Aerospace Engineering Research Works

Permanent URI for this collectionhttp://hdl.handle.net/1903/1655

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Start date: 1990End date: 1999

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Now showing 1 - 10 of 12
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    High-Frequency Nonlinear Vibrational Control
    (IEEE, 1997-01) Shapiro, Benjamin; Zinn, B. T.
    This paper discusses the feasibility of high-frequency nonlinear vibrational control. Such control has the advantage that it does not require state measurement and processing capabilities that are required in conventional feedback control. Bellman et al. [1] investigated nonlinear systems controlled by linear vibrational controllers and proved that vibrational control is not feasible if the Jacobian matrix has a positive trace. This paper extends previous work to include nonlinear vibrational controllers. A stability criteria is derived for nonlinear systems with nonlinear controllers, and it is shown that a nonlinear vibrational controller can stabilize a system even if the Jacobian matrix has a positive trace.
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    Symmetry Approach to Extension of Flutter Boundaries via Mistuning
    (American Institute of Aeronautics and Astronautics, 1998-05) Shapiro, Benjamin
    A general framework is presented for analyzing and optimizing stability increases resulting from mistuning. The framework given is model independent and is based primarily on symmetry arguments. Difficult practical issues are transformed to tractable mathematical questions. It is shown that mistuning analysis reduces to a block circular matrix eigenvalue/vector problem that can be solved efficiently even for large problems. Similarly, the optimization becomes a standard linear constraint quadratic programming problem and can be solved numerically. Because the methods given are model-independent, they can be applied to various models and allow the researcher to easily conclude which models accurately capture mistuning and which do not. A simple quasisteady model for flutter in a cascade is used to illustrate and validate results in this paper.
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    Solving for Mistuned Forced Response by Symmetry
    (American Institute of Aeronautics and Astronautics, 1999-03) Shapiro, Benjamin
    The introduction of mistuning in jet-engine bladed disks can lead to large changes in stability and forced response. Even small random mistuning (within the bounds of manufacturing tolerance) can lead to unacceptable response and high-cycle fatigue. Meanwhile, intentional mistuning may improve stability and forced response under manufacturing uncertainty. This paper presents a general framework for predicting forced response as a function of mistuning. Because the forced response problem is an almost singular linear problem, its solution is highly nonlinear in the mistuning parameters. Our methods exploit symmetry arguments and eigenstructure perturbation to provide a method valid for any model. It is shown that, by perturbing eigenvectors in the numerator and the inverse of eigenvalues in the denominator (exploiting symmetry in both computations), we can accurately approximate the forced response as a function of mistuning. Results are demonstrated for a simple lightly damped model, and the consequent sharp nonlinear behavior is captured almost perfectly. We also show that intentional mistuning may guarantee improved stability and forced response under fixed manufacturing tolerances. Thus, intentional mistuning should be considered as a practical means of increasing safety and enhancing engine performance.
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    Automatic Rendering of Astrodynamics Expressions for Efficient Evaluation
    (American Astronautical Society, 1998) Healy, Liam M.; Travisano, Jeffrey J.
    In this paper, we describe the automatic rendering of expressions computed using symbolic manipulation. Computations from astrodynamics frequently can be put in a fixed hierarchy of polynomials and Fourier series. Once in this form, FORTRAN subprograms can be generated automatically in a form that lends itself to numerical evaluation. The goal of the current work is to present an approach for using symbolic manipulation techniques to produce a Fortran representation of the normalized Hamiltonian and other supporting equations representing as many of the actual physical effects on satellites as possible.
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    Symbolic and Parallel Computation in Celestial Mechanics
    (Society for Industrial and Applied Mathematics, 1996) Healy, Liam
    One aspect of celestial mechanics is the computation of the long-term orbits of celestial bodies. This type of computation is complicated by the interaction of the many bodies that need to be considered to derive accurate long-term behavior. For reasons explained in this chapter, it is necessary to do this symbolically rather than numerically. Symbolic computations performed on a Lisp machine are described. The visualization of the solution is accomplished in a massively parallel SIMD machine.
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    Close Conjunction Detection on Parallel Computer
    (American Institute of Aeronautics and Astronautics, 1995-07) Healy, Liam
    Close conjunction detection is the task of finding which satellites will come within a given distance of other satellites. The algorithms described here are implemented on the Connection Machine (CM) in a program called CM-COMBO. It will find close conjunctions of satellites over a time range for one, a few, or all satellites against the original or another catalog and works with an arbitrary propagator. The problem of comparing an entire catalog against itself is beyond the computing power of current serial machines. This program does not prefilter any orbits and does not make assumptions about the type of orbit (that it be nearly circular, for instance). This paper describes the algorithm for this computation, the implementation on the CM, and resuls of several studies using this program.
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    Deterministic Studies of Debris Hazards with Parallel Processors
    (European Space Agency, 1993-04-05) Healy, Liam; Coffey, Shannon
    A new generation of parallel processing computers makes possible the ability to propagate all objects in the space surveillance catalog with simulated objects, and detect close approaches. With this capability, it is possible to test deterministically debris scenarios, without resorting to statistical models. To compare the positions of objects we have developed two methods, an all-to-all comparison and a one-to-all comparison. For the former, a seive significantly reduces computation time; for the latter, direct comparison is possible in parallel. We show results from several simulations, including simulated multiple sources of debris, hazard to the space station, and close contacts amongst the catalog itself, to show potential for debris studies. The techniques described here have potential application the general problem of catalog maintenance.
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    Parallel Computing for Space Surveillance
    (MIT Lincoln Laboratory, 1992) Healy, Liam; Coffey, Shannon
    This paper reports on an application of massively parallel processors to multiple satellite propagation and the calculation of miss distances between objects (COMBO). Unlike serial computations, we do not pre-filter the data but rather sort the data set in a way that dramatically cuts the number of comparisons required in order to be assured of a complete catalog-to-catalog comparison. The same general algorithm allows two logical sets to be compare to each other. Run time for this demonstration code on an 8K Connection Machine is about one second per time step, including propagation, complete catalog-to-catalog calculation of miss distances, plotting satellite positions, and recording of the miss distances to a file. Propagation of the objects is performed with an analytic propagator, using J2 only at present, though the code may easily be extended to other propagators. We demonstrate a second application of parallel computing to the problem of debris propagation resulting from a satellite breakup. The spread of such debris into n pieces is simulated by replicating the element set for the original satellite n times, then altering each to represent a distribution of velocities to the center of mass.
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    A Toolbox for Nonlinear Dynamics
    (Springer-Verlag, 1991) Coffey, Shannon; Deprit, André; Deprit, Eitenne; Healy, Liam; Miller, Bruce
    Using the main problem of artificial satellite theory as an illustration, we review several developments which have had a significant impact on research in nonlinear dynamics. On the mathematical front, we point to the theory of Lie transformations; in the area of computational software, we explain how massively data parallel machines open the way for symbolic solution of large problems. Finally, we show how color graphics assist in the qualitative analysis of dynamical systems.
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    Computation of error effects in nonlinear Hamiltonian systems using Lie algebraic methods
    (American Institute of Physics, 1992-06) Healy, Liam; Dragt, Alex; Gjaja, Ivan
    There exist Lie algebraic methods for obtaining transfer maps around any given trajectory of a Hamiltonian system. This paper describes an iterative procedure for finding transfer maps around the same trajectory when the Hamiltonian is perturbed by small linear terms. Such terms often result when an actual system deviates from an ideal one due to errors. Two examples from accelerator physics are worked out. Comparisons with numerical computations, and in simple cases exact analytical calculations, demonstrate the validity of the procedure.