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At least 37 records · Page 2

Nonlinear Dynamics of a Foil Bearing Supported Rotor System: Simulation and Analysis

Foil bearings provide noncontacting rotor support through a number of thin metal strips attached around the circumference of a stator and separated from the rotor by a fluid film. The resulting support stiffness is dominated by the characteristics of the foils and is a nonlinear function of the rotor deflection. The present study is concerned with characterizing this nonlinear effect and investigating its influence on rotordynamical behavior. A finite element model is developed for an existing bearing, the force versus deflection relation characterized, and the dynamics of a sample rotor system are studied. Some conclusions are discussed with regard to appropriate ranges of operation for such a system.

Li, Feng↗

Evaluation and Analysis of F-16XL Wind Tunnel Data From Static and Dynamic Tests

A series of wind tunnel tests were conducted in the NASA Langley Research Center as part of an ongoing effort to develop and test mathematical models for aircraft rigid-body aerodynamics in nonlinear unsteady flight regimes. Analysis of measurement accuracy, especially for nonlinear dynamic systems that may exhibit complicated behaviors, is an essential component of this ongoing effort. In this report, tools for harmonic analysis of dynamic data and assessing measurement accuracy are presented. A linear aerodynamic model is assumed that is appropriate for conventional forced-oscillation experiments, although more general models can be used with these tools. Application of the tools to experimental data is demonstrated and results indicate the levels of uncertainty in output measurements that can arise from experimental setup, calibration procedures, mechanical limitations, and input errors.

Kim, Sungwan↗

Evaluation and Analysis of F-16XL Wind Tunnel Data from Dynamic Tests

A series of wind tunnel tests were conducted in the NASA Langley Research Center as part of an ongoing effort to develop and test mathematical models for aircraft rigid-body aerodynamics in nonlinear unsteady flight regimes. Analysis of measurement accuracy, especially for nonlinear dynamic systems that may exhibit complicated behaviors, is an essential component of this ongoing effort. In this paper, tools for harmonic analysis of dynamic data and assessing measurement accuracy are presented. A linear aerodynamic model is assumed that is appropriate for conventional forced-oscillation experiments, although more general models can be used with these tools. Application of the tools to experimental data is demonstrated and results indicate the levels of uncertainty in output measurements that can arise from experimental setup, calibration procedures, mechanical limitations, and input errors.

Kim, Sungwan↗

A four-dimensional primitive equation model for coupled coastal-deep ocean studies

A prototype four dimensional continental shelf/deep ocean model is described. In its present form, the model incorporates the effects of finite amplitude topography, advective nonlinearities, and variable stratification and rotation. The model can be forced either directly by imposed atmospheric windstress and surface pressure distributions, and energetic mean currents imposed by the exterior oceanic circulation; or indirectly by initial distributions of shoreward propagation mesoscale waves and eddies. To avoid concerns over the appropriate specification of 'open' boundary conditions on the cross-shelf and seaward model boundaries, a periodic channel geometry (oriented along-coast) is used. The model employs a traditional finite difference expansion in the cross-shelf direction, and a Fourier (periodic) representation in the long-shelf coordinate.

Haidvogel, D. B.↗

Nonlinear force-free magnetic fields: Calculation and applicatin to astrophysics

The problem concerned in this work is that of calculating magnetic field configurations in which the Lorentz force (vector)j x (vector)B is everywhere zero, subject to specified boundary conditions. The magnetic field is represented in terms of Clebsch variables in the form (vector)B = del alpha x del beta. These variables are constant on any field line. The most appropriate choice of boundary conditions is to specify the values of alpha and beta on the bounding surface. It is proposed that the field lines move in the direction of local Lorentz force and relax towards a force-free field configuration. This concept leads to an iteration procedure for modifying the variables alpha and beta that tends asymptotically towards the force-free state. This method is first applied to a simple problem in two rectangular dimensions; the calculation shows that the convergence of magnetic field energy to a minimum state (force-free) is close to exponential. This method is then applied to study some astrophysical force-free magnetic fields, such as the structures and evolution of magnetic fields of rotating sunspots and accretion disks. The implication of the results, as related to the mechanisms of solar flares, extragalactic radio sources and radio jets, are discussed.

Yang, Wei-Hong↗

On the flight dynamics of aeroelastic vehicles

The nonlinear equations of motion for an elasic airplane are developed from first principles. Lagrange's Equation and the Principle of Virtual Work are used to generate the equations of motion and strip theory is then employed to obtain closed form integral expressions for the generalized forces. The inertial coupling is minimized by appropriate choice of the body reference axes and by making use of free vibration modes of the body. In addition, particular attention is paid to the simplifying assumptions used during the development of the equations of motion. A unique aspect of this modeling process is that since the generalized aerodynamic forces are determined from closed form, analytic expressions, this method can be used to gain insight into the effects of parameter variations not easily obtained from numerical models. A numerical example is also presented in which the modeling method is applied to a representative elastic aircraft. The model is used to address the effects of aerodynamic coupling which occurs between the rigid body degrees of freedom and the elastic degrees of freedom. Finally, model simplification is addressed and two methods are evaluated. The resulting frequency responses are compared.

Schmidt, D. K.↗

Design of a Minimum Surface-Effect Tendon-Based Microactuator for Micromanipulation

A piezoelectric (PZT) stack-based actuator was developed to provide a means of actuation with dynamic characteristics appropriate for small-scale manipulation. In particular, the design incorporates a highly nonlinear, large-ratio transmission that provides approximately two orders of magnitude motion amplification from the PZT stack. In addition to motion amplification, the nonlinear transmission was designed via optimization methods to distort the highly non-uniform properties of a piezoelectric actuator so that the achievable actuation force is nearly constant throughout the actuator workspace. The package also includes sensors that independently measure actuator output force and displacement, so that a manipulator structure need not incorporate sensors nor the associated wires. Specifically, the actuator was designed to output a maximum force of at least one Newton through a stroke of at least one millimeter. For purposes of small-scale precision position and/or force control, the actuator/sensor package was designed to eliminate stick-slip friction and backlash. The overall dimensions of the actuator/sensor package are approximately 40 x 65 x 25 mm.

Goldfarb, Michael↗

Numerical Stability and Control Analysis Towards Falling-Leaf Prediction Capabilities of Splitflow for Two Generic High-Performance Aircraft Models

Aerodynamic analysis are performed using the Lockheed-Martin Tactical Aircraft Systems (LMTAS) Splitflow computational fluid dynamics code to investigate the computational prediction capabilities for vortex-dominated flow fields of two different tailless aircraft models at large angles of attack and sideslip. These computations are performed with the goal of providing useful stability and control data to designers of high performance aircraft. Appropriate metrics for accuracy, time, and ease of use are determined in consultations with both the LMTAS Advanced Design and Stability and Control groups. Results are obtained and compared to wind-tunnel data for all six components of forces and moments. Moment data is combined to form a "falling leaf" stability analysis. Finally, a handful of viscous simulations were also performed to further investigate nonlinearities and possible viscous effects in the differences between the accumulated inviscid computational and experimental data.

Charlton, Eric F.↗

Dynamic characteristics of a two-stage variable-mass flexible missile with internal flow

A general formulation of the dynamical problems associated with powered flight of a two stage flexible, variable-mass missile with internal flow, discrete masses, and aerodynamic forces is presented. The formulation comprises six ordinary differential equations for the rigid body motion, 3n ordinary differential equations for the n discrete masses and three partial differential equations with the appropriate boundary conditions for the elastic motion. This set of equations is modified to represent a single stage flexible, variable-mass missile with internal flow and aerodynamic forces. The rigid-body motion consists then of three translations and three rotations, whereas the elastic motion is defined by one longitudinal and two flexural displacements, the latter about two orthogonal transverse axes. The differential equations are nonlinear and, in addition, they possess time-dependent coefficients due to the mass variation.

Meirovitch, L.↗

Influence of transverse-shear and large-deformation effects on the low-speed impact response of laminated composite plates

An analytical procedure is presented for determining the transient response of simply supported, rectangular laminated composite plates subjected to impact loads from airgun-propelled or dropped-weight impactors. A first-order shear-deformation theory is included in the analysis to represent properly any local short-wave-length transient bending response. The impact force is modeled as a locally distributed load with a cosine-cosine distribution. A double Fourier series expansion and the Timoshenko small-increment method are used to determine the contact force, out-of-plane deflections, and in-plane strains and stresses at any plate location due to an impact force at any plate location. The results of experimental and analytical studies are compared for quasi-isotropic laminates. The results indicate that using the appropriate local force distribution for the locally loaded area and including transverse-shear-deformation effects in the laminated plate response analysis are important. The applicability of the present analytical procedure based on small deformation theory is investigated by comparing analytical and experimental results for combinations of quasi-isotropic laminate thicknesses and impact energy levels. The results of this study indicate that large-deformation effects influence the response of both 24- and 32-ply laminated plates, and that a geometrically nonlinear analysis is required for predicting the response accurately.

Ambur, Damodar R.↗

Automatically reconfigurable control for rapid retargeting of flexible pointing systems

A reconfigurable nonlinear control system design methodology is proposed to automatically correct computed slew torque commands of space-based pointing systems for the effects of slew-induced structural deformations. The possibility of forcing an elastic structure, such as that of a space-based instrument frame, to deform in a preselected way in response to rapid slews is demonstrated. To accomplish this, a supervisory controller must select a pair of algorithms, one for structural counterexcitation and the other for slew torque correction. It is shown how the reachability and subsequent tracking of the appropriate 'slow manifold', where the control algorithms are valid, can be ensured by a fast tracking loop, with time-varying gain dependent only on the commanded angular acceleration.

Dwyer, Thomas A. W., III↗

Superconducting axisymmetric finite elements based on a gauged potential variational principle. Part 1: Formulation

The present work is part of a research program for the numerical simulation of electromagnetic (EM) fields within conventional Ginzburg-Landau (GL) superconductors. The final goal of this research is to formulate, develop and validate finite element (FE) models that can accurately capture electromagnetic thermal and material phase changes in a superconductor. The formulations presented here are for a time-independent Ginzburg-Landau superconductor and are derived from a potential-based variational principle. We develop an appropriate variational formulation of time-independent supercontivity for the general three-dimensional case and specialize it to the one-dimensional case. Also developed are expressions for the material-dependent parameters alpha and beta of GL theory and their dependence upon the temperature T. The one-dimensional formulation is then discretized for finite element purposes and the first variation of these equations is obtained. The resultant Euler equations contain nonlinear terms in the primary variables. To solve these equations, an incremental-iterative solution method is used. Expressions for the internal force vector, external force vector, loading vector and tangent stiffness matrix are therefore developed for use with the solution procedure.

Schuler, James J.↗

Hydrodynamic Force on a Cylinder Oscillating at Low Frequency

The hydrodynamic force on a cylinder oscillating transversely to its axis is a nonlinear function of the displacement amplitude x0. We report measurements and numerical calculations of the force at frequencies low enough that delta > R, where delta is the viscous penetration length and R is the cylinder radius. For small amplitudes, the numerically calculated Fourier transform of the force per unit length, F(sub small), agrees with Stokes' analytical calculation. For larger amplitudes, the force per unit length found by both calculation and measurement is F = F(sub small)C (x(sub 0)/delta,R/delta). The complex function C depends only weakly on R/delta, indicating that x0/delta is more appropriate as a scaling variable than the Keulegan-Carpenter number KC = pi*x(sub 0)/R. The measurements used a torsion oscillator driven at frequencies from 1 to 12 Hz while immersed in dense xenon. The oscillator comprised cylinders with an effective radius of R = 13.4 micron and oscillation amplitudes as large as x(sub 0)/delta = 4 (corresponding to KC as large as 71). The calculations used similar conditions except that the amplitudes were as large as x0/delta = 28.

Berg, Robert F.↗

Validation of Methodology for Estimating Aircraft Unsteady Aerodynamic Parameters from Dynamic Wind Tunnel Tests

A basic problem in flight dynamics is the mathematical formulation of the aerodynamic model for aircraft. This study is part of an ongoing effort at NASA Langley to develop a more general formulation of the aerodynamic model for aircraft that includes nonlinear unsteady aerodynamics and to develop appropriate test techniques that facilitate identification of these models. A methodology for modeling and testing using wide-band inputs to estimate the unsteady form of the aircraft aerodynamic model was developed previously but advanced test facilities were not available at that time to allow complete validation of the methodology. The new model formulation retained the conventional static and rotary dynamic terms but replaced conventional acceleration terms with more general indicial functions. In this study advanced testing techniques were utilized to validate the new methodology for modeling. Results of static, conventional forced oscillation, wide-band forced oscillation, oscillatory coning, and ramp tests are presented.

Murphy, Patrick C.↗

A mathematical simulation model of the CH-47B helicopter, volume 2

A nonlinear simulation model of the CH-47B helicopter, was adapted for use in a simulation facility. The model represents the specific configuration of the variable stability CH-47B helicopter. Modeling of the helicopter uses a total force approach in six rigid body degrees of freedom. Rotor dynamics are simulated using the Wheatley-Bailey equations, steady state flapping dynamics and included in the model of the option for simulation of external suspension, slung load equations of motion. Validation of the model was accomplished by static and dynamic data from the original Boeing Vertol mathematical model and flight test data. The model is appropriate for use in real time piloted simulation and is implemented on the ARC Sigma IX computer where it may be operated with a digital cycle time of 0.03 sec.

Weber, J. M.↗

Characterizing Droplet Formation from Non-Linear Slosh in a Propellant Tank

The Fluid Dynamics Branch (ER42) at the Marshall Space Flight Center (MSFC) was tasked with characterizing the formation and evolution of liquid droplets resulting from nonlinear propellant slosh in a storage tank. Lateral excitation of propellant tanks can produce high amplitude nonlinear slosh waves through large amplitude excitations and or excitation frequencies near a resonance frequency of the tank. The high amplitude slosh waves become breaking waves upon attaining a certain amplitude or encountering a contracting geometry such as the upper dome section of a spherical tank. Inherent perturbations in the thinning regions of breaking waves result in alternating regions of high and low pressure within the fluid. Droplets form once the force from the local pressure differential becomes larger than the force maintaining the fluid interface shape due to surface tension. Droplets released from breaking waves in a pressurized tank may lead to ullage collapse given the appropriate conditions due to the increased liquid surface area and thus heat transfer between the fluids. The goal of this project is to create an engineering model that describes droplet formation as a function of propellant slosh for use in the evaluation of ullage collapse during a sloshing event. The Volume of Fluid (VOF) model in the production level Computational Fluid Dynamics (CFD) code Loci-Stream was used to predict droplet formation from breaking waves with realistic surface tension characteristics. Various excitation frequencies and amplitudes were investigated at multiple fill levels for a single storage tank to create the engineering model of droplet formation from lateral propellant slosh.

Brodnick, Jacob↗

Gravity waves in Titan's atmosphere

Scintillations (high frequency variations) observed in the radio signal during the occultation of Voyager 1 by Titan (Hinson and Tyler, 1983) provide information concerning neutral atmospheric density fluctuations on scales on hundreds of meters to a few kilometers. Those seen at altitudes higher than 25 km above the surface were interpreted by Hinson and Tyler as being caused by linear, freely propagating (energy-conserving) gravity waves, but this interpretation was found to be inconsistent with the scintillation data below the 25-km altitude level. Here an attempt is made to interpret the entire scintillation profile between the surface and the 90-km altitude level in terms of gravity waves generated at the surface. Numerical calculations of the density fluctuations caused by two-dimensional, nonhydrostatic, finite-amplitude gravity waves propagating vertically through Titan's atmosphere are performed to produce synthetic scintillation profiles for comparison with the observations. The numerical model accurately treats the effects of wave transience, nonlinearity, and breakdown due to convective instability in the overturned part of the wave. The high-altitude scintillation data were accurately recovered with a freely propagating wave solution, confirming the analytic model of Hinson and Tyler. It is found that the low-altitude scintillation data can be fit by a model where a component of the gravity waves becomes convectively unstable and breaks near the 15 km level. The large-scale structure of the observed scintillation profile in the entire altitude range between 5 and 85 km can be simulated by a model where the freely propagating and breaking waves are forced at the surface simultaneously. Further analysis of the Voyager 1 Titan low-altitude scintillation data, using inversion theory appropriate for strong scattering, could potentially remove some of the ambiguities remaining in this analysis and allow a better determination of the strength and source of the waves.

Friedson, A. James↗

Multibody for Everybody (M4E) - A Linearization Approach to Enable Frequency Domain Analysis, Time Integration and Control Co-Design

1.1 Background/Objectives: Marine energy represents a promising yet underexploited source of power. To increase the harvested power, significant efforts have been made to improve wave energy converter (WEC) modeling capabilities and optimize power take-off (PTO) performance; however, these efforts have often treated WEC dynamics, PTO design, and controller development sequentially. In contrast, control co-design (CCD) is emerging as a promising strategy to address these issues directly, creating a growing need for fast analysis tools suitable for repeated simulation and parametric studies [1]. To support this need, this work presents the Multibody for Everybody (M4E) [2] linearization module, which employs a symbolic toolbox to provide deeper insight of WEC design parameters. The objective is to demonstrate that a minimal-coordinate linearization of articulated WEC dynamics can provide accurate wave response predictions and substantial computational savings relative to nonlinear time-domain simulation, while preserving compatibility with broader wave-energy analysis workflows, enabling CCD. 1.2 Approach/Activities: The proposed approach linearizes the equations of motion, generated by M4E, in minimal coordinates about a selected operating point and combines the resulting system with frequencydomain hydrodynamic terms to incorporate the reduced mass, damping, stiffness, and forcing operators. The linearized model is used for both impedance-based response amplitude operator (RAO) prediction and rapid regular-wave time integration. The methodology is demonstrated on a single-flap device and a FOSWEC configuration, with linearized M4E responses compared against the corresponding nonlinear M4E simulations and WEC-Sim results. Regular-wave time histories, RAO trends, and runtime differences are assessed. The framework is also compatible with broader wave-energy workflows, including coupling to WecOptTool, although that capability is not the focus of this work [3]. 1.3 Results/Lessons: The linearized M4E model reproduces key regularwave response characteristics such as integration and Response Amplitude over multiple frequencies. This module matches nonlinear M4E and WEC-Sim results while substantially reducing integration cost. Thus, the proposed framework can serve as a rapid analysis layer for articulated WEC design, parameter studies, and controls-oriented workflows. The analysis is most appropriate in the near-equilibrium regime, about the linearization point.

16 TIDAL AND WAVE POWER↗