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General-purpose computer program establishes dynamic response of two impacting elastic bodies, each containing linear or nonlinear impact attenuation mechanism. Program can be used for analysis of broad spectrum of impact motion response investigations.
The mathematical model and associated code to simulate a high speed civil transport aircraft - the Boeing Reference H configuration - are described. The simulation was constructed in support of advanced control law research. In addition to providing time histories of the dynamic response, the code includes the capabilities for calculating trim solutions and for generating linear models. The simulation relies on the nonlinear, six-degree-of-freedom equations which govern the motion of a rigid aircraft in atmospheric flight. The 1962 Standard Atmosphere Tables are used along with a turbulence model to simulate the Earth atmosphere. The aircraft model has three parts - an aerodynamic model, an engine model, and a mass model. These models use the data from the Boeing Reference H cycle 1 simulation data base. Models for the actuator dynamics, landing gear, and flight control system are not included in this aircraft model. Dynamic responses generated by the nonlinear simulation are presented and compared with results generated from alternate simulations at Boeing Commercial Aircraft Company and NASA Langley Research Center. Also, dynamic responses generated using linear models are presented and compared with dynamic responses generated using the nonlinear simulation.
This paper describes a new trim procedure, that includes the calculation of the steady-state response of the rotor blades, and that is applicable to straight flight and steady coordinated turns. This paper also describes the results of a validation study for a high order linearized model of helicopter flight dynamics, that includes rotor, inflow, and actuator dynamics. The model is obtained by numerical perturbations of a nonlinear, blade element type mathematical model. Predicted responses are compared with flight test data for two values of flight speed. The comparison is carried out in the frequency domain. Numerical simulations show that the trim algorithm is very accurate, and preserves the periodicity of the aircraft states. The results also indicate that the predictions of the linearized model are in good agreement with flight test data, especially at medium and high frequencies.
Proton-exchange membrane (PEM) water electrolysis is a promising technology for producing clean hydrogen by electrochemically splitting water when paired with renewable energy sources. A major roadblock to improving electrolyzer durability is the mechanical degradation of the cell components, which requires an understanding of their mechanical response under device-relevant conditions. However, there is a lack of studies on the mechanical characterization of the PEM and other components, as well as and their interactions. This study aims to address this gap by using a custom-designed testing apparatus to investigate the mechanics of electrolyzer components in uniaxial compression at 25 and 80 °C. Findings show stress-strain response of components have a varying degree of nonlinearity owing to their distinct deformation mechanisms and morphologies, from porous structures to polymers. These results are used to develop an expression for compressive stress-strain response of Nafion membranes and then analyze the deformation of components under applied pressure by using a 1-D spring network model of cell assembly. This work provides a new understanding of mechanical responses of the electrolyzer membrane and cell components, which can help assess material design and cell assembly strategies for improved electrolyzer durability.
Work supported by the grant, "Stability and Control of Burning Tokamak Plasmas with Resistive Walls" in the period Aug 2017 to 2023 can be cast in three general categories: (1) linear tearing regimes and the effects on the response to error fields and resistive walls: (2) nonlinear tearing modes in the presence of error fields, with locking; and (3) energetic particle effects. In the first category, we have completed a study of tearing mode regimes with extended MHD effects, including parallel dynamics and toroidal effects, notably favorable average curvature. This work has been presented at the 2018 Sherwood Conference. This work has been published in the ArXiv and is being prepared for publication in Physics of Plasmas. A systematic study of shaping in a tokamak plasma with resistive tearing layers and a resistive wall has been presented in the PhD dissertation by Dov Rhodes, a student of Andrew Cole at Columbia University. John Finn was on Rhodes's PhD committee, and was a co-author of a paper published in Physics of Plasmas on that work. A detailed study of nonlinear tearing modes in the presence of finite beta, favorable average curvature, and an error field has been nearly completed. In this study it was found that the response to an error field with real frequency a tearing layer agreed with analytic results, and that tearing mode saturation by flattening of the current profile as well as destabilization due to flattening of the pressure profile were important factors in the locking process. This work was presented at the 2017 APS/DPP Conference and at the 2018 Sherwood Conference. The effects of energetic ions on tearing modes was presented at the 2017 APS/DPP Conference and in the PhD dissertation of Michael Halfmoon. John Finn served as a committee member on Halfmoon's PhD committee. Extensions to this work including two fluid effects were performed and presented at the APS/DPP Conference in 2017.
Method for mathematically modeling joints to assess influences of joints on dynamic response of truss structures developed in study. Only structures with low-frequency oscillations considered; only Coulomb friction and viscous damping included in analysis. Focus of effort to obtain finite-element mathematical models of joints exhibiting load-vs.-deflection behavior similar to measured load-vs.-deflection behavior of real joints. Experiments performed to determine stiffness and damping nonlinearities typical of joint hardware. Algorithm for computing coefficients of analytical joint models based on test data developed to enable study of linear and nonlinear effects of joints on global structural response. Besides intended application to large space structures, applications in nonaerospace community include ground-based antennas and earthquake-resistant steel-framed buildings.
Climate response is often assumed to be linear in climate sensitivity studies. However, by examining the surface temperature (TS) response to pairs of oceanic forcings of equal amplitude but opposite sign in a large set of local q-flux perturbation experiments with CAM5 coupled to a slab, we find strong asymmetry in TS responses to the heating and cooling forcings, indicating a strong nonlinearity intrinsic to the climate system examined. Regardless of where the symmetric forcing is placed, the cooling response to the negative forcing always exceeds the warming to the positive forcing, implying an intrinsic inclination towards cooling of our current climate. Thus, the ongoing global warming induced by increasing greenhouse gases may have already been alleviated by the asymmetric component of the response. The common asymmetry in TS response peaks in high latitudes, especially along sea ice edges, with notable seasonal dependence. Decomposition into different radiative feedbacks through a radiative kernel indicates that the asymmetry in the TS response is realized largely through lapse rate and albedo feedbacks. Further process interference experiments disabling the seasonal cycle and/or sea ice reveal that the asymmetry originates ultimately from the presence of the sea ice component and is further amplified by the seasonal cycle. The fact that a pair of opposite tropical q-flux forcings can excite very similar asymmetric response as a pair placed at 55°S strongly suggests the asymmetric response is a manifestation of an internal mode of the climate model system.
Analysis of a typical nonlinear electrohydraulic servo-model establishes the dynamic-performance capabilities of servo-actuation systems.
Nonlinear equations of motion of symmetrically laminated anisotropic plates are derived considering von Karman strains and transverse shear effects. Using a single-mode Galerkin procedure, the nonlinear modal equation is obtained. The direct equivalent linearization method is employed for solution of this equation. The effects of transverse shear on large deflection vibration of laminated plates with mixed boundary support conditions under random excitation are studied. Mean-square deflections and mean-square inplane strains are obtained for symmetric graphite-epoxy laminates. Using equilibrium equations and the continuity requirements, the mean-square transverse shear stresses are calculated. The results obtained will be useful in the sonic fatigue design of composite aircraft panels. The analysis is presented in detail for plates with two opposing edges simply supported and the remaining edges clamped.
The need for describing materials under time or cycle dependent loading conditions has been emphasized in recent years by several investigators. In response to the need, various constitutive models describing the nonlinear behavior of materials under creep, fatigue, or other complex loading conditions were developed. The developed models for describing the fully dense (non-porous) materials were mostly based on uncoupled plasticity theory. The improved characterization of materials provides a better understanding of the structual response under complex loading conditions. The pesent studies demonstrate that the rate or time dependency of the response of a porous aggregate can be incorporated into the nonlinear constitutive behavior of a porous solid by appropriately modeling the incompressible matrix behavior. It is also sown that the yield function which wads determined by a continuum mechanics approach must be verified by appropriate experiments on void containing sintered materials in order to obtain meaningful numbers for the constants that appear in the yield function.
Within this research project, the following topics were studied: (1) foundation of the refined theory of flat cross-ply laminated composite flat and curved panels as well as their static and dynamic response analysis; (2) foundation of a geometrically-nonlinear shear-deformable theory of composite laminated flat panels including the effect of initial geometric imperfections and its application in the postbuckling analysis; (3) the study of the dynamic response of shear deformable elastic laminated composite panels to deterministic time-dependent external excitations as the sonic boom and explosive blast type-loadings; (4) the study of the dynamic response of shear deformable elastic laminated composite panels to random excitation as e.g. the one produced by a jet noise or by any time-dependent external excitation whose characteristics are expressed in a statistical sense; and (5) the dynamic stability of fiber-reinforced composite flat panels whose materials (due to e.g. an ambient high temperature field) exhibit a time-dependent physical behavior.
In this paper, a failure detection and correction strategy for turbofan engines is discussed. This strategy allows continuing control of the engines in the event of a sensor failure. An extended Kalman filter is used to provide the best estimate of the state of the engine based on currently available sensor outputs. Should a sensor failure occur the control is based on the best estimate rather than the sensor output. The extended Kalman filter consists of essentially two parts, a nonlinear model of the engine and up-date logic which causes the model to track the actual engine. Details on the model and up-date logic are presented. To allow implementation, approximations are made to the feedback gain matrix which result in a single feedback matrix which is suitable for use over the entire flight envelope. The effect of these approximations on stability and response is discussed. Results from a detailed nonlinear simulation indicate that good control can be maintained even under multiple failures.
The mechanisms responsible for the transition of the circumpolar flow from its normal midwinter state to the preconditioned state that should evolve before a wavenumber-2 major warming are investigated, through a combination of observational, numerical and theoretical studies. Observations of Eliassen-Palm flux cross sections indicate that while wave zonal mean flow interaction theory could account for the qualitative evolution of the circumpolar flow during the warming, substantial nonlinear wave interactions were active during the cooling period, and these interactions significantly influenced the evolution of the circumpolar flow. Numerical experiments employing a truncated, semispectral model indicate that this cooling phenomenon is realistically reproducible in an idealized integration in which wave-wave interactions are present. Two different mechanisms are proposed to account for these nonlinearities.
A variety of niobate crystals have found their places in nonlinear optical applications as well as in laser devices. In recent years much attention has been paid to study the ultrafast optical response in a variety of photorefractive crystals such as KTa(1-x)Nb(x)O3 and KNbO3 crystals, glasses, semiconductors and polymers for applications in optical switching, information processing, optical computing, and all-optical device systems. Third-order optical nonlinearity is the most important property for realization of all-optical switching. Therefore experiments have been performed on the third order susceptibility using a variety of techniques such as the third-order harmonic generation, EFISH and degenerate four-wave mixing(DFWM). The latter has been conducted with a variety of pump wavelengths and with nanosecond, picosecond and femtosecond pulses. Niobate crystals, such as potassium niobate KNbO3, potassium tantalate niobate KTN family (KTa(1-x)Nb(x)O3), strontium barium niobate SBN (Sr(x)Ba(1-x)Nb2O6) and potassium-sodium niobate SBN (KNSBN) are attractive due to their photorefractive properties for application in optical storage and processing. The pulsed probe experiments performed on theses materials have suggested two types of time responses. These responses have been associated with an coherent response due to Chi(sup 3), and a long lived component due to excited state population. Recent study of DFWM on KNbO3 and KTN family reveals that the long lived component of those crystals depends on the crystal orientation. A slowly decaying signal is observable when the grating vector K(sub g) is not perpendicular to the C-axis of those photorefractive crystals', otherwise the optical response signal would be only a narrow coherent peak with FWHM equal to the cross-correlation width of the write beam pulses. Based on this understanding, we study the photodynamical process of a variety of niobate crystals using DFWM in a Kg perpindicular to C geometry with a ps-YAG: Nd laser operating at 532nm. However, the discrepancies in numerical estimations of Chi(sup 3) in these materials and other nonlinear optical media have resulted in a number of discussions. In order to better understand the photodynamical process of niobate crystals after an short pulse excitation we analyze the factors governing the coherent signal and present the DFWM spectra of niobate crystals.
This paper presents a mooring system design featuring polymer springs for the VolturnUS-S 15-MW reference floating wind turbine in site conditions for the New York Bight at a 50-m water depth. Polymer springs have a nonlinear stress-strain curve that allows a stiffer response at low loads and a more flexible response at higher loads, potentially reducing peak mooring line tensions. The mooring dynamics model MoorDyn has been extended to model springs with nonlinear tension-strain curves from a user-inputted look-up table. This MoorDyn modeling advancement is verified against OrcaFlex simulation results. Using MoorDyn's updated capabilities, a spring-equipped catenary mooring system is designed for the 15-MW floating system, along with a baseline catenary mooring system that does not use polymer springs. The floating wind turbine simulator OpenFAST is used to simulate the mooring systems in design-driving load cases to show the effect of polymer springs on key dynamic behaviours. The results show that the spring-equipped design reduces peak tensions by up to 60%, whereas the turbine offsets stay within a maximum of 7.2 m, which is still a reasonable offset limit for cable considerations. The reduction in peak tensions results in a significant decrease in damage equivalent loads - on the order of 50% for upwind lines in fully loaded conditions. These results show that polymer springs can effectively reduce peak tensions and fatigue loads in mooring systems at shallow water depths.
In this paper, a mooring system featuring polymer springs is designed for the VolturnUS-S 15 MW reference floating wind turbine in site conditions for the New York Bight at a 50-m water depth. Polymer springs have a nonlinear stress-strain curve that allows a stiffer response at low loads and a more flexible response at higher loads, potentially reducing peak mooring line tensions. The mooring dynamics model MoorDyn has been extended to model springs with nonlinear tension-strain curves from a user-inputted look-up table. This MoorDyn modelling advancement is verified against OrcaFlex simulation results. Using MoorDyn's updated capabilities, a spring-equipped catenary mooring system is designed for the 15 MW floating system, along with a baseline catenary mooring system that does not use polymer springs. The floating wind turbine simulator OpenFAST is used to simulate the mooring systems in design-driving load cases to show the effect of polymer springs on key dynamic behaviours. The results show that the spring-equipped design reduces peak tensions by up to 60%, while the turbine offsets stay within a maximum of 7.2 m, which is still a reasonable offset limit for cable considerations. The reduction in peak tensions results in a significant decrease in damage equivalent loads, on the order of 50% for upwind lines in fully loaded conditions. These results show that polymer springs can effectively reduce peak tensions and fatigue loads in mooring systems at shallow water depths.
Nonlinear fuel sloshing in elastic cylindrical tank - steady state response and stability boundary determinations
This lecture is a review of the basic concepts involved In the mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers. The review leads from Bryan's original formulation through the concepts of linear aerodynamic indicial functions and superposition to the extension of these concepts into the nonlinear regime. The nonlinear generalization yields a form for the aerodynamic response that can be built up from the responses to a limited number of well-defined characteristic motions, reproducible in principle either in wind-tunnel experiments or flow-field computations. A further generalization leads to a torn, accommodating the discontinuous and double-valued behavior characteristic of hysteresis in the steady-state aerodynamic response