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Description of a variable step incremental procedure for the solution of nonlinear equations in finite element structural analysis. The proposed procedure is effective in improving the accuracy of the basic incremental technique and in providing, in addition, an accurate estimate of the discretization error. The proposed approach is highly appropriate for solving problems for which the user has no a priori estimate of the step size to use.
The primary objective of this paper is to present a constructive procedure for the synthesis of linear multivariable systems whose entire internal state and output are corrupted by unknown step disturbances. It is assumed that the dynamical behavior of the system is expressed in any one of three equivalent ways - i.e., the state space representation, the controllable and observable differential operator representation, and the transfer matrix representation. In terms of the transfer matrix representation, T(s), the synthesis procedure is shown to be capable of producing any stable, desired closed loop transfer matrix, Td(s), which can be expressed as the product of T(s) and any proper rational matrix, Tc(s), while simultaneously eliminating the steady-state effect of step disturbances at the output of the system. Furthermore, the synthesis scheme outlined employes only the known, directly measurable input and output signals.
Description of methods of solving first- and second-order systems of differential equations in which all derivatives are evaluated at off-grid locations in order to circumvent the Dahlquist stability limitation on the order of on-grid methods. The proposed multi-off-grid methods require off-grid state predictors for the evaluation of the n derivatives at each step. Progressing forward in time, the off-grid states are predicted using a linear combination of back on-grid state values and off-grid derivative evaluations. A comparison is made between the proposed multi-off-grid methods and the corresponding Adams and Cowell on-grid integration techniques in integrating systems of ordinary differential equations, showing a significant reduction in the error at larger step sizes in the case of the multi-off-grid integrator.
Some results of the application of a unified theory of small disturbances in nonuniform high-speed boundary layers to the small-step problem for the case of supersonic laminar nonadiabatic flow are described. Comparisons with experimental data are given which show good agreement in a variety of physical features, including useful new base pressure and heat-transfer correlation relations. Using a small perturbation approach, an analytical theory is developed that predicts the steady-state pressure, temperature, and heat-transfer disturbance fields including suction or blowing through the step. Particular emphasis is placed on the important effects of the highly nonuniform flow across the boundary layer, lateral pressure gradients, and the upstream influence associated with viscous-inviscid interaction. Approximate analytical expressions for the wall pressure, skin friction, and heat-transfer perturbations and upstream influence distance are derived by a Fourier transformation approach.
A finite difference formulation is presented for sound propagation in a rectangular two-dimensional duct without steady flow. Before the difference equations are formulated, the governing Helmholtz equation is first transformed to a form whose solution tends not to oscillate along the length of the duct. This transformation reduces the required number of grid points by an order of magnitude. Example solutions indicate that stepped noise source profiles have much higher attenuation than plane waves in a uniform impedance liner. Also, multiple stepped impedance liners are shown to have higher attenuation than uniform ducts if the impedances are chosen properly. For optimum noise reduction with axial variations in impedance, the numerical analysis indicates that for a plane wave input the resistance should be near zero at the entrance of a suppressor duct, while the reactance should be near the optimum value associated with the least-attenuated mode in a uniform duct.
A procedure is presented for the minimization of structural mass while satisfying flutter speed constraints. The procedure differs from other optimization methods in that the flutter speed is exactly satisfied at each resizing step, and the step size is determined by a direct minimization of the objective function (mass) for each set of flutter derivatives calculated. In conjunction with this method, a new move vector is suggested which results in a very efficient resizing procedure.
A theoretical investigation of the pressure distributions and drag characteristics was made for forward facing steps in turbulent flow at supersonic speeds. An approximate solution technique proposed by Uebelhack has been modified and extended to obtain a more consistent numerical procedure. A comparison of theoretical calculations with experimental data generally indicated good agreement over the experimentally available range of ratios of step height to boundary layer thickness from 7 to 0.05.
A mathematical model describing ground-wind induced flow fields around surface obstructions such as buildings, bridges or other man-made structures is presented. The Navier-Stokes equations with a two-equation turbulence model are used to analyze the flow over a two-dimensional forward facing step. A study of the assumed logarithmic approach velocity profile shows that an increase of surface roughness produces a rise to higher turbulence levels in the shear layer originating from the step corner. This rise leads to higher Reynolds stress and to faster reattachment of the separated flow.
Hydrodynamic effects are analyzed for a stepped piston moving within a tight clearance tube filled with an incompressible fluid. Hydrostatic effects are analyzed and a complete solution is obtained and an optimum step design for centering of the piston is suggested. The axial speed resulting from an axial driving force is calculated, and some experimental results for pistons falling in a water-filled tube are presented.
The phenomenon of atmospheric shear layer separation over a man-made structure such as a building (modeled as a backward-facing step) has been analyzed theoretically by (1) solving the two-dimensional equations of motion in the two variables, stream function and vorticity, and by (2) employing an approximate integral technique. Boundary conditions for the undisturbed flow are that of the turbulent atmospheric shear flow over a rough terrain. In the first approach a two-equation model of turbulence was used. In the second approach an approximate technique was utilized in an attempt to describe the details of the flow in the recirculation zone behind the step. The results predict velocity profiles in sufficient detail that the presence of the corner eddy in the region of negative surface pressure gradient is evident. The magnitude of the reversed flow velocity in the recirculation eddy has been found to agree with that found from experiments. Also, a surface eddy viscosity distribution has been an outgrowth of the method which realistically follows the magnitude of the surface pressure gradient distribution as found experimentally.
State-plane analysis techniques are employed to study the voltage step up energy storage dc-to-dc converter. Within this framework, an example converter operating under the influence of a constant on time and a constant frequency controller is examined. Qualitative insight gained through this approach is used to develop a conceptual free running control law for the voltage step up converter which can achieve steady state operation in one on/off cycle of control. Digital computer simulation data is presented to illustrate and verify the theoretical discussions presented.
Hydrodynamic effects are analyzed for a stepped piston moving within a tight clearance tube filled with an incompressible fluid. Together with the hydrostatic effects that were analyzed in an earlier paper, a complete solution is obtained and an optimum step design for centering of the piston is suggested. The axial speed resulting from an axial driving force is calculated, and some experimental results for pistons falling in a water filled tube are presented.
The finite-step method was programmed for computing the span loading and stability derivatives of trapezoidal shaped wings in symmetric, yawed, and rotary flight. Calculations were made for a series of different wing planforms and the results compared with several available methods for estimating these derivatives in the linear angle of attack range. The agreement shown was generally good except in a few cases. An attempt was made to estimate the nonlinear variation of lift with angle of attack in the high alpha range by introducing the measured airfoil section data into the finite-step method. The numerical procedure was found to be stable only at low angles of attack.
Ablation and condensation of water vapor are suggested as the principal factors responsible for the circumpolar layered and stepped terrain found at the North and South Poles of Mars. A metastable erosion rate due to decreasing albedo and increasing radiation input caused by dust deposits on the steeper slopes of the ablating layered deposits provides a mechanism for the development of the stepped topography. Loose excess dust accumulated during scarp ablation may then be removed by wind erosion.
A new approach to flying qualities specification and evaluation is presented which coordinates current research in the areas of pilot ratings, pilot-aircraft modeling techniques, and simulation and flight test procedures. A time-domain pilot model is described which can model discontinuous and nonlinear pilot behavior in conjunction with completely general time-varying nonlinear aircraft models to simulate discrete maneuvers. This pilot-aircraft model is applied to an existing set of in-flight simulation data, and calculates tracking error and time-on-target statistics for step target tracking that directly relate to the reported pilot comments and ratings. Predicted step target tracking data for eighteen F-5E flight conditions are presented, and the use of the method for control system design is demonstrated using the YF-17.
The effect of power/temperature step stress when applied to the transistor JANTX2N2905A manufactured by Texas Instruments and Motorola is reported. A total of 48 samples from each manufacturer was submitted to the process outlined. In addition, two control sample units were maintained for verification of the electrical parametric testing. All test samples were subjected to the electrical tests outlined in Table 2 after completing the prior power/temperature step stress point.
Reliability analysis of the transistor JANTX2N4150 manufactured by General Semiconductor and Transitron is reported. The discrete devices were subjected to power and temperature step stress tests and then to electrical tests after completing the power/temperature step stress point. Control sample units were maintained for verification of the electrical parametric testing. Results are presented.
Power/temperature step stress was applied to the transistor JANTX2N2432A manufactured by Crystalonics and Texas Instruments. A total of 48 samples from each manufacturer were submitted to the process outlined. In addition, two control sample units were maintained for verification of the electrical parametric testing. All test samples were subjected to the electrical tests after completing the prior power/temperature step stress point.