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At least 55 records · Page 3

Development and evaluation of two non-linear shell elements

Two plate and shell displacement elements are developed for use in large deflection non-linear analysis. The elements are of the 'stability' type, in which non-linear strains are included, with their values optimized by added higher order membrane functions and special types of elemental level constraints. The paper summarizes formulation and computational procedures, and discusses numerical results in detail. Conclusions are given regarding the effectiveness of the elements for solving both linear and non-linear shell analysis problems.

Jones, R. E.↗

Dynamic response analysis of geometrically non-linear structures subjected to high impact.

Description of an efficient digital computer method for the determination of the propagation of elastic stresses and deformations in certain geometrically nonlinear structures subjected to high impact loading. The finite-element matrix displacement approach utilizing curved quadrilateral shell elements in conjunction with a nodewise predictor-corrector method employing Runge-Kutta extrapolation techniques has been adopted for the present solution. The related computer program written in FORTRAN V for the UNIVAC 1108 computer has proved to be effective for the solution of a range of practical problems including rectangular and cylindrical panels. Numerical results are presented for a relevant structure, the cell container, and the negative electrode of an impact-resistant battery subjected to high impact, simulating its free landing on a planetary surface.

Gupta, K. K.↗

A finite element tensor approach to plate buckling and postbuckling.

A practical finite element method is presented for geometrically nonlinear (von Karman) plate problems. Symmetric strain energy tensors provide an efficient formulation and solution, and allow the effects of initial imperfections to be considered. An unbalanced force iteration is employed, with the advantage that the time consuming Gauss decomposition needs to be performed only once. The convergence is controlled by an automatically computed relaxation factor, and this makes the method applicable in advanced stages of non-linearity. Several different triangular elements are used in explicitly deriving the required tensors.

Vos, R. G.↗

Estimation of effective hydrologic properties of soils from observations of vegetation density

An existing one-dimensional model of the annual water balance is reviewed. Slight improvements are made in the method of calculating the bare soil component of evaporation, and in the way surface retention is handled. A natural selection hypothesis, which specifies the equilibrium vegetation density for a given, water limited, climate-soil system, is verified through comparisons with observed data and is employed in the annual water balance of watersheds in Clinton, Ma., and Santa Paula, Ca., to estimate effective areal average soil properties. Comparison of CDF's of annual basin yield derived using these soil properties with observed CDF's provides excellent verification of the soil-selection procedure. This method of parameterization of the land surface should be useful with present global circulation models, enabling them to account for both the non-linearity in the relationship between soil moisture flux and soil moisture concentration, and the variability of soil properties from place to place over the Earth's surface.

Tellers, T. E.↗

Displacement incrementation in non-linear structural analysis by the self-correcting method

The prediction of nonlinear structural behavior by the finite element method wherein buckling does not occur has received considerable attention and, with it, reasonable success has been achieved. However, the post-buckling problem has been less actively pursued probably because of the inherent numerical difficulties encountered. This note reviews very briefly the numerical methods currently being used for pre- and post-buckling analysis and presents a self-correcting approach based on load and displacement incrementation which is shown to be efficient, reliable, and easy to program. Numerical solutions are presented which demonstrate the effectiveness of the method.

Haisler, W. E.↗

Non-linear dynamic response of a wind turbine blade

The paper outlines the nonlinear dynamic analysis of an isolated three-degree flap-lag-feather wind turbine blade under a gravity field and with shear flow. Lagrangian equations are used to derive the nonlinear equations of motion of blade for arbitrarily large angular deflections. The limit cycle analysis for forced oscillations and the determination of the principal parametric resonance of the blade due to periodic forces from the gravity field and wind shear are performed using the harmonic balance method. Results are obtained first for a two-degree flap-lag blade, then the effect of the third degree of freedom (feather) is studied. The self-excited flutter solutions are obtained for a uniform wind and with gravity forces neglected. The effects of several parameters on the blade stability are examined, including coning angle, structural damping, Lock number, and feather frequency. The limit cycle flutter solution of a typical configuration shows a substantial nonlinear softening spring behavior.

Chopra, I.↗

Non-linear wave interaction in a plasma column

Non-linear three-wave interaction is analysed for propagation along a cylindrical plasma column surrounded by an infinite dielectric, in the absence of a static magnetic field. An averaged-Lagrangian method is used, and the results are specialized to parametric interaction and mode conversion, assuming an undepleted pump wave. The theory for these two types of interactions is extended to include imperfect synchronism, and the effects of loss. Computations are presented indicating that parametric growth rates of the order of a fraction of a decibel per centimeter should be obtainable for plausible laboratory plasma column parameters.

Larsen, J.-M.↗

Aeroelastic stability of complete rotors with application to a teetering rotor in forward flight

The derivation of a set of non-linear coupled flap-lag-torsion equations of motion for moderately large deflections of an elastic, two-bladed teetering helicopter rotor in forward flight is concisely outlined. The following degrees of freedom are included in the mathematical model: rigid body flapping, rigid body lead-lag, elastic bending in flap and lead-lag, blade root torsion, and shaft torsion. Quasi-steady aerodynamic loads are considered and the effects of reversed flow are included. The aeroelastic stability of the complete rotor is investigated by using a linearized system of equations of motion. The equilibrium position about which the equations are linearized is obtained by considering the trim state of the helicopter, in true or simulated forward flight conditions. The sensitivity of the aeroelastic stability boundaries to interblade structural and mechanical coupling is illustrated by comparing the complete rotor stability boundaries with those obtained from a single blade analysis for a number of hover and forward flight cases.

Shamie, J.↗

Full non-linear treatment of the global thermospheric wind system. I - Mathematical method and analysis of forces. II - Results and comparison with observations

The equations of horizontal motion of the neutral atmosphere between 120 and 500 km are integrated with the inclusion of all nonlinear terms of the convective derivative and the viscous forces due to vertical and horizontal velocity gradients. Empirical models of the distribution of neutral and charged particles are assumed to be known. The model of velocities developed is a steady state model. In Part I the mathematical method used in the integration of the Navier-Stokes equations is described and the various forces are analyzed. Results of the method given in Part I are presented with comparison with previous calculations and observations of upper atmospheric winds. Conclusions are that nonlinear effects are only significant in the equatorial region, especially at solstice conditions and that nonlinear effects do not produce any superrotation.

Blum, P. W.↗

Phase-bunching and other non-linear processes occurring in gyroresonant wave-particle interactions

Consideration of the movement of individual electrons in a magnetized plasma in which a monochromatic wave is propagating in the whistler mode. Simple expressions are derived which give the displacement of the electrons as a function of time, the phase angle that their velocity vector makes with the magnetic component of the wave, their pitch angle, and energy changes. A useful formula is obtained which gives the velocity range over which particles remain trapped inside the wave, as a function of the wave intensity and of the initial phase angle of the particle. It is shown that even strictly resonant particles can escape from the wave when their initial phase angle is very small. From the derived expressions, it is possible to compute the phase-bunching effect which occurs approximately at one trapping wavelength behind the leading edge of the interaction region.

Gendrin, R.↗

Transonic-supersonic high Reynolds number stability and control characteristics of a 0.015-scale (remotely controlled elevon) model 44-0 of the space shuttle orbiter tested in the VSD high speed wind tunnel (LA67)

A detailed aerodynamic data base which can be used to substantiate the aerodynamic design data book for the current shuttle orbiter configuration was generated. Special attention was directed to definition of non-linear aerodynamic characteristics by taking data at small increments in the angle of attack, angle of sideslip, Mach number, and elevon position. Six-component aerodynamic force and moment and elevon position data were recorded over an angle-of-attack range from -2 deg to as high as 32 deg at angles of sideslip of 0 deg, 1 deg, and +2 deg. The test Mach numbers were 0.60, 0.80, 0.90, 1.2, 1.5, 2.0, 3.0, and 4.6. The effects of Reynolds number were investigated and covered a range from 5.0 to 16.0 million per foot.

Source record↗

The role of microturbulence on collisionless reconnection

The linear, non-linear and anomalous transport properties associated with various microinstabilities driven by cross field currents in reconnecting geometries are reviewed. An assessment of their role in collisionless tearing based on analytic theory, computer simulations and experimental evidence, supports the dominant role of lower hybrid waves. The relevance of microturbulence on macroscopic stationary and time dependent models of merging is presented. It is concluded that a fluid-numerical simulation approach that includes (at each space and time step) the effects of anomalous transport in a self consistent manner, similar to the one used for laboratory collisionless shocks, represents the best method for studying and modeling the details of the reconnection process.

Papadopoulos, K.↗

Theoretical analysis of rotating two phase detonation in a rocket motor

Tangential mode, non-linear wave motion in a liquid propellant rocket engine is studied, using a two phase detonation wave as the reaction model. Because the detonation wave is followed immediately by expansion waves, due to the side relief in the axial direction, it is a Chapman-Jouguet wave. The strength of this wave, which may be characterized by the pressure ratio across the wave, as well as the wave speed and the local wave Mach number, are related to design parameters such as the contraction ratio, chamber speed of sound, chamber diameter, propellant injection density and velocity, and the specific heat ratio of the burned gases. In addition, the distribution of flow properties along the injector face can be computed. Numerical calculations show favorable comparison with experimental findings. Finally, the effects of drop size are discussed and a simple criterion is found to set the lower limit of validity of this strong wave analysis.

Shen, I.↗

High Temperature Dielectric Properties and Differential Scanning Calorimetry of Lunar Simulants

To guide development of microwave process technology that could be used during in situ construction on the Moon, we measured the high-temperature basic dielectric properties (εʹ and εʺ) of 17 lunar simulants and related materials. In order to confidently use these data one needs to understand the data’s strengths and weaknesses. Therefore, a goal of this publication is to provide insights into the comparative effects of sample composition, pre-treatments, experimental variables, high temperatures, and other factors on the measured response. The dielectric measurements were performed using the cavity perturbation method over a temperature range between room temperature to 1000 °C, or higher, and provided the real and imaginary components of permittivity at six frequencies. The utility of the original values was limited by the varying density of the pellets used in the measurement. Therefore, all of the εʹ and εʺ measurements at the frequency of 2466 MHz have been scaled to a constant density, 1.75 g/cm 3 . Here the data are presented as graphs chosen to aid analysis within and across simulant groups. To gain additional insight into the processes happening at the elevated temperatures in the dielectric measurements, heat capacity data was obtained using differential scanning calorimetry (DSC) on several of the simulant materials. Our data show that over the frequency range 397 MHz – 2985 MHz a material’s behavior does not greatly change, as compared to the scale of differences observed between lunar mare and highland simulants at high temperatures. For example at 1000 °C, the mare simulant JSC-1A absorbs 10 times more power than the highland simulant NUW-LHT-5M. We observe that as melting temperatures are reached both permittivity and dielectric loss rise non-linearly, helping to explain thermal runaway during microware heating. Our data show that even less than a few weight % of many non-lunar minerals, and the use of mixtures in simulants can affect the dielectric behavior at higher temperatures. A comparison of our results with published dielectric data for Apollo samples and with remote sensing of the Moon supports the conclusion the simulants and lunar material at room temperature have very similar dielectric values.

Differential Scanning Calorimetry↗

Synthesis of a non-linear feedback system with significant plant-ignorance for prescribed time-domain tolerances

The problem considered is the design of a feedback system containing a linear, time invariant, minimum phase plant, whose parameters are known only within given bounds, such that the time response of the system remains within specified limits. A quasi-optimal design, for given design constraints, is one which minimizes the effect of white sensor noise on the input to the plant. An investigation was conducted on the use of the non linear device known as the Clegg integrator in the design of such a system. The describing function of the Clegg integrator has the same magnitude characteristic, apart from a scale factor, as the linear integrator, but has 52 deg less phase-lag, at all frequencies, than the linear integrator; thus, when used in a feedback system, it provides a larger stability margin than the linear integrator. This property allows the nonlinear feedback system to be designed so that the sensor noise is attenuated more than in the linear design.

Krishnan, K. R.↗

The calculation of steady non-linear transonic flow over finite wings with linear theory aerodynamics

The feasibility of calculating steady mean flow solutions for nonlinear transonic flow over finite wings with a linear theory aerodynamic computer program is studied. The methodology is based on independent solutions for upper and lower surface pressures that are coupled through the external flow fields. Two approaches for coupling the solutions are investigated which include the diaphragm and the edge singularity method. The final method is a combination of both where a line source along the wing leading edge is used to account for blunt nose airfoil effects; and the upper and lower surface flow fields are coupled through a diaphragm in the plane of the wing. An iterative solution is used to arrive at the nonuniform flow solution for both nonlifting and lifting cases. Final results for a swept tapered wing in subcritical flow show that the method converges in three iterations and gives excellent agreement with experiment at alpha = 0 deg and 2 deg. Recommendations are made for development of a procedure for routine application.

Cunningham, A. M., Jr.↗

Transfer function verification and block diagram simplification of a very high-order distributed pole closed-loop servo by means of non-linear time-response simulation

Linear frequency domain methods are inadequate in analyzing the 1975 Viking Orbiter (VO75) digital tape recorder servo due to dominant nonlinear effects such as servo signal limiting, unidirectional servo control, and static/dynamic Coulomb friction. The frequency loop (speed control) servo of the VO75 tape recorder is used to illustrate the analytical tools and methodology of system redundancy elimination and high order transfer function verification. The paper compares time-domain performance parameters derived from a series of nonlinear time responses with the available experimental data in order to select the best possible analytical transfer function representation of the tape transport (mechanical segment of the tape recorder) from several possible candidates. The study also shows how an analytical time-response simulation taking into account most system nonlinearities can pinpoint system redundancy and overdesign stemming from a strictly empirical design approach. System order reduction is achieved through truncation of individual transfer functions and elimination of redundant blocks.

Mukhopadhyay, A. K.↗

Dynamical theory of stability for elastic rods with nonlinear curvature and twist

Considering non-linear terms in the curvature as well as in the twist, the governing boundary value problem for lateral bending of elastic, transverse loaded rods is formulated by means of Hamilton's principle. Using the method of small vibrations, the associated linearized equations of stability are derived, which complete the currently accepted relations. The example of the simplest lateral bending problem illustrates the improved effect of the proposed equations.

Wauer, J.↗