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Composite materials research and education program: The NASA-Virginia Tech composites program

Major areas of study include: (1) edge effects in finite width laminated composites subjected to mechanical, thermal and hygroscopic loading with temperature dependent material properties and the influence of edge effects on the initiation of failure; (2) shear and compression testing of composite materials at room and elevated temperatures; (3) optical techniques for precise measurement of coefficients of thermal expansion of composites; (4) models for the nonlinear behavior of composites including material nonlinearity and damage accumulation and verification of the models under biaxial loading; (5) compressive failure of graphite/epoxy plates with circular holes and the buckling of composite cylinders under combined compression and torsion; (6) nonlinear mechanical properties of borsic/aluminum, graphite/polyimide and boron/aluminum; (7) the strength characteristics of spliced sandwich panels; and (8) curved graphite/epoxy panels subjected to internal pressure.

Herakovich, C. T.↗

Dynamic Analysis and Control of Lightweight Manipulators with Flexible Parallel Link Mechanisms

The objective is the theoretical analysis and the experimental verification of dynamics and control of a two link flexible manipulator with a flexible parallel link mechanism. Nonlinear equations of motion of the lightweight manipulator are derived by the Lagrangian method in symbolic form to better understand the structure of the dynamic model. The resulting equation of motion have a structure which is useful to reduce the number of terms calculated, to check correctness, or to extend the model to higher order. A manipulator with a flexible parallel link mechanism is a constrained dynamic system whose equations are sensitive to numerical integration error. This constrained system is solved using singular value decomposition of the constraint Jacobian matrix. Elastic motion is expressed by the assumed mode method. Mode shape functions of each link are chosen using the load interfaced component mode synthesis. The discrepancies between the analytical model and the experiment are explained using a simplified and a detailed finite element model.

Lee, Jeh Won↗

A survey of the core-congruential formulation for geometrically nonlinear TL finite elements

This article presents a survey of the core-congruential formulation (CCF) for geometrically nonlinear mechanical finite elements based on the total Lagrangian (TL) kinematic description. Although the key ideas behind the CCF can be traced back to Rajasekaran and Murray in 1973, it has not subsequently received serious attention. The CCF is distinguished by a two-phase development of the finite element stiffness equations. The initial phase developed equations for individual particles. These equations are expressed in terms of displacement gradients as degrees of freedom. The second phase involves congruential-type transformations that eventually binds the element particles of an individual element in terms of its node-displacement degrees of freedom. Two versions of the CCF, labeled direct and generalized, are distinguished. The direct CCF (DCCF) is first described in general form and then applied to the derivation of geometrically nonlinear bar, and plane stress elements using the Green-Lagrange strain measure. The more complex generalized CCF (GCCF) is described and applied to the derivation of 2D and 3D Timoshenko beam elements. Several advantages of the CCF, notably the physically clean separation of material and geometric stiffnesses, and its independence with respect to the ultimate choice of shape functions and element degrees of freedom, are noted. Application examples involving very large motions solved with the 3D beam element display the range of applicability of this formulation, which transcends the kinematic limitations commonly attributed to the TL description.

Felippa, Carlos A.↗

A resonance phenomenon observed in a swept frequency experiment on a mother-daughter ionospheric rocket

The report presents observations obtained in a swept frequency experiment conducted in a mother-daughter rocket flight at auroral latitudes. The discussion is essentially restricted to the possible interpretation of the experimental signal structures noted at and in the vicinity of a resonance frequency where signal components apparently are generated by nonlinear mechanisms. Various resonance frequencies have been considered in attempts to identify this multichannel response frequency. It is concluded that of all the possibilities invoked, the best consistency is provided by identifying the frequency concerned with the cone resonance frequency demonstrated experimentally in the case of a laboratory plasma by Fisher and Gould (1971).

Folkestad, K.↗

Miniature load cell instrumentation for finite deformation biaxial testing of elastomers

Accuracy of biaxial test equipment to examine the nonlinear mechanical behavior of thin sheet specimens of elastomeric materials has been hampered by lack of precise determination of the force distribution along the sides of the specimen. It has been necessary to use an effective width established by approximate means to obtain the stress from the overall force applied along the edges. To avoid this experimental difficulty, individual miniature proof-ring load cells utilizing semiconductor strain gages have been developed and applied to the support hooks for the thin sheet specimens. Typical results are shown for time-dependent stress distributions for all degrees of biaxiality. An accurate evaluation of the effective specimen width is now possible.

Arenz, R. J.↗

A note on obtaining an approximate value for the period of a periodic solution of x-double prime = -V prime /x/

The first integral of x-double prime = - V prime (x) yields an integral for the period of a periodic solution, if such exists. In general, this integral cannot be evaluated. By means of an approximate solution along with the minimization of a mean-square error, one can obtain an approximate value for the period in terms of the amplitude of the motion. The calculated period agrees very well with the period obtained by means of numerical integration for the case of orbit-orbit resonance involving the motion of two satellites of a planet. The same method is applied to obtain an alternative derivation of the first Krylov-Bogoliuboff averaging method in nonlinear mechanics.

Lass, H.↗

Flowfield and acoustic properties of a Mach number 0.9 jet at a low Reynolds number

An anechoic vacuum chamber test facility is used to assess the flow field and acoustic properties of a jet with a low Reynolds number of about 3600 and a Mach number of 0.9. A conventional Pitot pressure probe is used to monitor the mean flow field, a hot-wire probe is employed to detect flow fluctuations, and the acoustic field is probed by condenser microphones. The jet is operated at the low Reynolds number in order to examine the behavior of the large-scale 'orderly' structure with particular emphasis on its noise-generating capabilities. It is shown that a nonlinear mechanism involving the large-scale flow instability is responsible for a dominant portion of the noise generated from the jet.

Stromberg, J. L.↗

Evolution of weak disturbances in inert binary mixtures

The evolution of weak disturbances in inert binary mixtures is determined for the one-dimensional piston problem. The interaction of the dissipative and nonlinear mechanisms is described by Burgers' equation. The binary mixture diffusion mechanisms enter as an additive term in an effective diffusivity. Results for the impulsive motion of a piston moving into an ambient medium and the sinusoidally oscillating piston are used to illustrate the results and elucidate the incorrect behavior pertaining to the associated linear theory.

Rasmussen, M. L.↗

Siple station experiments on wave-particle interactions in the magnetosphere

Natural and controlled whistler-mode signals have been used to study nonlinear mechanisms of wave growth and wave-wave interactions (WWI) in the magnetosphere; three general classes of WWI (triggering, suppression, and entrainment) are identified and interpreted in terms of a model based on cyclotron resonance interaction. This model is also used to estimate the wave field intensity associated with different types of WWI. A new type of triggered emission, the band-limited impulse (BLI) is interpreted in terms of the switching of phase-bunched currents. In addition, an experiment to find a threshold for the excitation of the coherent wave instability is discussed, and observed VLF wave-induced transient bursts of X-rays, light and E-region ionization enhancements are considered with regard to a step function wave interacting with all resonant electrons in a given energy range.

Helliwell, R. A.↗

Ion heating by strong electrostatic ion cyclotron turbulence

A theory of the ion heating due to electrostatic ion cyclotron (EIC) waves in the auroral zone is presented. Due to the slowly convecting nature of the EIC mode, quasi-linear plateau formation cannot stabilize the waves, and growth occurs until the nonlinear mechanisms of ion resonance broadening and electron trapping provide saturation. The large amplitude and coherent nature of the resulting wave imply that quasi-linear theory provides only a lower limit to the ion heating. An upper bound on the heating rate is derived using a time-average model of ion dynamics in the coherent waves. The effects of ion heating in the presence of the magnetic gradient force and parallel electric fields are considered, with the result that perpendicular energies over 100 eV are easily attainable from a 1 eV source plasma. Perpendicular heating in the absence of a parallel electric field yields conical ion distributions, which in the presence of an electric field become field-aligned beams.

Lysak, R. L.↗

Flow field and acoustic properties of a Mach number 0.9 jet at a low Reynolds number

An experimental study of the flow field and acoustic properties of a low Reynolds number M = 0.9 jet has been performed in a low pressure anechoic test chamber. The mean flow field was surveyed with a conventional pitot pressure probe and flow fluctuations were detected with a normal hot wire probe. Also, condenser microphone measurements were made in the acoustic field. The flow fluctuations within the jet were found to be dominated initially by a relatively discrete, large-scale, wave-like instability centered around a Strouhal number of 0.44. The axial wavelength of this instability was determined to be 1.45 jet diameters and its azimuthal character includes the n = 0 and n = plus or minus 1 modes. The growth of this instability coupled with its nonlinear breakdown are major contributors to the termination of the potential core region of the jet. The acoustic field of the jet, in contrast to the flow field, has a broad frequency spectrum with a peak amplitude near a Strouhal number of St = 0.2. The results indicate that a nonlinear mechanism involving the large-scale flow instability is responsible for a dominant portion of the noise generated from this jet.

Stromberg, J. L.↗

Geophysical fluid flow cell experiment

The primary purpose of the geophysical flow experiments is to simulate large-scale baroclinic (density-stratified) flows which occur naturally in the atmospheres of rotating planets and stars and to gain insights and obtain answers to crucial questions concerning the large-scale nonlinear mechanics of the global geophysical flows. Those external conditions related to fluid viscosity, rotation, gravity are identified, which allow qualitatively different modes of instability or waves in the model.

Hart, J. E.↗

Theoretical and software considerations for nonlinear dynamic analysis

In the finite element method for structural analysis, it is generally necessary to discretize the structural model into a very large number of elements to accurately evaluate displacements, strains, and stresses. As the complexity of the model increases, the number of degrees of freedom can easily exceed the capacity of present-day software system. Improvements of structural analysis software including more efficient use of existing hardware and improved structural modeling techniques are discussed. One modeling technique that is used successfully in static linear and nonlinear analysis is multilevel substructuring. This research extends the use of multilevel substructure modeling to include dynamic analysis and defines the requirements for a general purpose software system capable of efficient nonlinear dynamic analysis. The multilevel substructuring technique is presented, the analytical formulations and computational procedures for dynamic analysis and nonlinear mechanics are reviewed, and an approach to the design and implementation of a general purpose structural software system is presented.

Schmidt, R. J.↗

Dynamic effects of combustion

The dynamic effects of combustion are due to the evolution of exothermic energy and its deposition in the compressible medium where the process takes place. The paper examines the dynamics of combustion phenomena, including ignition, turbulent flame propagation (inflammation), explosion, and detonation, with emphasis on their exothermic characteristics. Ignition and explosion are treated as problems of nonlinear mechanics, and their dynamic behavior is described in terms of phase space models and cinematographic laser shear interferograms. The results of a numerical random vortex model of turbulent flame propagation are confirmed in a combustion tunnel experiment, where it was observed that a fresh mixture of burnt and unburnt gases can sustain combustion with a relatively small expenditure of overall mass flow, due to the increasing specific volume of burnt gases inside the flame front. An isentropic pressure wave is found to precede the accelerating flame in the process of detonation, and components of this presssure wave are shown to propagate at local sonic velocities.

Oppenheim, A. K.↗

X-ray-illuminated stellar winds - Optically thick wind models for massive X-ray binaries

The work of Stevens and Kallman (1990) on the effect of accretion-powered X-rays from the neutron star on the dynamics of the line-driven stellar wind of the early-type primary is extended. Radiative force multipliers that now depend on the column of attenuating material, as well as the ionization parameter, are calculated. Optical depth effects are found to suppress the effects of X-ray ionization on the force multipliers. A number of dynamical models for the winds of massive X-ray binary systems (MXRBs) are calculated with these force multipliers. Unlike the optically thin models, self-consistent dynamical solutions are found for reasonable values of the X-ray luminosity. These solutions also reveal the presence of nonlinear mechanisms that affect wind dynamics, whereby relatively small changes in the force multipliers can lead to significant changes in the wind structure. The models find the existence of a self-consistent region of solution at an X-ray luminosity of about 10 to the 36th ergs/s and suggest the possible existence of high-luminosity states.

Stevens, Ian R.↗

Continuum radiation in planetary magnetospheres

With the completion of the Voyager tour of the outer planets, radio and plasma wave instruments have executed the first survey of the wave spectra of Earth, Jupiter, Saturn, Uranus, and Neptune. One of the most notable conclusions of this survey is that there is a great deal of qualitative similarity in both the plasma wave and radio wave spectra from one magnetosphere to the next. In particular, in spite of detailed differences, most of the radio emissions at each of the planets have been tentatively classified into two primary categories. First, the most intense emissions are generally associated with the cyclotron maser instability. Second, a class of weaker emissions can be found at each of the magnetospheres which appears to be the result of conversion from intense electrostatic emissions at the upper hybrid resonance frequency into (primarily) ordinary mode radio emission. It is this second category, often referred to as nonthermal continuum radiation, which we will discuss in this review. We review the characteristics of the continuum spectrum at each of the planets, discuss the source region and direct observations of the generation of the emissions where available, and briefly describe the theories for the generation of the emissions. Over the past few years evidence has increased that the linear mode conversion of electrostatic waves into the ordinary mode can account for at least some of the continuum radiation observed. There is no definitive evidence which precludes the possibility that a nonlinear mechanism may also be important.

Kurth, W. S.↗

Projections on structures and material strength in the computational context

The ideas associated with the subsequent viewgraphs are summarized. The primary motivation behind this presentation is to observe that certain macroscopic, microscopic, and submicroscopic phenomena are being understood that have basic influence on understanding the durability and high temperature sensitivity of polymers and polymer-based composites. This understanding covers important issues of long term stability with respect to residual stresses and deformations which can have very deleterious effects on structures used for long periods of time as a result of the heat-involving manufacturing process. Beyond this, important progress is being made in understanding the nonlinear material response of polymers in the fracture context, because the nonlinear mechanics of the material at the tip of a crack, either propagating or ready to do so, is being understood with increasing precision.

Knauss, Wolfgang G.↗