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At least 91 records · Page 5

Software for continuum modeling of controls-structures interactions

It is clear that computer software is needed to assist in the generation of the equations of motion for complex, flexible spacecraft. Daniel Poelaert of ESTEC has developed the software DISTEL with which he has modeled the structural dynamics for different satellites. He is interested in expanding the capabilities of DISTEL to include structural damping and control systems. Unfortunately, the software has not been released. The author has developed similar software, PDEMOD, which has been used to model the Spacecraft control Laboratory Experiment (SCOLE), the Solar Array Flight Experiment (SAFE), the Mini-MAST truss, and the LACE satellite. PDEMOD has been used also for optimal parameter estimation and integrated control-structures design. PDEMOD is also being extended to include structural damping and control systems which are imbedded into the same equations for the structural dynamics. This paper will address the formulation of the equations for the structural dynamics of spacecraft structures which are constructed of a 3-dimensional arrangement of rigid bodies and flexible beam elements. Control system dynamics are imbedded into the same equations so that model order reduction approximations are not necessary. The input data consists of the physical data of the elements and the topological information describing how the elements are connected. PDEMOD accomplishes the following: (1) automatically assembles the equations of motion for the entire structural model; (2) calculates the modal frequencies; (3) calculates the mode shapes; (4) generates perspective views of the mode shapes; and (5) forms selected transfer functions. The software PDEMOD continues to be developed to provide additional features to assist in analyzing and synthesizing control and structural systems for flexible spacecraft.

Taylor, Lawrence W., Jr.↗

A linear thermal stability analysis for the vertical structure of alpha model accretion disks

The linear equations that describe the thermal stability of the convective and radiative vertical structure of an alpha model accretion disk are derived. For a specific model chosen to be representative of a dwarf nova disk, it is found that the eigenfunction for the temperature shows large excursions in the zone of partial ionization, but that the eigenfunctions for the unstable fundamental mode perturbations of the vertical distance and flux are nearly constant over the vertical extent of the disk. The growth of any instability is thus nearly homologous and the stability criteria derived for vertically averaged structures represent an adequate approximation.

Saio, Hideyuki↗

Selection principles and pattern formation in fluid mechanics and nonlinear shell theory

Research accomplishments are summarized and publications generated under the contract are listed. The general purpose of the research was to investigate various symmetry breaking problems in fluid mechanics by the use of structure parameters and selection principles. Although all of the nonlinear problems studied involved systems of partial differential equations, many of these problems led to the study of a single nonlinear operator equation of the form F(w, lambda, gamma) = 0, (w is an element of H), (lambda is an element of R1), (gamma is an element of R1). Instead of varying only the load parameter lambda, as is often done in the study of such equations, one of the main ideas used was to vary the structure parameter gamma in such a way that stable solutions were obtained. In this way one determines detailed stability results by making use of the structure of the model equations and the known physical parameters of the problem. The approach was carried out successfully for Benard-type convection problems, Taylor-like problems for short cylinders, rotating Couette-Poiseuille channel flows, and plane Couette flows. The main focus of the research was on wave theory of vortex breakdown in a tube. A number of preliminary results for inviscid axisymmetric flows were obtained.

Sather, Duane P.↗

Unsteady transonic aerodynamics and aeroelastic calculations at low-supersonic freestreams

A computational procedure is presented to simulate transonic unsteady flows and corresponding aeroelasticity of wings at low-supersonic freestreams. The flow is modeled by using the transonic small-perturbation theory. The structural equations of motions are modeled using modal equations of motion directly coupled with aerodynamics. Supersonic freestreams are simulated by properly accounting for the boundary conditions based on pressure waves along the flow characteristics in streamwise planes. The flow equations are solved using the time-accurate, alternating-direction implicit finite-difference scheme. The coupled aeroelastic equations of motion are solved by an integration procedure based on the time-accurate, linear-acceleration method. The flow modeling is verified by comparing calculations with experiments for both steady and unsteady flows at supersonic freestreams. The unsteady computations are made for oscillating wings. Comparisons of computed results with experiments show good agreement. Aeroelastic responses are computed for a rectangular wing at Mach numbers ranging from subtransonic to upper-transonic (supersonic) freestreams. The extension of the transonic dip into the upper transonic regime is illustrated.

Guruswamy, Guru P.↗

Microscopic activated dynamics theory of the shear rheology and stress overshoot in ultradense glass-forming fluids and colloidal suspensions

We formulate a particle and force level, activated dynamics-based statistical mechanical theory for the continuous startup nonlinear shear rheology of ultradense glass-forming hard sphere fluids and colloidal suspensions in the context of the elastically collective nonlinear Langevin equation approach and a generalized Maxwell model constitutive equation. Activated structural relaxation is described as a coupled local-nonlocal event involving caging and longer range collective elasticity which controls the characteristic stress relaxation time. Theoretical predictions for the deformation-induced enhancement of mobility, the onset of relaxation acceleration at remarkably low values of stress, strain, or shear rate, apparent power law thinning of the steady-state structural relaxation time and viscosity, a nonvanishing activation barrier in the shear thinning regime, an apparent Herschel–Buckley form of the shear rate dependence of the steady-state shear stress, exponential growth of different measures of a yield or flow stress with packing fraction, and reduced fragility and dynamic heterogeneity under deformation were previously shown to be in good agreement with experiments. The central new question we address here is the defining feature of the transient response—the stress overshoot. In contrast to the steady-state flow regime, understanding the transient response requires an explicit treatment of the coupled nonequilibrium evolution of structure, elastic modulus, and stress relaxation time. We formulate a new quantitative model for this aspect in a physically motivated and computationally tractable manner. Theoretical predictions for the stress overshoot are shown to be in good agreement with experimental observations in the metastable ultradense regime of hard sphere colloidal suspensions as a function of shear rate and packing fraction, and accounting for deformation-assisted activated motion appears to be crucial for both the transient and steady-state responses.

Mechanics↗

Solitary zonal structures in subcritical drift waves: a minimum model

Solitary zonal structures have recently been identified in gyrokinetic simulations of subcritical drift-wave (DW) turbulence with background shear flows. However, the nature of these structures has not been fully understood yet. Here, we show that similar structures can be obtained within a reduced model, which complements the modified Hasegawa–Mima equation with a generic primary instability and a background shear flow. We also find that these structures can be qualitatively reproduced in the modified Hasegawa–Wakatani equation, which subsumes the reduced model as a limit. In particular, we illustrate that in both cases, the solitary zonal structures approximately satisfy the same 'equation of state', which is a local relation connecting the DW envelope with the zonal-flow velocity. Due to this generality, our reduced model can be considered as a minimum model for solitary zonal structures in subcritical DWs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

BioRT‐HBV 1.0: A Biogeochemical Reactive Transport Model at the Watershed Scale

Abstract Reactive Transport Models (RTMs) are essential tools for understanding and predicting intertwined ecohydrological and biogeochemical processes on land and in rivers. While traditional RTMs have focused primarily on subsurface processes, recent watershed‐scale RTMs have integrated ecohydrological and biogeochemical interactions between surface and subsurface. These emergent, watershed‐scale RTMs are often spatially explicit and require extensive data, computational power, and computational expertise. There is however a pressing need to create parsimonious models that require minimal data and are accessible to scientists with limited computational background. To that end, we have developed BioRT‐HBV 1.0, a watershed‐scale, hydro‐biogeochemical RTM that builds upon the widely used, bucket‐type HBV model known for its simplicity and minimal data requirements. BioRT‐HBV uses the conceptual structure and hydrology output of HBV to simulate processes including advective solute transport and biogeochemical reactions that depend on reaction thermodynamics and kinetics. These reactions include, for example, chemical weathering, soil respiration, and nutrient transformation. The model uses time series of weather (air temperature, precipitation, and potential evapotranspiration) and initial biogeochemical conditions of subsurface water, soils, and rocks as input, and output times series of reaction rates and solute concentrations in subsurface waters and rivers. This paper presents the model structure and governing equations and demonstrates its utility with examples simulating carbon and nitrogen processes in a headwater catchment. As shown in the examples, BioRT‐HBV can be used to illuminate the dynamics of biogeochemical reactions in the invisible, arduous‐to‐measure subsurface, and their influence on the observed stream or river chemistry and solute export. With its parsimonious structure and easy‐to‐use graphical user interface, BioRT‐HBV can be a useful research tool for users without in‐depth computational training. It can additionally serve as an educational tool that promotes pollination of ideas across disciplines and foster a diverse, equal, and inclusive user community.

Sadayappan, Kayalvizhi↗

Finite Control in Underdamped Distributed Parameter Systems

Specifically, a class of distributed parameter systems is defined using Hilbert space methods based on a partial differential equation model of a structure. In this space a simple, easy to check definition of underdamping is constructed based on the well known single degree of freedom concept of critical damping. It is then shown that if a given distributed parameter system satisfies this definition, each mode of the modal expansion of the solution is in fact an underdamped function of time. It is noted that a distributed parameter system which is underdamped is also uniformly exponentially stable. By appealing to the work of Gibson, a finite dimensional model of the system will yield satisfactory control laws. Furthermore, it is shown that the assumption of the underdamping also allows straightforward computation of rough bounds on the magnitude of the unmodeled or residual modes for a modal truncation scheme. Hence, underdamped systems are precisely that class of distributed parameter systems which are not likely to have spillover problems and which will yield convergence of finite dimensional control laws to control laws which are optimal for the full distributed parameter model of the system.

Inman, D. J.↗

Aerodynamic parameters of High-Angle-of attack Research Vehicle (HARV) estimated from flight data

Aerodynamic parameters of the High-Angle-of-Attack Research Aircraft (HARV) were estimated from flight data at different values of the angle of attack between 10 degrees and 50 degrees. The main part of the data was obtained from small amplitude longitudinal and lateral maneuvers. A small number of large amplitude maneuvers was also used in the estimation. The measured data were first checked for their compatibility. It was found that the accuracy of air data was degraded by unexplained bias errors. Then, the data were analyzed by a stepwise regression method for obtaining a structure of aerodynamic model equations and least squares parameter estimates. Because of high data collinearity in several maneuvers, some of the longitudinal and all lateral maneuvers were reanalyzed by using two biased estimation techniques, the principal components regression and mixed estimation. The estimated parameters in the form of stability and control derivatives, and aerodynamic coefficients were plotted against the angle of attack and compared with the wind tunnel measurements. The influential parameters are, in general, estimated with acceptable accuracy and most of them are in agreement with wind tunnel results. The simulated responses of the aircraft showed good prediction capabilities of the resulting model.

Klein, Vladislav↗

Application of partial differential equation modeling of the control/structural dynamics of flexible spacecraft

Partial differential equations for modeling the structural dynamics and control systems of flexible spacecraft are applied here in order to facilitate systems analysis and optimization of these spacecraft. Example applications are given, including the structural dynamics of SCOLE, the Solar Array Flight Experiment, the Mini-MAST truss, and the LACE satellite. The development of related software is briefly addressed.

Taylor, Lawrence W., Jr.↗

System IDentification Programs for AirCraft (SIDPAC)

A collection of computer programs for aircraft system identification is described and demonstrated. The programs, collectively called System IDentification Programs for AirCraft, or SIDPAC, were developed in MATLAB as m-file functions. SIDPAC has been used successfully at NASA Langley Research Center with data from many different flight test programs and wind tunnel experiments. SIDPAC includes routines for experiment design, data conditioning, data compatibility analysis, model structure determination, equation-error and output-error parameter estimation in both the time and frequency domains, real-time and recursive parameter estimation, low order equivalent system identification, estimated parameter error calculation, linear and nonlinear simulation, plotting, and 3-D visualization. An overview of SIDPAC capabilities is provided, along with a demonstration of the use of SIDPAC with real flight test data from the NASA Glenn Twin Otter aircraft. The SIDPAC software is available without charge to U.S. citizens by request to the author, contingent on the requestor completing a NASA software usage agreement.

Morelli, Eugene A.↗

Optimization-based design of control systems for flexible structures

The purpose of this presentation is to show that it is possible to use nonsmooth optimization algorithms to design both closed-loop finite dimensional compensators and open-loop optimal controls for flexible structures modeled by partial differential equations. An important feature of our approach is that it does not require modal decomposition and hence is immune to instabilities caused by spillover effects. Furthermore, it can be used to design control systems for structures that are modeled by mixed systems of coupled ordinary and partial differential equations.

Polak, E.↗

Transonic aeroelastic analysis of launch vehicle configurations

A numerical study of the aeroelastic stability of typical launch vehicle configurations in transonic flight is performed. Recent computational fluid dynamics techniques are used to simulate the transonic aerodynamic flow fields, as opposed to relying on experimental data for the unsteady aerodynamic pressures. The flow solver is coupled to an appropriate structural representation of the vehicle. The aerodynamic formulation is based on the thin layer approximation to the Reynolds-Averaged Navier-Stokes equations, where the account for turbulent mixing is done by the two-layer Baldwin and Lomax algebraic eddy viscosity model. The structural-dynamic equations are developed considering free-free flexural vibration of an elongated beam with variable properties and are cast in modal form. Aeroelastic analyses are performed by integrating simultaneously in the two sets of equations. By tracing the growth or decay of a perturbed oscillation, the aeroelastic stability of a given constant configuration can be ascertained. The method is described in detail, and results that indicate its application are presented. Applications include some validation cases for the algorithm developed, as well as the study of configurations known to have presented flutter programs in the past.

Filgueirasdeazevedo, Joao Luiz↗

Microscopic constraints for the equation of state and structure of neutron stars: A Bayesian model mixing framework

Bayesian model mixing (BMM) is a statistical technique that can combine constraints from different regions of an input space in a principled way. Here we extend our BMM framework for the equation of state (EOS) of strongly interacting matter from symmetric nuclear matter to asymmetric matter, specifically focusing on zero-temperature, charge-neutral, 𝛽-equilibrated matter. We use Gaussian processes (GPs) to infer constraints on the neutron-star matter EOS at intermediate densities from two different microscopic theories: chiral effective-field theory (𝜒⁢EFT) at baryon densities around nuclear saturation, 𝑛 𝐵 ∼ 𝑛 0 , and perturbative QCD at asymptotically high baryon densities, 𝑛 𝐵 ⩾ 20⁢𝑛 0 . The uncertainties of the 𝜒⁢EFT and pQCD EOSs are obtained using the BUQEYE truncation error model. We demonstrate the flexibility of our framework through the use of two categories of GP kernels: conventional stationary kernels and a nonstationary changepoint kernel. We use the latter to explore potential constraints on the dense matter EOS by including exogenous data representing theory predictions and heavy-ion collision measurements at densities ⩾ 2⁢𝑛 0 . We also use our EOSs to obtain neutron-star mass-radius relations and their uncertainties. Finally, our framework, whose implementation will be available through a GitHub repository, provides a prior distribution for the EOS that can be used in large-scale neutron-star inference frameworks.

Bayesian methods↗

Numerical solution of the vertical structure equation in the normal mode method

In the present model of multilayered stability stratification, aimed at obtaining the analytic eigensolutions of the vertical structure equation, each layer is characterized by its own static stability value. By requiring continuity of pressure and vertical velocity across each interface level, and by imposing suitable upper and lower boundary conditions, matching eigensolutions are obtained in terms of the Bessel functions. Attention is given to an explicit example of a double-layered stratified atmosphere which demonstrates the mathematical manipulations involved; the resultant vertical structure functions are used to check the accuracy of the numerical solutions by the finite difference and finite element methods.

Sasaki, Y. K.↗

The stability of coupled renewal-differential equations with econometric applications

Concepts and results are presented in the fields of mathematical modeling, economics, and stability analysis. A coupled renewal-differential equation structure is presented as a modeling form for systems possessing hereditary characteristics, and this structure is applied to a model of the Austrian theory of business cycles. For realistic conditions, the system is shown to have an infinite number of poles, and conditions are presented which are both necessary and sufficient for all poles to lie strictly in the left half plane.

Rhoten, R. P.↗

An emulator for minimizing finite element analysis implementation resources

A finite element analysis emulator providing a basis for efficiently establishing an optimum computer implementation strategy when many calculations are involved is described. The SCOPE emulator determines computer resources required as a function of the structural model, structural load-deflection equation characteristics, the storage allocation plan, and computer hardware capabilities. Thereby, it provides data for trading analysis implementation options to arrive at a best strategy. The models contained in SCOPE lead to micro-operation computer counts of each finite element operation as well as overall computer resource cost estimates. Application of SCOPE to the Memphis-Arkansas bridge analysis provides measures of the accuracy of resource assessments. Data indicate that predictions are within 17.3 percent for calculation times and within 3.2 percent for peripheral storage resources for the ELAS code.

Melosh, R. J.↗