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Equivalent nonlinear potential systems: Review of previous assumptions

PROBABILISTIC ENGINEERING MECHANICS 2010年第1期25卷 142-152页

作者： Floris, Claudio Politecn Milan Dept Struct Engn I-20133 Milan Italy

Few exact solutions for the response of stochastic dynamical systems are available. Thus, the methods of the equivalent linearization and of the equivalent nonlinear system are often used. While the former yields a Gaussian response to a Gaussian excitation, the latter gives a non-Gaussian response, which is nearer to the exact unknown response of a nonlinear system. Among the equivalent nonlinear system methods the one based on the replacement of the actual dynamic system by means of a potential system is promising, Cavaleri and Di Paola (2000) 1411, as it leads to a fixed procedure differently from other methods. The procedure is developed under the assumption that the ratio of the moments E[Lambda(j)(X) over dot(2) and E [Lambda(j+1)] is a constant alpha not depending on j, A being the mechanical energy of the oscillator and (X) over dot its velocity. This relationship is demonstrated only for the so called Robert's oscillator, that is an oscillator with restoring force g(X) = omega(0) sgn(X) . |X|(nu), but in the above mentioned reference it is argued that it is valid in general. In this paper, numerical analyses are presented to ascertain its validity in order to apply the method to systems with different restoring forces. It is found that in some cases it is true, some others are doubtful, while there are cases in which alpha clearly depends on j. The effects of considering alpha constant when it is not are ascertained for a Duffing oscillator with linear plus cubic damping. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Stochastic dynamics Nonlinear systems Equivalent nonlinear system Potential systems solution algorithm

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A study of mixed discrete bilevel programs using semidefinite and semi-infinite programming

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OPERATIONS RESEARCH LETTERS 2023年第1期51卷 84-91页

作者： Kue, Floriane Mefo Dempe, Stephan Univ Yaounde I Higher Training Coll Dept Math POB 812 Yaounde Cameroon AIMS Cameroon Res Ctr POB 608 Limbe Cameroon TU Bergakad Freiberg Dept Math & Comp Sci Akad str 6 D-09596 Freiberg Germany

In this paper, we study the bilevel programming problem with discrete polynomial lower level problem. We start by transforming the problem into a bilevel problem comprising a semidefinite program (SDP for short) in the lower level problem. Then, we are able to deduce some conditions of existence of solutions for the original problem. After that, we again change the bilevel problem with SDP in the lower level problem into a semi-infinite program. With the aid of the exchange technique, for simple bilevel programs, an algorithm for computing a global optimal solution is suggested, the convergence is shown, and a numerical example is given.(c) 2022 Elsevier B.V. All rights reserved.

关键词： Bilevel programming Semidefinite programming Semi -infinite programming solution algorithm

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Differential Aerodynamic Force-Based Formation Control of Nanosatellites Using Yaw Angle Deviation

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2021年第12期44卷 2199-2213页

作者： Hu, Yuandong Lu, Zhengliang Liao, Wenhe Zhang, Xiang Nanjing Univ Sci & Technol Sch Mech Engn Nanjing 210094 Peoples R China

This paper investigates a formation control technique for low-Earth-orbit nanosatellites based on the differential aerodynamic drag and lift. An innovative method of using only the yaw angle deviation, instead of the three-axis attitude rotation, is proposed to simultaneously control the in-plane and out-of-plane relative motions. This method can be used for the formation control of the Earth-pointing satellite. A control scheme consisting of four steps is designed considering complex input constraints. In this scheme, two control inputs are defined based on the predicted atmospheric density, and the explicit expressions of their time-varying feasible regions are analyzed. To obtain the yaw angle of each nanosatellite, a yaw angle solution algorithm based on the grid interpolation method is designed with online solving nonlinear optimization avoided. A dynamic surface control algorithm based on the hyperbolic tangent function and a linear model predictive control algorithm are, respectively, used to limit two control inputs within their feasible regions. In addition, a nonlinear finite-time disturbance observer is used to track the total system disturbance. Numerical simulations are carried out for along-track and circular formations, in which the uncertainties of aerodynamic forces, the attitude dynamics, and the unknown perturbation are taken into account.

关键词： Aerodynamic Coefficients Yaw Satellite Formation solution algorithm Atmospheric Environment Earth Model Predictive Control Numerical Simulation Attitude Dynamics Aerodynamic Performance

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Coupled ordinates method for multigrid acceleration of radiation calculations

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 1999年第4期13卷 467-473页

作者： Mathur, SR Murthy, JY Fluent Inc Lebanon NH 03766 USA Carnegie Mellon Univ Dept Mech Engn Pittsburgh PA 15213 USA

The finite volume and discrete ordinates methods are known to converge increasingly slowly as the optical thickness is increased. This is a result of the sequential nature of the solution procedure;the equations for energy and the directional intensities are solved one by one, assuming prevailing values for other variables. The coupled ordinates method is proposed whereby the discrete energy and intensity equations at each cell are solved simultaneously assuming spatial neighbors to be known. The point-coupled procedure is used as a relaxation sweep in a multigrid scheme. The formulation of coarse-level discrete equations admits arbitrary nonconvex polyhedra, making the scheme suitable for use with arbitrary unstructured polyhedral meshes. The scheme is shown to substantially accelerate convergence over a range of optical thicknesses.

关键词： Optical Thickness Energy Intensity Aspect Ratio Radiative Transfer Thermal Conductivity Numerical Integration Convection Radiation Heat Transfer solution algorithm Unstructured Grid

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HELICOPTER ROTOR BLADE AEROELASTICITY IN FORWARD FLIGHT WITH AN IMPLICIT STRUCTURAL FORMULATION

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AIAA JOURNAL 1992年第9期30卷 2274-2282页

作者： CELI, R University of Maryland College Park Maryland 20742

This paper describes an aeroelastic stability and response analysis in which the structural operator is formulated numerically, without expanding analytically the various algebraic expressions that make up the beam model. No ordering schemes need to be invoked to simplify the algebraic manipulations, and the various components of the mathematical model of the beam can be implemented and modified independently. The formulation is compatible with most solution algorithms. Two different implicit formulations are presented. The results of four illustrative examples are also presented. The first focuses on the effects of higher order kinematic nonlinearities on the aeroelastic stability and response of a hingeless rotor blade. The remaining three show how to introduce, using the implicit formulation, a nonlinear stress-strain relation in table look-up form, a composite cross section, and cross-sectional warping. Aeroelastic stability results are presented for all examples.

关键词： Aeroelastic Stability Helicopter Rotor Bernoulli Euler Beams Stress Strain Curve Hingeless Rotor Blade Composite Materials Mathematical Models Rotary Wing Elastic Deformation solution algorithm

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Transition prediction for three-dimensional boundary layers in computational fluid dynamics applications

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AIAA JOURNAL 2002年第8期40卷 1536-1541页

作者： Crouch, JD Crouch, IWM Ng, LL Boeing Commercial Airplane Grp Aerodynam Res Seattle WA 98124 USA Boeing Commercial Airplane Grp Acoust & Fluid Mech Seattle WA 98124 USA

A method is presented for estimating the laminar/turbulent transition location in three-dimensional boundary layers for computational fluid dynamics (CFD) applications requiring numerous transition estimates with no user intervention. Given the Reynolds number and the C-P distribution, the location of transition is estimated based on the attachment-line state, the potential for relaminarization, the occurrence of laminar separation, and the growth of instabilities. Transition caused by instability is estimated based on N factors calculated for Tollmien-Schlichting waves and for stationary crossflow instabilities. A neural network is used (in place of solving the Orr-Sommerfeld stability equation) for determining the instability growth rates. The current version of the method assumes incompressible How. The boundary-layer flow and instabilities are calculated based on an infinite-sweep (strip boundary layer) approximation;the instability calculations also employ the parallel-How approximation. Comparisons with traditional stability codes show good N-factor agreement over a practical range of C-P distributions. The method is several hundred times faster than traditional stability calculations, and it is robust enough to function as a simple "subroutine" in CFD codes. The method is biased toward application efficiency and simplicity as balanced against improvements in the detailed physical modeling.

关键词： Three Dimensional Boundary Layer CFD Neural Network Methods Freestream Mach Number CFD Codes Tollmien Schlichting waves Swept Wing Neutral Point Sweep Angle solution algorithm

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UNSTRUCTURED ADAPTIVE MESH COMPUTATIONS OF ROTORCRAFT HIGH-SPEED IMPULSIVE NOISE

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JOURNAL OF AIRCRAFT 1995年第4期32卷 754-760页

作者： STRAWN, RC BISWAS, R GARCEAU, M NASA Ames Research Center Moffett Field California 94035 Stanford University Stanford California 94305

A new method is developed for modeling helicopter high-speed impulsive (HSI) noise. The aerodynamics and acoustics near the rotor blade tip are computed by solving the Euler equations on an unstructured grid, A stationary Kirchhoff surface integral is then used to propagate these acoustic signals to the far field, The near-field Euler solver uses a solution-adaptive grid scheme to improve the resolution of the acoustic signal, Grid points are locally added and/or deleted from the mesh at each adaptive step, An important part of this procedure is the choice of an appropriate error indicator, The error indicator is computed from the flowfield solution and determines the regions for mesh coarsening and refinement, Computed results for HSI noise compare favorably with experimental data for three different hovering rotor cases.

关键词： Rotary Wing Aerodynamics Unstructured Grid Rotor Blades Acoustics Helicopter Rotor Euler Equations Supersonic Flow solution algorithm Tetrahedral Element

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Effect of Insulations and Coatings on Hypersonic Heat Flux Reconstruction

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 2021年第1期35卷 63-79页

作者： Nguyen, Nhat M. Ruda, Mathew L. Massa, Luca Virginia Polytech Inst & State Univ Kevin T Crofton Dept Aerosp & Ocean Engn 460 Old Turner St Blacksburg VA 24061 USA

The present study investigates the effects of material discontinuities and thermal resistances on the temperature reconstruction and heat flux evaluation via an inverse heat transfer method in hypersonic wind-tunnel tests. Thin coating layers and adhesive interfaces support a localized multidimensional temperature perturbation that alters the near-surface field. A technique is developed for the real-time evaluation of the heat transfer based on approximating the Green's function of the heat conduction equation in bounded complex domains and resolving the heat flux on a B-spline basis, leading to an efficient and robust algorithm. Evaluating the Green's function for three-dimensional problems with material discontinuities is generally difficult. A new approach is developed in which the Green's function is evaluated independently for the regular partitions of the domain, and appropriate connection conditions are derived to determine the full "system" Green's function. This paper describes the verification, validation, and application of the approach to the heat flux reconstruction for a nonaxisymmetric flat-faced article with coating and potting interfaces. The article was tested at Mach 6 in the Virginia Tech Hypersonic wind tunnel using four temperature sensors arranged in a cross pattern on the flat face. Good agreement was obtained between computational fluid dynamics predictions and the heat flux deduced from the experiments using the new data analysis method.

关键词： Heat Flux Distribution Green's Function Inverse Heat Conduction Hypersonic Wind Tunnels Heat Flow CFD Simulation Temperature Sensors Conduction Equation solution algorithm Data Analysis

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ARTIFICIAL DISSIPATION MODELS FOR THE EULER EQUATIONS

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AIAA JOURNAL 1986年第12期24卷 1931-1940页

作者： PULLIAM, TH NASA Ames Research Center Moffett Field California

Various artificial dissipation models that are used with central difference algorithms for the Euler equations are analyzed for their effect on accuracy, stability, and convergence rates. In particular, linear and nonlinear models are investigated using an implicit approximate factorization code (ARC2D) for transonic airfoils. Fully implicit application of the dissipation models is shown to improve robustness and convergence rates. The treatment of dissipation models at boundaries will be examined. It will be shown that accurate, error free solutions with sharp shocks can be obtained using a central difference algorithm coupled with an appropriate nonlinear artificial dissipation model. © 1986 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Rankine Hugoniot Relation Total Variation Diminishing Supersonic Flow Viscosity NACA 0012 Navier Stokes Equations solution algorithm Angle of Attack Numerical algorithms Specific Heat

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Navier-Stokes computations for body/cruciform grid fin configuration

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JOURNAL OF SPACECRAFT AND ROCKETS 2003年第1期40卷 30-38页

作者： Lin, H Huang, JC Chieng, CC Chung Shan Inst Sci & Technol Lung Tan 325 Peoples R China Natl Tsing Hua Univ Dept Engn & Syst Sci Hsinchu 300 Taiwan

A grid fin is an unconventional aerodynamic lifting and control device consisting of an outer frame with internal grid framework of small chord. The present study performs the Navier-Stokes computations of turbulent flows past 1) a grid fin alone and 2) fin/body combination shapes at Mach numbers of 2.5 and 0.7. This work designs a procedure to generate a structure grid with a simple and efficient algorithm combining "block-off" and "multiblock" methods for the complex configurations. Full Navier-Stokes equations with a pointwise version of the Baldwin-Barth one-equation turbulence model are discretized into finite difference form and solved by an algorithm in a fully coupled, implicit, and large block structure, and the solution algorithm achieves satisfactory convergence. The comparisons between computations and experimental data are made, and the detailed flow structure near grid fins can be obtained and examined.

关键词： Aerodynamic Characteristics Turbulence Models Navier Stokes Simulation Grid Fin solution algorithm Angle of Attack Bending Moment Eddy Viscosity Total Variation Diminishing Triangular Element

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