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NASA NTRS1981

Analytical performance prediction for large antennas

A linear mathematical modeling of the static and dynamic characteristics of a deployable offset wrap rib antenna was attempted using small motions in an effort to simulate the surface distortion resulting from thermal loading and transient oscillations from control. Both cyclic symmetry and model synthesis were used for parametric analysis. Although the ribs can be modeled as slender beams varying cross sections and equivalent linear material properties, the mesh poses a problem since its equivalent stress strain relations are highly nonlinear and sensitive to the biaxial prestressed state. Consequently, the macroscopic material properties were measured experimentally in the neighborhood of the design prestress. An equivalent tangent modulus technique was then adopted about this equilibrium state and assumed to be valid within a small range of incremental stresses.

El-Raheb, M.↗

NASA NTRS1988

A finite element method for time varying geometry in multibody structures

A three-dimensional finite element formulation using convected coordinates is presented for the multibody dynamics of truss-like configurations. Unlike existing formulations, the present one does not superimpose nonlinear rigid body kinematics with linear structural mode shapes, an approach that has recently been shown to be grossly inaccurate under certain conditions. Instead, the finite element method is extended to treat large motions/deformations. The formulation is oriented toward joint dominated structures and places the generalized coordinates at the joints. For the planar spin-up of a flexible beam, results are compared with those derived from a commercially available computer program. The two programs predict nearly identical results.

Housner, J. M.↗

NASA NTRS1990

Cold plasma heating in the plasma sheet boundary layer - Theory and simulations

Satellite observations in recent years have confirmed that the plasma sheet boundary layer is a permanent feature of the earth's magnetotail located between the lobe and central plasma sheet during both quiet and active magnetic periods. Distinct features of the boundary layer include field aligned ion beams and intense electrostatic emissions known as broadband electrostatic noise. Since the plasma sheet boundary layer is a spatial feature of the magnetotail, within it will occur thermal mixing of the resident warm boundary layer plasma with inflowing (convecting) cold ionospheric plasma. A theoretical study involving linear theory and nonlinear numerical particle simulations is presented which examines ion beam instabilities in the presence of a thermally mixed hot and cold background plasma. It is found that the free energy in the ion beams can heat the cool ionospheric plasma to ambient plasma sheet boundary layer temperatures via broadband electrostatic noise. These results, along with recent observational reports that ionospheric outflow can account for measured plasma sheet densities, suggest that the ionospheric role in plasma sheet dynamics and content may be as large as the solar wind.

Schriver, David↗

NASA NTRS1989

Element-specific modal formulations for large-displacement multibody dynamics

Large dispacement assumed-mode modeling techniques are examined in the context of multibody elastodynamics. The range of both general and element-specific approaches are studied with the aid of examples involving beams, plates, and shells. For systems undergoing primarily structural bending and twisting with little or no membrane distortion, it is found that fully-linear, element-specific, modal formulations provide the most accurate time history solutions at the least expense. When membrane effects become dominant in structural problems due to loading and boundary conditions, one must naturally resort to a formulation involving a nonlinear stress-strain relationship in addition to nonlinear terms associated with large overall system motion. Such nonlinear models were investigated using assumed modes and found to lead to modal convergence difficulties when standard free-free structural modes are employed. A constrained mode formulation aimed at addressing the convergence problem is proposed.

Ryan, R. R.↗

NASA NTRS1988

The influence of and the identification of nonlinearity in flexible structures

Several models were built at NASA Langley and used to demonstrate the following nonlinear behavior: internal resonance in a free response, principal parametric resonance and subcritical instability in a cantilever beam-lumped mass structure, combination resonance in a parametrically excited flexible beam, autoparametric interaction in a two-degree-of-freedom system, instability of the linear solution, saturation of the excited mode, subharmonic bifurcation, and chaotic responses. A video tape documenting these phenomena was made. An attempt to identify a simple structure consisting of two light-weight beams and two lumped masses using the Eigensystem Realization Algorithm showed the inherent difficulty of using a linear based theory to identify a particular nonlinearity. Preliminary results show the technique requires novel interpretation, and hence may not be useful for structural modes that are coupled by a guadratic nonlinearity. A literature survey was also completed on recent work in parametrically excited nonlinear system. In summary, nonlinear systems may possess unique behaviors that require nonlinear identification techniques based on an understanding of how nonlinearity affects the dynamic response of structures. In this was, the unique behaviors of nonlinear systems may be properly identified. Moreover, more accutate quantifiable estimates can be made once the qualitative model has been determined.

Zavodney, Lawrence D.↗

NASA NTRS1972

Structural model optimization using statistical evaluation

The results of research in applying statistical methods to the problem of structural dynamic system identification are presented. The study is in three parts: a review of previous approaches by other researchers, a development of various linear estimators which might find application, and the design and development of a computer program which uses a Bayesian estimator. The method is tried on two models and is successful where the predicted stiffness matrix is a proper model, e.g., a bending beam is represented by a bending model. Difficulties are encountered when the model concept varies. There is also evidence that nonlinearity must be handled properly to speed the convergence.

Collins, J. D.↗

NASA NTRS1993

Modeling of composite beams and plates for static and dynamic analysis

The main purpose of this research was to develop a rigorous theory and corresponding computational algorithms for through-the-thickness analysis of composite plates. This type of analysis is needed in order to find the elastic stiffness constants for a plate and to post-process the resulting plate solution in order to find approximate three-dimensional displacement, strain, and stress distributions throughout the plate. This also requires the development of finite deformation plate equations which are compatible with the through-the-thickness analyses. After about one year's work, we settled on the variational-asymptotical method (VAM) as a suitable framework in which to solve these types of problems. VAM was applied to laminated plates with constant thickness in the work of Atilgan and Hodges. The corresponding geometrically nonlinear global deformation analysis of plates was developed by Hodges, Atilgan, and Danielson. A different application of VAM, along with numerical results, was obtained by Hodges, Lee, and Atilgan. An expanded version of this last paper was submitted for publication in the AIAA Journal.

Hodges, Dewey H.↗

NASA NTRS1990

Configuration design sensitivity analysis of built-up structures

In the design of complex built-up structures that are made of truss, beam, membrane, shell, and solid, there are five different kinds of design variables: material property, sizing, shape, configuration, and topological variables. Previous research has shown that the improvement in performances obtained by altering the configuration of structural components can be much more significant than those obtained when the geometry is assumed to be fixed. Using the variational approach, a unified design sensitivity was developed for the first three kinds of design variables, and was further extended recently in many structural analysis problems such as nonlinear, structural dynamics, and frequency response analysis. A continuum design sensitivity analysis method is developed for the configuration design variable of built-up structures.

Choi, Kyung K.↗

NASA NTRS1971

Dynamic responses of railroad car models to vertical and lateral rail inputs

Simplified dynamic models were applied in a study of vibration in a high-speed railroad car. The mathematical models used were a four-degree-of-freedom model for vertical responses to vertical rail inputs and a ten-degree-of-freedom model for lateral response to lateral or rolling (cross-level) inputs from the rails. Elastic properties of the passenger car body were represented by bending and torsion of a uniform beam. Rail-to-car (truck) suspensions were modeled as spring-mass-dashpot oscillators. Lateral spring nonlinearities approximating certain complicated truck mechanisms were introduced. The models were excited by displacement and, in some cases, velocity inputs from the rails by both deterministic (including sinusoidal) and random input functions. Results were obtained both in the frequency and time domains. Solutions in the time domain for the lateral model were obtained for a wide variety of transient and random inputs generated on-line by an analog computer. Variations in one of the damping properties of the lateral car suspension gave large fluctuations in response over a range of car speeds for a given input. This damping coefficient was significant in reducing lateral car responses that were higher for nonlinear springs for three different inputs.

Sewall, J. L.↗

NASA NTRS1989

Load-shortening behavior of an initially curved eccentrically loaded column

To explore the feasibility of using buckled columns to provide a soft support system for simulating a free-free boundary condition in dynamic testing, the nonlinear load-shortening behavior of initially imperfect, eccentrically loaded slender columns is analyzed. Load-shortening curves are obtained for various combinations of load eccentricity and uniform initial curvature and are compared, for reference purposes, with the limiting case of the classical elastica. Results for numerous combinations of initial curvature and load eccentricity show that, over a wide range of shortening, an axially loaded slender column exhibits load-deflection compliance which is of the same order as that of a straight but otherwise identical cantilever beam under lateral tip loading.

Fichter, W. B.↗

NASA NTRS1994

Dynamics and efficiency of type III solar radio emission

Existing calculations of nonlinear coupling coefficients for fundamental and harmonic emission via three-wave interactions are refined and used to calculate the conversion efficiency of Langmuir energy into electromagnetic waves when the Langmuir waves have the observed bursty form. Resulting field strengths for harmonic emission are found to be consistent with typical International Sun Earth Explorer 3 (ISSE 3) observations at 1 AU. Fundamental emission at 1 AU is found to proceed only when stimulated by the presence of a source of ion sound waves. However, it is argued that electrostatic decay of Langmuir waves can supply the necessary waves provided the driving electron beam is sufficiently fast. Under these conditions, the predicted fundamental field strengths can account for both the highest and typical fields observed; they also dominate the predicted harmonic fields, consistent with observations. This mechanism is also consistent with previous observations that fundamental emission generally occurs early in type III events, when the beam is fastest. For typical parameters it is shown that neither fundamental nor harmonic emission saturates its respective source instability, contrary to previous assumptions. However, saturation cannot be ruled out under particularly favorable conditions.

Robinson, P. A.↗

NASA NTRS1998

The Dynamics of Coupled Oscillator Phase Control

Arrays of coupled oscillators have been proposed as means of realizing high power rf sources via coherent spatial power combining. In such applications, a uniform phase distribution over the aperture is usually desired. However, it has been shown that by detuning some of the oscillators away from the oscillation frequency of the ensemble of oscillators, one may achieve other useful aperture phase distributions. Of particular interest among those achievable are linear phase distributions because these result in steering of the output rf beam away from the broadside direction. The theory describing the behavior of such arrays of coupled oscillators is quite complicated since the phenomena involved are inherently nonlinear. However, a simplified theory has been developed which facilitates intuitive understanding. This simplified theory is based on a "continuum model" in which the aperture phase is represented by a continuous function of the aperture coordinates. A challenging aspect of the development of this theory is the derivation of appropriate boundary conditions at the edges or ends of the array.

Pogorzelski, R. J.↗

NASA NTRS1985

ICIASF '85 - International Congress on Instrumentation in Aerospace Simulation Facilities, 11th, Stanford University, CA, August 26-28, 1985, Record

Developments related to laser Doppler velocimetry are discussed, taking into account a three-component dual beam laser-Doppler-anemometer to be operated in large wind tunnels, a new optical system for three-dimensional laser-Doppler-anemometry using an argon-ion and a dye laser, and a two-component laser Doppler velocimeter by switching fringe orientation. Other topics studied are concerned with facilities, instrumentation, control, hot wire/thin film measurements, optical diagnostic techniques, signal and data processing, facilities and adaptive wall test sections, data acquisition and processing, ballistic instrument systems, dynamic testing and material deformation measurements, optical flow measurements, test techniques, force measurement systems, and holography. Attention is given to nonlinear calibration of integral wind tunnel balances, a microcomputer system for real time digitized image compression, and two phase flow diagnostics in propulsion systems.

Source record↗

NASA NTRS1989

Nonlinear strain-displacement relations and flexible multibody dynamics

Dynamics of chains of flexible bodies undergoing large rigid body motions, but small elastic deflections are considered. The role of nonlinear strain-displacement relations in the development of the motion equations correct to first order in elastic deflections is investigated. The general form of these equations linearized only in the small elastic deflections is presented, and the relative significance of various nonlinear terms is studied both analytically and through the use of the numerical simulations. Numerical simulations are performed for a two link chain constrained to move in the plane, subject to hinge torques. Each link is modeled as a thin beam. Slew maneuver simulation results are compared for models with and without properly modeled kinematics of deformation. The goal of this case study is to quantify the importance of the terms in the equations of motion which arise from the inclusion of nonlinear strain-displacement relations. It is concluded that unless the consistently linearized equations in elastic deflections and speeds are available and necessary, the inconsistently (prematurely) linearized equations should be replaced in all cases by ruthlessly linearized equations: equations in which all nonlinear terms involving the elastic deflections and speeds are ignored.

Padilla, Carlos E.↗

NASA NTRS1979

The dynamics and control of large flexible space structures, 2. Part A: Shape and orientation control using point actuators

The equations of planar motion for a flexible beam in orbit which includes the effects of gravity gradient torques and control torques from point actuators located along the beam was developed. Two classes of theorems are applied to the linearized form of these equations to establish necessary conditions for controlability for preselected actuator configurations. The feedback gains are selected: (1) based on the decoupling of the original coordinates and to obtain proper damping, and (2) by applying the linear regulator problem to the individual model coordinates separately. The linear control laws obtained using both techniques were evaluated by numerical integration of the nonlinear system equations. Numerical examples considering pitch and various number of modes with different combination of actuator numbers and locations are presented. The independent model control concept used earlier with a discretized model of the thin beam in orbit was reviewed for the case where the number of actuators is less than the number of modes. Results indicate that although the system is controllable it is not stable about the nominal (local vertical) orientation when the control is based on modal decoupling. An alternate control law not based on modal decoupling ensures stability of all the modes.

Bainum, P. M.↗

NASA NTRS1989

Parallel processors and nonlinear structural dynamics algorithms and software

A nonlinear structural dynamics finite element program was developed to run on a shared memory multiprocessor with pipeline processors. The program, WHAMS, was used as a framework for this work. The program employs explicit time integration and has the capability to handle both the nonlinear material behavior and large displacement response of 3-D structures. The elasto-plastic material model uses an isotropic strain hardening law which is input as a piecewise linear function. Geometric nonlinearities are handled by a corotational formulation in which a coordinate system is embedded at the integration point of each element. Currently, the program has an element library consisting of a beam element based on Euler-Bernoulli theory and trianglar and quadrilateral plate element based on Mindlin theory.

Belytschko, Ted↗

NASA NTRS1985

Simulation study of Type 2 counterstreaming electrons along auroral field lines

The production of counterstreaming electrons associated with parallel fields along auroral field lines is examined through the use of computer simulation. A 2 1/2-dimensional (two spatial and three velocity dimensions) electrostatic particle algorithm and auroral boundary conditions are used to set up a self-consistent V potential structure. The simulation produces signatures of counterstreaming electrons resembling those observed by the Dynamics Explorer 1 satellite. The main signatures are as follows: (1) the phase space contours of the electron distribution function are elongated along the V-parallel axis, and (2) the energy of electrons streaming in the upward direction is comparable to the energy of the accelerated electron beam. The simulation indicates that a portion of the accelerated electron beam is trapped by large amplitude electrostatic waves produced through the two-stream instability. Strong wave-particle interactions then thermalize the trapped electrons to produce suprathermal electrons streaming in the direction opposite to that of the accelerated electron beam. These results suggest a possible mechanism of producing counterstreaming electron fluxes through nonlinear processes of the two-stream instability.

Wagner, J. S.↗

NASA NTRS2021

Transmission Telescope Optical Dynamic Alignment

The Integrated Radio Optical Communication System (iROC) is designed to transmit data between Mars and Earth by means of radio waves at 32.67 GHz (Ka Band) and laser beam at 1550 nm, both transmitted via a combined teletenna. The iROC terminal will provide ‘beaconless’ operations to allow full function from the outer planets. In order to point without the aid of an uplink beacon, the proof of concept presented here is addressing the need for an accurate determination and control of the relative position of the laser beam with respect to a reference star. The experiment presented simulates a surrogate transmission telescope system in laboratory setting and presents the model used in the correction of the outgoing beam. The results of the model show a nonlinear dependence between the outgoing and the reference beam, indicating the necessity of a minimum of two metrology instruments placed along the optical system for increased pointing precision.

optical communication↗