. The results of wave mode identification based on the Hall-magnetohydrodynamic (MHD) model of plasma and observed wave polarization suggested that these waves propagate in the high beta intermediate mode. However, the underlying instability was not unambiguously determined. In the present paper we use the full electromagnetic dispersion relation derived from linear Vlasov theory in order to examine which of the plasma modes, with observed properties, are unstable in an isotropic Maxwellian plasma in the presence of backstreaming proton beams consistent with Voyager 2 observations at Saturn. As a result we find that the unstable 'Alfvenic' beam mode, as well as resonant and non-resonant fast magnetosonic modes have properties consistent with the data. Moreover, we find that in contrast to the Earth's upstream waves, at Saturn no 'kinetic' normal mode can account for the observed magnetic polarization.

Orlowski, D. S.↗

NASA NTRS1988

Axisymmetric perturbations of thin gaseous disks. I - Unstable convective modes and their consequences for the solar nebula

The axisymmetric perturbations of a thin, differentially rotating gas disk in which the vertical temperature stratification is superadiabatic are analyzed. The growth rate of adiabatic convective normal modes is calculated, departures from simple polytropic disk models are briefly discussed, and the detailed vertical structure of the eigenfunctions is analyzed. The stabilizing effect of radiative diffusion on convective modes is considered. It is found that rotation and compressibility tend to reduce the rate of growth of the disturbances, and that the growth rate increases without limit and is proportional to the square root of the radial wavenumber in polytropic equilibria. The maximum radial size of convective eddies scales like the square root of the degree of superadiabaticity times the size of the convective zone. There is significant convective penetration into radiatively stable layers only for the fundamental and low-order harmonic modes, whose vertical wavelength is comparable to the size of the convective layer.

Ruden, Steven P.↗

NASA NTRS2022

Structural and chemical complexity of minerals: An update

The complexities of chemical composition and crystal structure are fundamental characteristics of minerals that have high relevance to the understanding of their stability, occurrence and evolution. This review summarises recent developments in the field of mineral complexity and outlines possible directions for its future elaboration. The database of structural and chemical complexity parameters of minerals is updated by H-correction of structures with unknown H positions and the inclusion of new data. The revised average complexity values (arithmetic means) for all minerals are 3.54(2) bits/atom and 345(10) bits/cell (based upon 4443 structure reports). The distributions of atomic information amounts, chemIG and strIG, versus the number of mineral species fit the normal modes, whereas the distributions of total complexities, chemIG,total and strIG,total, along with numbers of atoms per formula and per unit cell are log normal. The three most complex mineral species known today are ewingite, morrisonite and ilmajokite, all either discovered or structurally characterised within the last five years. The most important complexity-generating mechanisms in minerals are: (1) the presence of isolated large clusters; (2) the presence of large clusters linked together to form three-dimensional frameworks; (3) formation of complex three-dimensional modular frameworks; (4) formation of complex modular layers; (5) high hydration state in salts with complex heteropolyhedral units; and (6) formation of ordered superstructures of relatively simple structure types. The relations between symmetry and complexity are considered. The analysis of temporal dynamics of mineralogical discoveries since 1875 with the step of 25 years show the increasing chemical and structural complexities of human knowledge of the mineral kingdom in the history of mineralogy. In the Earth’s history, both diversity and complexity of minerals experience dramatic increases associated with the formation of Earth’s continental crust, initiation of plate tectonics and the Great Oxidation event.

complexity↗

NASA NTRS1974

Spacecraft control/flexible structures interaction study

An initial study to begin development of a flight experiment to measure spacecraft control/flexible structure interactions was completed. The approach consisted of developing the equations of motion for a vehicle possessing a flexible solar array, then linearizing about some nominal motion of the craft. A set of solutions is assumed for array deflection using a continuous normal mode method and important parameters are identified. Interrelationships between these parameters, measurement techniques, and input requirements are discussed which assure minimization of special vehicle maneuvers and optimization of data to be obtained during the normal flight sequence. Limited consideration is given to flight data retrieval and processing techniques as correlated with the requirements imposed by the measurement system. Results indicate that inflight measurement of the bending and torsional mode shapes and respective frequencies, and damping ratios, is necessary. Other parameters may be measured from design data.

Kaplan, M. H.↗

NASA NTRS1984

Interference phenomena in the refraction of a surface polariton by vertical dielectric barriers

A normal mode analysis is used to calculate the transmission and reflection coefficients for a surface polariton propagating along the interface between a surface active medium and a dielectric and incident normally on a vertical dielectric barrier of finite thickness or a thin dielectric film of finite length. The efficiencies of conversion of the surface polariton into transmitted and reflected bulk waves are also determined. The radiation patterns associated with the latter waves are presented.

Shen, T. P.↗

NASA NTRS1990

Instabilities and subharmonic resonances of subsonic heated round jets, volume 2

When a jet is perturbed by a periodic excitation of suitable frequency, a large-scale coherent structure develops and grows in amplitude as it propagates downstream. The structure eventually rolls up into vortices at some downstream location. The wavy flow associated with the roll-up of a coherent structure is approximated by a parallel mean flow and a small, spatially periodic, axisymmetric wave whose phase velocity and mode shape are given by classical (primary) stability theory. The periodic wave acts as a parametric excitation in the differential equations governing the secondary instability of a subharmonic disturbance. The (resonant) conditions for which the periodic flow can strongly destabilize a subharmonic disturbance are derived. When the resonant conditions are met, the periodic wave plays a catalytic role to enhance the growth rate of the subharmonic. The stability characteristics of the subharmonic disturbance, as a function of jet Mach number, jet heating, mode number and the amplitude of the periodic wave, are studied via a secondary instability analysis using two independent but complementary methods: (1) method of multiple scales, and (2) normal mode analysis. It is found that the growth rates of the subharmonic waves with azimuthal numbers beta = 0 and beta = 1 are enhanced strongly, but comparably, when the amplitude of the periodic wave is increased. Furthermore, compressibility at subsonic Mach numbers has a moderate stabilizing influence on the subharmonic instability modes. Heating suppresses moderately the subharmonic growth rate of an axisymmetric mode, and it reduces more significantly the corresponding growth rate for the first spinning mode. Calculations also indicate that while the presence of a finite-amplitude periodic wave enhances the growth rates of subharmonic instability modes, it minimally distorts the mode shapes of the subharmonic waves.

Ng, Lian Lai↗

NASA NTRS2005

STS-114: Discovery Post MMT Press Conference

Bruce Buckingham of NASA Public Affairs hosted this press conference. Wayne Hill, Space Shuttle Deputy Program Manager; John Muratore, Shuttle Systems and Integration Manager; Mike Wetmore, Director for Shuttle Processing were present. Wayne started with a video from Shuttle Logistics Depot showing details of a point sensor box commonly named the black box. Work with the trouble shooting continues on a day to day basis, no definite launching date is set. John reports that they are in a mission support mode all over the country until the sensor problem is solved. Mike reports his team will complete scrub and securing tasks through the next day, restore the facility to its normal mode, and will start to a four day process of getting back to launch once trouble shooting is completed. Tanking test, thermal environment, problem identification, engine cut-off sensor problems, sensors, risk, design reviews, test and analysis, correlation of the problem with Columbia, are some of the topics covered with the News media.

Source record↗

NASA NTRS2009

Modeling and Simulation of Variable Mass, Flexible Structures

The advent of the new Ares I launch vehicle has highlighted the need for advanced dynamic analysis tools for variable mass, flexible structures. This system is composed of interconnected flexible stages or components undergoing rapid mass depletion through the consumption of solid or liquid propellant. In addition to large rigid body configuration changes, the system simultaneously experiences elastic deformations. In most applications, the elastic deformations are compatible with linear strain-displacement relationships and are typically modeled using the assumed modes technique. The deformation of the system is approximated through the linear combination of the products of spatial shape functions and generalized time coordinates. Spatial shape functions are traditionally composed of normal mode shapes of the system or even constraint modes and static deformations derived from finite element models of the system. Equations of motion for systems undergoing coupled large rigid body motion and elastic deformation have previously been derived through a number of techniques [1]. However, in these derivations, the mode shapes or spatial shape functions of the system components were considered constant. But with the Ares I vehicle, the structural characteristics of the system are changing with the mass of the system. Previous approaches to solving this problem involve periodic updates to the spatial shape functions or interpolation between shape functions based on system mass or elapsed mission time. These solutions often introduce misleading or even unstable numerical transients into the system. Plus, interpolation on a shape function is not intuitive. This paper presents an approach in which the shape functions are held constant and operate on the changing mass and stiffness matrices of the vehicle components. Each vehicle stage or component finite element model is broken into dry structure and propellant models. A library of propellant models is used to describe the distribution of mass in the fuel tank or Solid Rocket Booster (SRB) case for various propellant levels. Based on the mass consumed by the liquid engine or SRB, the appropriate propellant model is coupled with the dry structure model for the stage. Then using vehicle configuration data, the integrated vehicle model is assembled and operated on by the constant system shape functions. The system mode shapes and frequencies can then be computed from the resulting generalized mass and stiffness matrices for that mass configuration. The rigid body mass properties of the vehicle are derived from the integrated vehicle model. The coupling terms between the vehicle rigid body motion and elastic deformation are also updated from the constant system shape functions and the integrated vehicle model. This approach was first used to analyze variable mass spinning beams and then prototyped into a generic dynamics simulation engine. The resulting code was tested against Crew Launch Vehicle (CLV-)class problems worked in the TREETOPS simulation package and by Wilson [2]. The Ares I System Integration Laboratory (SIL) is currently being developed at the Marshall Space Flight Center (MSFC) to test vehicle avionics hardware and software in a hardware-in-the-loop (HWIL) environment and certify that the integrated system is prepared for flight. The Ares I SIL utilizes the Ares Real-Time Environment for Modeling, Integration, and Simulation (ARTEMIS) tool to simulate the launch vehicle and stimulate avionics hardware. Due to the presence of vehicle control system filters and the thrust oscillation suppression system, which are tuned to the structural characteristics of the vehicle, ARTEMIS must incorporate accurate structural models of the Ares I launch vehicle. The ARTEMIS core dynamics simulation models the highly coupled nature of the vehicle flexible body dynamics, propellant slosh, and vehicle nozzle inertia effects combined with mass and flexible body properties that vary significant with time during the flight. All forces that act on the vehicle during flight must be simulated, including deflected engine thrust force, spatially distributed aerodynamic forces, gravity, and reaction control jet thrust forces. These forces are used to excite an integrated flexible vehicle, slosh, and nozzle dynamics model for the vehicle stack that simulates large rigid body translations and rotations along with small elastic deformations. Highly effective matrix math operations on a distributed, threaded high-performance simulation node allow ARTEMIS to retain up to 30 modes of flex for real-time simulation. Stage elements that separate from the stack during flight are propagated as independent rigid six degrees of freedom (6DOF) bodies. This paper will present the formulation of the resulting equations of motion, solutions to example problems, and describe the resulting dynamics simulation engine within ARTEMIS.

Tobbe, Patrick A.↗

NASA NTRS1989

Issues in CSI analysis for large scale systems

Future spacecraft such as the International Space Station result in flexible models with hundreds, or perhaps thousands of modes in a frequency range where the potential for control/structure interaction exists. This provides the analyst with a formidable model reduction problem at both the component and the system level. Approaches to normal modes as a structural representation, applicability of alternate structural representations and algorithms for selecting important modal degrees of freedom at both the component and the system level are discussed. Practical implementation of these techniques on a large scale model of the Space Station are presented.

Blelloch, Paul↗

NASA NTRS1991

Feedback instability of the ionospheric resonant cavity

A model is developed that provides a theoretical basis for previous numerical results showing a feedback instability with frequencies characteristic of Alfven travel times within the region of the large increase of Alfven speed above the ionosphere. These results have been extended to arbitrary ionospheric conductivity by developing a numerical solution of the cavity dispersion relation that involves Bessel functions of complex order and argument. It is concluded that the large contrast between the magnetospheric and ionospheric Alfven speed leads to the formation of resonant cavity modes with frequencies ranging from 0.1 to 1 Hz. The presence of the cavity leads to a modification of the reflection characteristics of Alfven waves with frequencies that compare to the cavity's normal modes.

Lysak, Robert L.↗

NASA NTRS1993

Three-dimensional numerical simulation of thermal tides in the Martian atmosphere

Analysis of the Mariner 9 IRIS and Viking Orbiter IRTM temperature data and of the time series of surface pressure from the Viking landers has indicated that atmospheric thermal tides are a significant component of the martian general circulation. Classical tidal theory, considering only the Sun synchronous components, has been shown to at least roughly account for the amplitudes of the observed diurnal and semidirunal surface pressure oscillations. In particular, Zurek and Leovy have demonstrated that classical tidal theory can reproduce the observed dependence of the strength of the semidiurnal tide on aerosol optical depth. The high-amplitude topograph of Mars, however, can cause longitudinal distortions in the thermotidal forcing, leading to additional tidal modes that are not Sun synchronous. In particular, observation and theory have suggested the likely presence of a diurnal, zonal wavenumber-1 K wave. Hamilton and Garcia noted that the wavenumber-1 K normal mode has a period of close to 24 hr and may be detectable in surface pressure observations. Zurek has discussed the possibility of this mode being resonantly excited for various atmospheric temperature studies. The semidiurnal wavenumber-2 K mode, with roughly a 12-hr period, could also be resonantly excited. A numerical model with finite amplitude topography and a self-consistent thermotidal forcing resulting from the daily heat flux at the surface and atmospheric absorption of solar radiation by aerosols is used here to explore the influence of topography on martian thermal tides and to examine the possibility of Kelvin wave resonance.

Wilson, R. John↗