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Nonlinear combustion stability problems in liquid propellant rocket engines, describing unsteady combustion response by Crocco time lag hypothesis
The development of a means of computing free-fall (nonthrusting) trajectories from one specified point in the solar system to another specified point in the solar system in a given amount of time was studied. The problem is that of solving a two-point boundary value problem for which the initial slope is unknown. Two standard methods of attack exist for solving two-point boundary value problems. The first method is known as the initial value or shooting method. The second method of attack for two-point boundary value problems is to approximate the nonlinear differential equations by an appropriate linearized set. Parts of both boundary value problem solution techniques described above are used. A complete velocity history is guessed such that the corresponding position history satisfies the given boundary conditions at the appropriate times. An iterative procedure is then followed until the last guessed velocity history and the velocity history obtained from integrating the acceleration history agree to some specified tolerance everywhere along the trajectory.
Methods are discussed for determining the characteristics of elements of nonlinear vibrational systems, from the results of analyzing forced vibrations which are approximate in themselves, since they are based on the use of experimental data. The constant components of the linearized characteristics and linearization coefficients are determined experimentally by finding the values of these quantities at different vibration amplitudes and frequencies and subsequent approximation of their analytical expressions. Simple and convenient, although approximate, formulas for determining the characteristics of vibrational systems from experimentally known functions are derived.
Limb emission measurements are characterized by sharp weighting functions at high altitudes, and for temperature determinations, strongly nonlinear dependence of the weighting function on the temperature. Several methods for inverting this type of measurement have been described and used, including iterative, statistical, nonlinear and approximate direct approaches. These approaches are described and advantages and disadvantages of each are outlined.
Starting with MAP estimation theory as a basis for optimally estimating carrier phase of BPSK and QPSK modulations, it is shown in this paper that the closed loop phase trackers, which are motivated by this approach, are indeed closed loop optimum in the minimum mean-square phase tracking jitter sense. The corresponding squaring loss performance of these so-called MAP estimation loops is compared with that of more practical implementations wherein the hyperbolic tangent nonlinearity is approximated by simpler functions.
Truncated modal equations are used to study the time evolution of thermal convection. In the Boussinesq approximation these nonlinear equations are obtained by expanding the fluctuating velocity and temperature fields in a finite set of planforms of the horizontal coordinates. Numerical studies dealing with two or three modes with triad interactions are discussed. Rich time dependence was found in these cases: periodic and aperiodic solutions can be obtained, along with various steady solutions. Three-mode solutions reproduce the qualitative appearance of spoke-pattern convection as observed in experiments at high Prandtl numbers. Though the values of the periods of the time-dependent solutions do not agree with those of the experiments, their variation with Rayleigh number compares favorably. Except at the highest Rayleigh number considered (10,000,000), the theoretical Nusselt numbers agree well with experiment.
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A main disadvantage of using spectral methods for nonlinear conservation laws lies in the formation of Gibbs phenomenon, once spontaneous shock discontinuities appear in the solution. The global nature of spectral methods than pollutes the unstable Gibbs oscillations overall the computational domain, and the lack of entropy dissipation prevents convergences in these cases. The Spectral Viscosity method, which is based on high frequency dependent vanishing viscosity regularization of the classical spectral methods is discussed. It is shown that this method enforces the convergence of nonlinear spectral approximations without sacrificing their overall spectral accuracy.
The k-epsilon-v(sup 2)(bar) model has been investigated to quantify its predictive performance on two high-lift configurations: 2D flow over a single-element aerofoil, involving closed-type separation; 3D flow over a prolate spheroid, involving open-type separation. A 'code-friendly' modification has been proposed which enhances the numerical stability, in particular, for explicit and uncoupled flow solvers. As a result of introducing Reynolds-number dependence into a coefficient of the s-equation, the skin-friction distribution for the by-pass transitional flow over a flat plate is better predicted. In order to improve deficiencies arising from the Boussinesq approximation, a nonlinear stress-strain constitutive relation was adopted, in which the only one free constant is calibrated on the basis of DNS data, and the Reynolds-stress anisotropy near the wall is fairly well represented.
A system identification model that combines generalized-spline function approximation with a nonlinear control system is described. The complete control system contains three main elements: a nonlinear-inverse-dynamic control law that depends on a comprehensive model of the plant, a state estimator whose outputs drive the control law, and a function approximation scheme that models the system dynamics. The system-identification task, which combines an extended Kalman filter with a function approximator modeled as an artificial neural network, is considered. The results of an application of the identification techniques to a nonlinear transport aircraft model are presented.
Finite dimensional approximations of optimal nonlinear filters for class of large-noise, nonlinear, continuous-time problems
A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite rectangular thin plates. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite rectangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, different boundary conditions, aspect ratios, lamination angles and number of plies are presented. The finite element results are compared with available approximate continuum solutions.
A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite thin plates using the Discrete Kirchhoff Theory (DKT) triangular elements. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite triangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, triangular plates, different boundary conditions, lamination angles, number of plies, and uniform versus concentrated loads are presented.
Using the method of strained coordinates, a uniformly valid approximation to the nonlinear equatorial Kelvin wave is derived. It is shown that nonlinear effects are negligible for the Kelvin waves associated with the Gulf of Guinea upwelling. The Kelvin waves involved in El Nino, however, are significantly distorted both in shape and speed. The leading edge is smoothed and expanded rather than steepened, but the trailing edge will form sharp fronts and eventually break.
Approximate solutions for three nonlinear orthotropic plate problems are presented: (1) a thick plate attached to a pad having nonlinear material properties which, in turn, is attached to a substructure which is then deformed; (2) a long plate loaded in inplane longitudinal compression beyond its buckling load; and (3) a long plate loaded in inplane shear beyond its buckling load. For all three problems, the two dimensional plate equations are reduced to one dimensional equations in the y-direction by using a one dimensional trigonometric approximation in the x-direction. Each problem uses different trigonometric terms. Solutions are obtained using an existing algorithm for simultaneous, first order, nonlinear, ordinary differential equations subject to two point boundary conditions. Ordinary differential equations are derived to determine the variable coefficients of the trigonometric terms.
A development status evaluation is presented for applications of main approximation concepts in nonlinear programming for structural optimization requiring local, midrange, and global approximations. It is noted that there is not yet a sufficient basis for a comprehensive evaluation of relative effectiveness among approximation concepts. Attention is presently given to the careful selection of intermediate-variable and response quantity, and improvements in the traditional Taylor-series expansion by inclusion of either some higher-order terms or information at various points in the design space.
A MAP (maximum a posteriori) estimation loop is derived for a QPSK signal and, by suitable approximation to the nonlinearity which arises as a consequence of the MAP theory, is reconfigured with practical realizations that are valid for high and low SNRs. In particular, it is shown that by approximating the hyperbolic tangent nonlinearity in the MAP estimation loop by the first two terms in its power series, an interesting practical realization of this loop results which applies at low SNRs. The error signal in this loop is formed by multiplying the error signal and lock detector output signal of a conventional biphase Costas loop. A generalized linear in-phase channel configuration is proposed which allows carrier reconstruction from an unbalanced QPSK signal at all ratios of data rates and powers in the two channels, even in the limit as these ratios simultaneously approach unity, i.e., balanced quadriphase.
Nonlinear different equations, Gauss-Seidel or relaxation processes as methods for approximating solutions of nonlinear systems of equations