Stability and convergence analysis of the harmonic balance method for a Duffing oscillator with freeplay nonlinearity.
Abstract not provided.
Saunders, Brian E.↗
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Application of a transonic potential flow code to the static aeroelastic analysis of three-dimensional wings
A method for including elastic effects in steady, transonic wing analysis is presented. Since the aerodynamic theory is nonlinear, the method requires the coupling of two iterative processes - an aerodynamic analysis and a structural analysis. A full potential analysis code, FL022, is combined with a linear structural analysis to yield aerodynamic load distributions on and deflections of elastic wings. This method was used to analyze an aeroelastically-scaled wind tunnel model of a proposed executive-jet transport wing and an aeroelastic research wing. The results are compared with the corresponding rigid-wing analyses, and some effects of elasticity on the aerodynamic loading are noted.
Whitlow, W., Jr.↗
Stability and convergence analysis of the harmonic balance method for a Duffing oscillator with freeplay nonlinearity.
Abstract not provided.
Saunders, Brian↗
String Stability of a Linear Formation Flight Control System
String stability analysis of an autonomous formation flight system was performed using linear and nonlinear simulations. String stability is a measure of how position errors propagate from one vehicle to another in a cascaded system. In the formation flight system considered here, each i(sup th) aircraft uses information from itself and the preceding ((i-1)(sup th)) aircraft to track a commanded relative position. A possible solution for meeting performance requirements with such a system is to allow string instability. This paper explores two results of string instability and outlines analysis techniques for string unstable systems. The three analysis techniques presented here are: linear, nonlinear formation performance, and ride quality. The linear technique was developed from a worst-case scenario and could be applied to the design of a string unstable controller. The nonlinear formation performance and ride quality analysis techniques both use nonlinear formation simulation. Three of the four formation-controller gain-sets analyzed in this paper were limited more by ride quality than by performance. Formations of up to seven aircraft in a cascaded formation could be used in the presence of light gusts with this string unstable system.
Allen, Michael J.↗
Dynamic tooth loads and stressing for high contact ratio spur gears
A time history, closed form solution is presented for a dynamic model of spur gear systems for all practical contact ratios. The analysis determines the dynamic response of the gear system and the associated tooth loads and stressing. The dynamic model assumes the two gears act as a rigid inertia and the teeth act as a variable spring of a dynamic system excited by the meshing action of the teeth. Included in the analysis are the effects of the nonlinearity of the tooth pair stiffness during mesh, the tooth errors, and the tooth profile modifications. Besides reviewing the features, solution, and program of this analysis, preliminary results from applying the analysis are presented, which show that tooth profile modification, system inertia and damping, and system critical speeds can affect the dynamic gear tooth loads and stressing significantly.
Cornell, R. W.↗
Broadband IR Lidar for Gas Analysis of the Atmosphere
Results from energy measurements in the ranges 1.8–2.5 and 3–4 μm of radiation from IR lasers based on KTP and KTA nonlinear crystals with an optical parametric oscillator for lidar remote gas analysis of the atmosphere are presented. Lidar measurements of atmospheric gas components are simulated. Experimentally recorded IR lidar echo signals in these ranges are recorded.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Nonlinear Instability of Hypersonic Flow past a Wedge
The nonlinear stability of a compressible flow past a wedge is investigated in the hypersonic limit. The analysis follows the ideas of a weakly nonlinear approach. Interest is focussed on Tollmien-Schlichting waves governed by a triple deck structure and it is found that the attached shock can profoundly affect the stability characteristics of the flow. In particular, it is shown that nonlinearity tends to have a stabilizing influence. The nonlinear evolution of the Tollmien-Schlichting mode is described in a number of asymptotic limits.
Seddougui, Sharon O.↗
PETSc TSAdjoint: A Discrete Adjoint ODE Solver for First-Order and Second-Order Sensitivity Analysis
Here, we present a new software system PETSc TSAdjoint for first-order and second order adjoint sensitivity analysis of time-dependent nonlinear differential equations. The derivative calculation in PETSc TSAdjoint is essentially a high-level algorithmic differentiation process. The adjoint models are derived by differentiating the timestepping algorithms and implementing them based on the parallel infrastructure in PETSc. Full differentiation of the library code, including MPI routines, is avoided, and users do not need to derive their own adjoint models for their specific applications. PETSc TSAdjoint can compute the first-order derivative, that is, the gradient of a scalar functional, and the Hessian-vector product, which carries second-order derivative information, while requiring minimal input (a few callbacks) from the users. The adjoint model employs optimal checkpointing schemes in a manner that is transparent to users. Finally, usability, efficiency, and scalability are demonstrated through examples from a variety of applications.
79 ASTRONOMY AND ASTROPHYSICS↗
A lifting surface theory for the analysis of nonplanar lifting systems
A new nonlinear, nonplanar lifting surface theory is presented. The method is regarded as a lifting surface theory in that the effects of wing thickness are neglected, but none of the usual small perturbation assumptions inherent in most other lifting surface theories are made. The method represents nonplanar lifting systems by distributed vorticity, including the leading edge singular behavior characteristic of thin wings. The method is well suited to the computation of induced drag of nonplanar systems because leading edge suction is calculated from the leading edge singularity. The method has been used to compute the induced drag benefit of winglets (vortex diffusers), and the agreement with NASA experimental data is excellent.
Goldhammer, M. I.↗
Parameter identification for nonlinear aerodynamic systems
Work continues on frequency analysis for transfer function identification, both with respect to the continued development of the underlying algorithms and in the identification study of two physical systems. Some new results of a theoretical nature were recently obtained that lend further insight into the frequency domain interpretation of the research. Progress in each of those areas is summarized. Although not related to the system identification problem, some new results were obtained on the feedback stabilization of linear time lag systems.
Pearson, Allan E.↗
Parameter identification for nonlinear aerodynamic systems
Continuing work on frequency analysis for transfer function identification is discussed. A new study was initiated into a 'weighted' least squares algorithm within the context of the Fourier modulating function approach. The first phase of applying these techniques to the F-18 flight data is nearing completion, and these results are summarized.
Pearson, Allan E.↗
Design optimization and probabilistic analysis of a hydrodynamic journal bearing
A nonlinear constrained optimization of a hydrodynamic bearing was performed yielding three main variables: radial clearance, bearing length to diameter ratio, and lubricating oil viscosity. As an objective function a combined model of temperature rise and oil supply has been adopted. The optimized model of the bearing has been simulated for population of 1000 cases using Monte Carlo statistical method. It appeared that the so called 'optimal solution' generated more than 50 percent of failed bearings, because their minimum oil film thickness violated stipulated minimum constraint value. As a remedy change of oil viscosity is suggested after several sensitivities of variables have been investigated.
Liniecki, Alexander G.↗
Effects of electron beam parameters and velocity spread on radio frequency output of a photonic band gap cavity gyrotron oscillator
In this paper, the effects of electron beam parameters and velocity spread on the RF behavior of a metallic photonic band gap (PBG) cavity gyrotron operating at 35 GHz with TE{sub 041}–like mode have been theoretically demonstrated. PBG cavity is used here to achieve a single mode operation of the overmoded cavity. The nonlinear time-dependent multimode analysis has been used to observe the beam-wave interaction behavior of the PBG cavity gyrotron, and a commercially available PIC code “CST Particle Studio” has been reconfigured to obtain 3D simulation results in order to validate the analytical values. The output power for this typical PBG gyrotron has been obtained ∼108 kW with ∼15.5% efficiency in a well confined TE{sub 041}–like mode, while all other competing modes have significantly low values of power output. The output power and efficiency of a gyrotron depend highly on the electron beam parameters and velocity spread. The influence of several electron beam parameters, e.g., beam voltage, beam current, beam velocity pitch factor, and DC magnetic field, on the PBG gyrotron operations has been investigated. This study would be helpful in optimising the electron beam parameters and estimating accurate RF output power of the high frequency PBG cavity based gyrotron oscillators.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
On the input-output stability of time-varying nonlinear feedback systems. I - Conditions derived using concepts of loop gain, conicity, and positivity.
Input-output stability conditions of time-varying nonlinear feedback systems obtained, using concepts of loop gain, conicity and positivity
FEEDBACK CONTROL SYSTEM↗
Evaluation of a fault tolerant system for an integrated avionics sensor configuration with TSRV flight data
The performance analysis results of a fault inferring nonlinear detection system (FINDS) using sensor flight data for the NASA ATOPS B-737 aircraft in a Microwave Landing System (MLS) environment is presented. First, a statistical analysis of the flight recorded sensor data was made in order to determine the characteristics of sensor inaccuracies. Next, modifications were made to the detection and decision functions in the FINDS algorithm in order to improve false alarm and failure detection performance under real modelling errors present in the flight data. Finally, the failure detection and false alarm performance of the FINDS algorithm were analyzed by injecting bias failures into fourteen sensor outputs over six repetitive runs of the five minute flight data. In general, the detection speed, failure level estimation, and false alarm performance showed a marked improvement over the previously reported simulation runs. In agreement with earlier results, detection speed was faster for filter measurement sensors soon as MLS than for filter input sensors such as flight control accelerometers.
Caglayan, A. K.↗
Boundary formulations for shape sensitivity of temperature dependent conductivity problems
Used in concert with the Kirchhoff transformation, implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solids with temperature dependent thermal conductivity is shown to generate an accurate and economical approach for computation of shape sensitivities. For problems with specified temperature and heat flux boundary conditions, a linear problem results for both the analysis and sensitivity analysis. In problems with either convection or radiation boundary conditions, a nonlinear problem is generated. Several iterative strategies are presented for the solution of the resulting sets of nonlinear equations and the computational performances examined in detail. Multizone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized nonlinear boundary conditions or regions of geometric insensitivity to design variables. A series of nonlinear example problems is presented that have closed form solutions. Exact analytical expressions for the shape sensitivities associated with these problems are developed and these are compared with the sensitivities computed using the boundary element formulation.
Kane, James H.↗
On a solution of the nonlinear differential equation for transonic flow past a wave-shaped wall
The Prandtl-Busemann small-perturbation method is utilized to obtain the flow of a compressible fluid past an infinitely long wave-shaped wall. When the essential assumption for transonic flow (that all Mach numbers in the region of flow are nearly unity) is introduced, the expression for the velocity potential takes the form of a power series in the transonic similarity parameter. On the basis of this form of the solution, an attempt is made to solve the nonlinear differential equation for transonic flow past the wavy wall. The analysis utilized exhibits clearly the difficulties inherent in nonlinear-flow problems.
Kaplan, Carl↗
Digital signal processing in coupled photonic crystal waveguides and its application to an all-optical AND logic gate
The realization of all-optical AND logic gates for pulsed signal operation based on the photonic bandgap transmission phenomenon is proposed. We are using realistic planar air-hole type coupled photonic crystal waveguides (C-PCWs) with Kerr-type nonlinear background medium. The novelty of our analysis is that the proposed AND logic gate operates with the temporal solitons, which maintain a stable envelope propagating in the nonlinear C-PCWs, enabling true ultrafast full-optical digital signal processing in the time-domain. The bandgap transmission takes place when the operating frequency is chosen at the very edge of the dispersion curve of one of the supermodes in the C-PCWs. In this regard, our original fast and accurate method is used to efficiently calculate the supermodes of the C-PCW system. The underlying semi-analytical full-wave modal analysis is based on the evaluation of the lattice sums for complex wavenumbers using the transition-matrix method in combination with the generalized reflection-matrix approach. As a proof of concept successful pulse operation of the all-optical AND logic gate is demonstrated in the framework of extensive full-wave finite-difference time-domain electromagnetics analysis.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗