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Orion MPCV Nonlinear Dynamic Correlation and Model Updating using Quasi-Static Modal Analysis
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Computation of Nonlinear One-Turn Maps from Measurement with Model-Independent Analysis
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Parameter Estimation of Actuators for Benchmark Active Control Technology (BACT) Wind Tunnel Model with Analysis of Wear and Aerodynamic Loading Effects
This report describes the development of transfer function models for the trailing-edge and upper and lower spoiler actuators of the Benchmark Active Control Technology (BACT) wind tunnel model for application to control system analysis and design. A simple nonlinear least-squares parameter estimation approach is applied to determine transfer function parameters from frequency response data. Unconstrained quasi-Newton minimization of weighted frequency response error was employed to estimate the transfer function parameters. An analysis of the behavior of the actuators over time to assess the effects of wear and aerodynamic load by using the transfer function models is also presented. The frequency responses indicate consistent actuator behavior throughout the wind tunnel test and only slight degradation in effectiveness due to aerodynamic hinge loading. The resulting actuator models have been used in design, analysis, and simulation of controllers for the BACT to successfully suppress flutter over a wide range of conditions.
Stability and time-domain analysis of the dispersive tristability in microresonators under modal coupling
Coupled nonlinear resonators have potential applications for the integration of multistable photonic devices. The dynamic properties of two coupled-mode nonlinear microcavities made of Kerr material are studied by linear stability analysis. Using a suitable combination of the modal coupling rate and the frequency detuning, it is possible to obtain configurations where a hysteresis loop is included inside other bistable cycles. We show that a single resonator with two modes both linearly and nonlinearly coupled via the cross-Kerr effect can have a multistable behavior. This could be implemented in semiconductor nonlinear whispering-gallery-mode microresonators under modal coupling for all optical signal processing or ternary optical logic applications.
Observability Analysis of a Power System Stochastic Dynamic Model Using a Derivative-Free Approach
Serving as a prerequisite to power system dynamic state estimation, the observability analysis of a power system dynamic model has recently attracted the attention of many power engineers. However, because this model is typically nonlinear and large-scale, the analysis of its observability is a challenge to the traditional derivative-based methods. Indeed, the linear-approximation-based approach may provide unreliable results while the nonlinear-technique-based approach inevitably faces extremely complicated derivations. Furthermore, because power systems are intrinsically stochastic, the traditional deterministic approaches may lead to inaccurate observability analyses. In this work, facing these challenges, we propose a novel polynomial-chaos-based derivative-free observability analysis approach that not only is free of any linear approximations, but also accounts for the stochasticity of the dynamic model while bringing a low implementation complexity. Furthermore, this approach enables us to quantify the degree of observability of a stochastic model, what conventional deterministic methods cannot do. The excellent performance of the proposed method has been demonstrated by performing extensive simulations using a synchronous generator model with IEEE-DC1A exciter and the TGOV1 turbine governor.
A non-modal analytical method to predict turbulent properties applied to the Hasegawa-Wakatani model
Linear eigenmode analysis often fails to describe turbulence in model systems that have non-normal linear operators and thus nonorthogonal eigenmodes, which can cause fluctuations to transiently grow faster than expected from eigenmode analysis. When combined with energetically conservative nonlinear mode mixing, transient growth can lead to sustained turbulence even in the absence of eigenmode instability. Since linear operators ultimately provide the turbulent fluctuations with energy, it is useful to define a growth rate that takes into account non-modal effects, allowing for prediction of energy injection, transport levels, and possibly even turbulent onset in the subcritical regime. We define such a non-modal growth rate using a relatively simple model of the statistical effect that the nonlinearities have on cross-phases and amplitude ratios of the system state variables. In particular, we model the nonlinearities as delta-function-like, periodic forces that randomize the state variables once every eddy turnover time. Furthermore, we estimate the eddy turnover time to be the inverse of the least stable eigenmode frequency or growth rate, which allows for prediction without nonlinear numerical simulation. We test this procedure on the 2D and 3D Hasegawa-Wakatani model [A. Hasegawa and M. Wakatani, Phys. Rev. Lett. 50, 682 (1983)] and find that the non-modal growth rate is a good predictor of energy injection rates, especially in the strongly non-normal, fully developed turbulence regime.
Generation of residual energy in the turbulent solar wind
In situ observations of the fluctuating solar wind flow show that the energy of magnetic field fluctuations always exceeds that of the kinetic energy, and therefore the difference between the kinetic and magnetic energies, known as the residual energy, is always negative. The same behaviour is found in numerical simulations of magnetohydrodynamic turbulence. We study the dynamics of the residual energy for strong, anisotropic, critically balanced magnetohydrodynamic turbulence using the eddy damped quasi-normal Markovian approximation. Our analysis shows that for stationary critically balanced magnetohydrodynamic turbulence, negative residual energy will always be generated by nonlinear interacting Alfven waves. This offers a general explanation for the observation of negative residual energy in solar wind turbulence and in the numerical simulations.
Rapid solution of large-scale systems of equations
The analysis and design of complex aerospace structures requires the rapid solution of large systems of linear and nonlinear equations, eigenvalue extraction for buckling, vibration and flutter modes, structural optimization and design sensitivity calculation. Computers with multiple processors and vector capabilities can offer substantial computational advantages over traditional scalar computer for these analyses. These computers fall into two categories: shared memory computers and distributed memory computers. This presentation covers general-purpose, highly efficient algorithms for generation/assembly or element matrices, solution of systems of linear and nonlinear equations, eigenvalue and design sensitivity analysis and optimization. All algorithms are coded in FORTRAN for shared memory computers and many are adapted to distributed memory computers. The capability and numerical performance of these algorithms will be addressed.
Variations on the Davenport Gyroscope Calibration Algorithm
This paper presents a number of variations on the Davenport algorithm for in-flight gyroscope recalibration, or first order initial calibration, specifically tailored for use with a minimum of satellite telemetry data. Central to one of the techniques described is the use of onboard integration of gyroscope data together with a detailed model of scheduled satellite slew profiles. Methods are presented for determining adjustments to either parameters for the standard linear model (i.e., a drift rate bias vector and/or a scale factor/alignment transformation matrix) or individual gyroscope scale parameters, both linear and nonlinear, in cases where the alignments are well known. The results of applying the methods in an analysis of the temporal evolution and nonlinear response of the gyroscopes installed on the Hubble Space Telescope following its first servicing mission are discussed. The two effects, when working coherently, have been found to result in slew errors of almost 1 arcsecond per degree. Procedures for selecting optimal operational gyroscope parameters subject to the constraint of using a linear model are discussed.
Vibrational spectroscopic and non-linear optical activity studies on nicotinanilide : A DFT approach
The molecular structure of nicotinanilide was optimized by the DFT/B3LYP method with cc-pVTZ basis set using Gaussian 09 program. The first order hyperpolarizability of the molecule was calculated, which exhibits the higher nonlinear optical activity. The natural bond orbital analysis confirms the presence of intramolecular charge transfer and the hydrogen bonding interaction, which leads to the higher nonlinear optical activity of the molecule. The Frontier molecular orbitals analysis of the molecule shows that the delocalization of electron density occurs within the molecule. The lower energy gap indicates that the hydrogen bond formation between the charged species. The vibrational frequencies were calculated and assigned on the basis of potential energy distribution calculation using the VEDA 4.0 program and the corresponding vibrational spectra were simulated. Hence, the nicotinanilide molecule can be a good candidate for second-order NLO material.
Finite Element Analysis of Wrinkled Membrane Structures for Sunshield Applications
The deployable sunshield is an example of a gossamer structure envisioned for use on future space telescopes. The basic structure consists of multiple layers of pretensioned, thin-film membranes supported by deployable booms. The prediction and verification of sunshield dynamics has been identified as an area in need of technology development due to the difficulties inherent in predicting nonlinear structural behavior of the membranes and because of the challenges involved. in ground testing of the full-scale structure. This paper describes a finite element analysis of a subscale sunshield that has been subjected to ground testing in support of the Next Generation Space Telescope (NGST) program. The analysis utilizes a nonlinear material model that accounts for wrinkling of the membranes. Results are presented from a nonlinear static preloading analysis and subsequent dynamics analyses to illustrate baseline sunshield structural characteristics. Studies are then described which provide further insight into the effect of membrane. preload on sunshield dynamics and the performance of different membrane modeling techniques. Lastly, a comparison of analytical predictions and ground test results is presented.
Response of nonlinear panels to random loads
Lightweight aircraft structures exposed to a high intensity noise environment can fatigue prematurely if adequate consideration is not given to the problem. Design methods and design criteria for sonic fatigue prevention were developed based on analytical and experimental techniques. Most of the analytical work was based upon small deflection or linear structural theory which did not agree with the experimental results. A large deflection geometrical nonlinearity was incorporated into the analysis methods for determining the structural response to high intensity noise. The Karman-Herrmann large deflection equations with a single mode Galerkin approximation, and the method of equivalent linearization were used to predict mean square amplitude, mean square stresses, and nonlinear frequency at various acoustic loadings for rectangular panels. Both simply supported and clamped support conditions with immovable or movable inplane edges are considered. Comparisons with experimental results are presented.
Upper Atmosphere Research Satellite (UARS) onboard attitude determination using a Kalman filter
The Upper Atmospheric Research Satellite (UARS) requires a highly accurate knowledge of its attitude to accomplish its mission. Propagation of the attitude state using gyro measurements is not sufficient to meet the accuracy requirements, and must be supplemented by a observer/compensation process to correct for dynamics and observation anomalies. The process of amending the attitude state utilizes a well known method, the discrete Kalman Filter. This study is a sensitivity analysis of the discrete Kalman Filter as implemented in the UARS Onboard Computer (OBC). The stability of the Kalman Filter used in the normal on-orbit control mode within the OBC, is investigated for the effects of corrupted observations and nonlinear errors. Also, a statistical analysis on the residuals of the Kalman Filter is performed. These analysis is based on simulations using the UARS Dynamics Simulator (UARSDSIM) and compared against attitude requirements as defined by General Electric (GE). An independent verification of expected accuracies is performed using the Attitude Determination Error Analysis System (ADEAS).
Dynamical analysis of an orbiting three-rigid-body system
The development of multi-joint-spacecraft mission concepts calls for a deeper understanding of their nonlinear dynamics to inform and enhance system design. This paper presents a study of a three-finite-shape rigid-body system under the action of an ideal central gravitational field. The aim of this paper is to gain an insight into the natural dynamics of this system. The Hamiltonian dynamics is derived and used to identify relative attitude equilibria of the system with respect to the orbital reference frame. Then a numerical investigation of the behaviour far from the equilibria is provided using tools from modern dynamical systems theory such as energy methods, phase portraits and Poincarè maps. Results reveal a complex structure of the dynamics as well as the existence of connections between some of the equilibria. Stable equilibrium configurations appear to be surrounded by very narrow regions of regular and quasi-regular motions. Trajectories evolve on chaotic motions in the rest of the domain.
Distributed parameter model and experimental validation of a compressive-mode energy harvester under harmonic excitations
This paper presents the modeling and parametric analysis of the recently proposed nonlinear compressive-mode energy harvester (HC-PEH) under harmonic excitation. Both theoretical and experimental investigations are performed in this study over a range of excitation frequencies. Specially, a distributed parameter electro-elastic model is analytically developed by means of the energy-based method and the extended Hamilton’s principle. An analytical formulation of bending and stretching forces are derived to gain insight on the source of nonlinearity. Furthermore, the analytical model is validated against with experimental data and a good agreement is achieved. Both numerical simulations and experiment illustrate that the harvester exhibits a hardening nonlinearity and hence a broad frequency bandwidth, multiple coexisting solutions and a large-amplitude voltage response. Using the derived model, a parametric study is carried out to examine the effect of various parameters on the harvester voltage response. It is also shown from parametric analysis that the harvester’s performance can be further improved by selecting the proper length of elastic beams, proof mass and reducing the mechanical damping.
Spatiotemporal vortex solitons in hexagonal arrays of waveguides
By means of a systematic numerical analysis, we demonstrate that hexagonal lattices of parallel linearly coupled waveguides, with the intrinsic cubic self-focusing nonlinearity, give rise to three species of stable semidiscrete complexes (which are continuous in the longitudinal direction) with embedded vorticity S: triangular modes with S=1, hexagonal ones with S=2, both centered around an empty central core, and compact triangles with S=1, which do not not include the empty site. Collisions between stable triangular vortices are studied too. These waveguiding lattices can be realized in optics and Bose-Einstein condensate.
On minimal surfaces, membranes and compressible flows
The theory, variational formulation and finite element analysis of a class of nonlinear problems arising in optimization, thin membrane deflection and compressible flows are developed. Error estimates are summarized, and representative numerical results are presented. Particular theoretical questions pertaining to the existence and uniqueness of solutions are addressed, and their implications for such applications of finite element analysis as the study of compressible flows indicated.