Search NASA⌕ Search

SEARCH · Search NASA

Results for “Nonlinear Analysis”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,675 records · Page 93

Time-resolved biphase signatures of quadratic nonlinearity observed in coupled Alfvén eigenmodes on the DIII-D tokamak

We report the detection of nonstationary quadratic coupling between toroidicity-induced Alfvén eigenmodes (TAEs) on sub-millisecond time scales. Identification of phase coherency between multiple TAEs and nonlinearly generated modes is facilitated by wavelet-based bicoherence analysis of time-series from inductive coils, taken from a DIII-D discharge heated by neutral beam injection (NBI). Characterization of nonlinear three-wave interaction is inferred by stationary local bispectrum phase (biphase) and confirmed via bandpass filtering. Biphase dynamics associated with prominent bispectral features are well-resolved in time and consistent with transient quadratic coupling. Onset and duration of nonlinearity are correlated with enhanced amplitude of participating TAEs; coincident changes in amplitude are observed for modes at difference frequency |f TAE,1 - f TAE,2 |.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Panel Flutter and Sonic Fatigue Analysis for RLV

A methodology is presented for the flutter analysis of the seal of thermal protection system (TPS) panel of X-33 Advanced Technology Demonstrator test vehicle. The seal is simulated as a two-dimensional cantilevered panel with an elastic stopper, which is modeled as an equivalent spring. This cantilever beam-spring model under the aerodynamic pressure at supersonic speeds turns out to be an impact nonlinear dynamic system. The flutter analysis of the seal is thus carried out using, time domain numerical simulation with a displacement stability criterion. The flutter boundary of the seal is further verified with a family of three traditional and one nontraditional panel flutter models. The frequency domain method that applies eigenanalysis on the traditional panel flutter problem was used. The results showed that the critical dynamic pressure could be more than doubled with properly chosen material for the base stopper. The proposed methodology can be easily extended to three-dimensional panel seals with flow angularity.

Mei, Chuh↗

Fatigue Life Methodology for Tapered Hybrid Composite Flexbeams

Nonlinear-tapered flexbeam specimens from a full-size composite helicopter rotor hub flexbeam were tested under combined constant axial tension and cyclic bending loads. Two different graphite/glass hybrid configurations tested under cyclic loading failed by delamination in the tapered region. A 2-D finite element model was developed which closely approximated the flexbeam geometry, boundary conditions, and loading. The analysis results from two geometrically nonlinear finite element codes, ANSYS and ABAQUS, are presented and compared. Strain energy release rates (G) associated with simulated delamination growth in the flexbeams are presented from both codes. These results compare well with each other and suggest that the initial delamination growth from the tip of the ply-drop toward the thick region of the flexbeam is strongly mode II. The peak calculated G values were used with material characterization data to calculate fatigue life curves for comparison with test data. A curve relating maximum surface strain to number of loading cycles at delamination onset compared well with the test results.

urri, Gretchen B.↗

Error analysis for reducing noisy wide-gap concentric cylinder rheometric data for nonlinear fluids - Theory and applications

This work discusses the propagation of errors for the recovery of the shear rate from wide-gap concentric cylinder viscometric measurements of non-Newtonian fluids. A least-square regression of stress on angular velocity data to a system of arbitrary functions is used to propagate the errors for the series solution to the viscometric flow developed by Krieger and Elrod (1953) and Pawlowski (1953) ('power-law' approximation) and for the first term of the series developed by Krieger (1968). A numerical experiment shows that, for measurements affected by significant errors, the first term of the Krieger-Elrod-Pawlowski series ('infinite radius' approximation) and the power-law approximation may recover the shear rate with equal accuracy as the full Krieger-Elrod-Pawlowski solution. An experiment on a clay slurry indicates that the clay has a larger yield stress at rest than during shearing, and that, for the range of shear rates investigated, a four-parameter constitutive equation approximates reasonably well its rheology. The error analysis presented is useful for studying the rheology of fluids such as particle suspensions, slurries, foams, and magma.

Borgia, Andrea↗

Subharmonic Shapiro steps in depinning dynamics of a two-dimensional solid dusty plasma modulated by one-dimensional nonlinear deformed periodic substrates

Langevin dynamical simulations are performed to investigate the depinning dynamics of a two-dimensional (2D) solid dusty plasma, which is modulated by one-dimensional (1D) nonlinear deformed periodic substrates, and also driven by the combination of the DC and AC forces. As the DC driving force increases gradually, pronounced subharmonic and harmonic Shapiro steps are discovered under the combined modulation of the deformed substrate and the external AC drive. Here, these observed subharmonic and harmonic Shapiro steps are attributed to the dynamic mode locking. The data analysis results indicate that the nonlinear deformed substrate strongly influences these subharmonic Shapiro steps, which can be accurately diagnosed using the fraction of sixfold coordinated particles. Furthermore, the diagnostic of the kinetic temperature clearly indicates the difference between harmonic and subharmonic Shapiro steps, i.e., the particle motion is slightly less synchronized at subharmonic Shapiro steps, caused by the unstable locations of the deformed substrate.

36 MATERIALS SCIENCE↗

Scaling Behavior of Thermally Driven Fractures in Deep Low‐Permeability Formations: A Plane Strain Model With 1‐D Heat Conduction

Abstract Injection of cold fluids through/into deep formations may cause significant cooling, thermal stress, and possible thermal fracturing. In this study, the thermal fracturing of low‐permeability formations under one‐dimensional heat conduction was investigated using a plane strain model. Dimensionless governing equations, with dimensionless fracture length , aperture , spacing , time , and effective confining stress , were derived. Solution of single thermal fracture was derived analytically, while solution of multiple fractures with constant (or dynamic) spacing were obtained using the displacement discontinuity method (and stability analysis). For single fracture, increases nonlinearly with and then transitions to scaling law , indicating that late‐time fracture length increases linearly with the square root of cooling time. For constantly spaced fractures, deviates from the single‐fracture solution at a later for a larger , showing slower propagation under inter‐fracture stress interaction . For dynamically spaced fractures, fracture arrest induced by stress interaction was determined by the stability analysis; the fully transient solution provides evolution of dimensionless fracture length, spacing, aperture, and pattern; a similar scaling law, with , obtained shows the effect of both stress interaction and fracture arrest. The solution and scaling law provide fast predictions for all reservoir and cooling conditions using (single) model parameter . Application to a geothermal site with demonstrates that thermal fractures reach 0.67, 6.25, and 78.00 m in length, 0.49, 2.30, and 13.00 m in spacing, and 0.43, 2.09, and 12.19 mm in aperture at 1, 100, and 10,000 days.

Chen, Bin↗

Prediction of jump phenomena in rotationally-coupled maneuvers of aircraft, including nonlinear aerodynamic effects

An analytical method has been developed for predicting critical control inputs for which nonlinear rotational coupling may cause sudden jumps in aircraft response. The analysis includes the effect of aerodynamics which are nonlinear in angle of attack. The method involves the simultaneous solution of two polynomials in roll rate, whose coefficients are functions of angle of attack and the control inputs. Results obtained using this procedure are compared with calculated time histories to verify the validity of the method for predicting jump-like instabilities.

Young, J. W.↗

Evaluation of a Progressive Failure Analysis Methodology for Laminated Composite Structures

A progressive failure analysis methodology has been developed for predicting the nonlinear response and failure of laminated composite structures. The progressive failure analysis uses C plate and shell elements based on classical lamination theory to calculate the in-plane stresses. Several failure criteria, including the maximum strain criterion, Hashin's criterion, and Christensen's criterion, are used to predict the failure mechanisms. The progressive failure analysis model is implemented into a general purpose finite element code and can predict the damage and response of laminated composite structures from initial loading to final failure.

Sleight, David W.↗

Magnetotail dynamics under isobaric constraints

Using linear theory and nonlinear MHD simulations, we investigate the resistive and ideal MHD stability of two-dimensional plasma configurations under the isobaric constraint dP/dt = 0, which in ideal MHD is equivalent to conserving the pressure function P = P(A), where A denotes the magnetic flux. This constraint is satisfied for incompressible modes, such as Alfven waves, and for systems undergoing energy losses. The linear stability analysis leads to a Schroedinger equation, which can be investigated by standard quantum mechanics procedures. We present an application to a typical stretched magnetotail configuration. For a one-dimensional sheet equilibrium characteristic properties of tearing instability are rediscovered. However, the maximum growth rate scales with the 1/7 power of the resistivity, which implies much faster growth than for the standard tearing mode (assuming that the resistivity is small). The same basic eigen-mode is found also for weakly two-dimensional equilibria, even in the ideal MHD limit. In this case the growth rate scales with the 1/4 power of the normal magnetic field. The results of the linear stability analysis are confirmed qualitatively by nonlinear dynamic MHD simulations. These results suggest the interesting possibility that substorm onset, or the thinning in the late growth phase, is caused by the release of a thermodynamic constraint without the (immediate) necessity of releasing the ideal MHD constraint. In the nonlinear regime the resistive and ideal developments differ in that the ideal mode does not lead to neutral line formation without the further release of the ideal MHD constraint; instead a thin current sheet forms. The isobaric constraint is critically discussed. Under perhaps more realistic adiabatic conditions the ideal mode appears to be stable but could be driven by external perturbations and thus generate the thin current sheet in the late growth phase, before a nonideal instability sets in.

Birn, Joachim↗

Effects of T-tabs and large deflections in double cantilever beam specimen tests

A simple strength of materials analysis was developed for a double-cantilever beam (DCB) specimen to account for geometric nonlinearity effects due to large deflections and T-tabs. A new DCB data analysis procedure was developed to include the effects of these nonlinearities. The results of the analysis were evaluated by DCB tests performed for materials having a wide range of toughnesses. The materials used in the present study were T300/5208, IM7/8551-7, and AS4/PEEK. Based on the present analysis, for a typical deflection/crack length ratio of 0.3 (for AS4/PEEK), T-tabs and large deflections cause a 15 and 3 percent error, respectively, in the computer Mode I strain energy release rate. Design guidelines for DCB specimen thickness and T-tab height were also developed in order to keep errors due to these nonlinearities within 2 percent. Based on the test results, for both hinged and tabbed specimens, the effects of large deflection on the Mode I fracture toughness (G sub Ic) were almost negligible (less than 1 percent) in the case of T300/5208 and IM7/8551-7; however, AS4/PEEK showed a 2 to 3 percent effect. The effects of T-tabs G sub Ic were more significant for all the materials with T300/5208 showing a 5 percent error, IM7/8551-7 a 15 percent error, and, AS4/PEEK a 20 percent error.

Naik, Rajiv A.↗

Effects of T-tabs and large deflections in DCB specimen tests

A simple strength of materials analysis was developed for a double-cantilever beam (DCB) specimen to account for geometric nonlinearity effects due to large deflections and T-tabs. A new DCB data analysis procedure was developed to include the effects of these nonlinearities. The results of the analysis were evaluated by DCB tests performed for materials having a wide range of toughnesses. The materials used in the present study were T300/5208, IM7/8551-7, and AS4/PEEK. Based on the present analysis, for a typical deflection/crack length ratio of 0.3 (for AS4/PEEK), T-tabs and large deflections cause a 15 percent and 3 percent error, respectively, in the computer Mode 1 strain energy release rate. Design guidelines for DCB specimen thickness and T-tab height were also developed in order to keep errors due to these nonlinearities within 2 percent. Based on the test results, for both hinged and tabbed specimens, the effects of large deflection on the Mode 1 fracture toughness (G sub Ic) were almost negligible (less than 1 percent) in the case of T300/5208 and IM7/8551-7; however, AS4/PEEK showed a 2 to 3 percent effect. The effects of T-tabs G sub Ic were more significant for all the materials with T300/5208 showing a 5 percent error, IM7/8551-7 a 15 percent error, and, AS4/PEEK a 20 percent error.

Naik, R. A.↗

Fast response of electron-scale turbulence to auxiliary heating cessation in National Spherical Torus Experiment

In this letter, we report the first observation of the fast response of electron-scale turbulence to auxiliary heating cessation in National Spherical Torus eXperiment [Ono et al., Nucl. Fusion 40, 557 (2000)]. The observation was made in a set of RF-heated L-mode plasmas with toroidal magnetic field of 0.55 T and plasma current of 300 kA. It is observed that electron-scale turbulence spectral power (measured with a high-k collective microwave scattering system) decreases significantly following fast cessation of RF heating that occurs in less than 200 μs. The large drop in the turbulence spectral power has a short time delay of about 1–2 ms relative to the RF cessation and happens on a time scale of 0.5–1 ms, much smaller than the energy confinement time of about 10 ms. Power balance analysis shows a factor of about 2 decrease in electron thermal diffusivity after the sudden drop of turbulence spectral power. Measured small changes in equilibrium profiles across the RF cessation are unlikely able to explain this sudden reduction in the measured turbulence and decrease in electron thermal transport, supported by local linear stability analysis and both local and global nonlinear gyrokinetic simulations. The observations imply that nonlocal flux-driven mechanism may be important for the observed turbulence and electron thermal transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Dynamic analysis of satellites with deployable hinged appendages

The nonlinear equations of motion determining the planar dynamical behavior of an orbiting satellite deploying both one and two rigid appendages have been formulated using Lagrange's equations. The analysis accounts for large angle rotations, Coriolis effects, and the gravitational gradient, and the resulting coupled governing equations are integrated numerically. The analysis is applied to the Space Shuttle based deployment of rigid truss-like members, and results show that spacecraft inertia parameters, appendage mass and length, deployment velocity, and initial conditions all influence the system response. It is found that the resulting librational movement is related to the size of the deployment payload, and that gravitational forces lead to vehicle stabilization.

Oakes, Kevin F.↗

Weakly relativistic and ponderomotive effects on self-focusing and self-compression of laser pulses in near critical plasmas

The spatiotemporal dynamics of high power laser pulses in near critical plasmas are studied taking in to account the effects of relativistic and ponderomotive nonlinearities. First, within one-dimensional analysis, the effects of initial parameters such as laser intensity, plasma density, and plasma electron temperature on the self-compression mechanism are discussed. The results illustrate that the ponderomotive nonlinearity obstructs the relativistic self-compression above a certain intensity value. Moreover, the results indicate the existence of the turning point temperature in which the compression process has its strongest strength. Next, the three-dimensional analysis of laser pulse propagation is investigated by coupling the self-focusing equation with the self-compression one. It is shown that in contrast to the case in which the only relativistic nonlinearity is considered, in the presence of ponderomotive nonlinearity, the self-compression mechanism obstructs the self-focusing and leads to an increase of the laser spot size.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Contemporary Impact Analysis Methodology for Planetary Sample Return Missions

Development of an Earth entry vehicle and the methodology created to evaluate the vehicle's impact landing response when returning to Earth is reported. NASA's future Mars Sample Return Mission requires a robust vehicle to return Martian samples back to Earth for analysis. The Earth entry vehicle is a proposed solution to this Mars mission requirement. During Earth reentry, the vehicle slows within the atmosphere and then impacts the ground at its terminal velocity. To protect the Martian samples, a spherical energy absorber called an impact sphere is under development. The impact sphere is composed of hybrid composite and crushable foam elements that endure large plastic deformations during impact and cause a highly nonlinear vehicle response. The developed analysis methodology captures a range of complex structural interactions and much of the failure physics that occurs during impact. Numerical models were created and benchmarked against experimental tests conducted at NASA Langley Research Center. The postimpact structural damage assessment showed close correlation between simulation predictions and experimental results. Acceleration, velocity, displacement, damage modes, and failure mechanisms were all effectively captured. These investigations demonstrate that the Earth entry vehicle has great potential in facilitating future sample return missions.

Perino, Scott V.↗

Parametric decay of an extraordinary electromagnetic wave in relativistic plasma

Parametric instability of an extraordinary electromagnetic wave in plasma preheated to a relativistic temperature is considered. A set of self-similar nonlinear differential equations taking into account the electron “thermal” mass is derived and investigated. Small perturbations of the parameters of the heated plasma are analyzed in the linear approximation by using the dispersion relation determining the phase velocities of the fast and slow extraordinary waves. In contrast to cold plasma, the evanescence zone in the frequency range above the electron upper hybrid frequency vanishes and the asymptotes of both branches converge. Theoretical analysis of the set of nonlinear equations shows that the growth rate of decay instability increases with increasing initial temperature of plasma electrons. This result is qualitatively confirmed by numerical simulations of plasma heating by a laser pulse injected from vacuum.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A CFD/CSD Interaction Methodology for Aircraft Wings

With advanced subsonic transports and military aircraft operating in the transonic regime, it is becoming important to determine the effects of the coupling between aerodynamic loads and elastic forces. Since aeroelastic effects can contribute significantly to the design of these aircraft, there is a strong need in the aerospace industry to predict these aero-structure interactions computationally. To perform static aeroelastic analysis in the transonic regime, high fidelity computational fluid dynamics (CFD) analysis tools must be used in conjunction with high fidelity computational structural fluid dynamics (CSD) analysis tools due to the nonlinear behavior of the aerodynamics in the transonic regime. There is also a need to be able to use a wide variety of CFD and CSD tools to predict these aeroelastic effects in the transonic regime. Because source codes are not always available, it is necessary to couple the CFD and CSD codes without alteration of the source codes. In this study, an aeroelastic coupling procedure is developed which will perform static aeroelastic analysis using any CFD and CSD code with little code integration. The aeroelastic coupling procedure is demonstrated on an F/A-18 Stabilator using NASTD (an in-house McDonnell Douglas CFD code) and NASTRAN. In addition, the Aeroelastic Research Wing (ARW-2) is used for demonstration of the aeroelastic coupling procedure by using ENSAERO (NASA Ames Research Center CFD code) and a finite element wing-box code (developed as part of this research).

Bhardwaj, Manoj K.↗

Edge turbulence and divertor heat flux width simulations of Alcator C-Mod discharges using an electromagnetic two-fluid model

The BOUT++ code has been utilized in order to improve the understanding of the role of turbulent modes in controlling edge transport and resulting scaling of the scrape-off layer (SOL) heat flux width. For the C-Mod enhanced D α (EDA) H-mode discharges, BOUT++ six-field two-fluid nonlinear simulations show a reasonable agree- ment of upstream turbulence and divertor target heat flux behavior: a) The simulated quasi-coherent modes (QCMs) show consistent characteristics of the frequency versus poloidal wave number spectra of the electromagnetic fluctuations when compared with experimental measurements: frequencies are around 60-120 kHz (experiment: about 70-110 kHz), k θ are around 2.0 cm ₋1 which is similar to the Phase Contrast Imaging data; b) Linear spectrum analysis is consistent with the nonlinear phase relationship cal- culation which indicates the dominance of resistive-ballooning modes and drift-Alfven wave instabilities; c) The SOL heat flux width λ q vs current I p scaling is reproduced by turbulent transport: the simulations yield similar λ q to experimental measurements within a factor of 2. Yet the magnitudes of divertor heat fluxes can be varied, depending on the physics models, sources and sinks, sheath boundary conditions, or flux limiting coefficient; d) Simple estimate by the "2-point model" for λ q is consistent with simulation. Moreover, blobby turbulent spreading is confirmed for these relatively high B p shots.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗