Performance of third order nonlinear control systems
Method of predicting step response of control systems described by third order nonlinear differential equations
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Results for “nonlinear response”
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.
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Application of gradient search procedures for the identification of unknown system parameters from system response observations
Gradient search procedures application for nonlinear system unknown parameters identification from system dynamic response observations
Baumgarten, J. R.↗
Physically constrained 3D diffusion for inverse design of fiber-reinforced polymer composite materials
Designing fiber-reinforced polymer composites (FRPCs) with a tailored nonlinear stress-strain response is crucial for applications such as energy absorption in crash structures, flexible robotics, and impact-resistant protective gear. However, the inherent complexities of composite materials and the multitude of parameters involved, render traditional design and optimization methods inadequate for achieving effective inverse design of composites. In this paper, we present an AI-based inverse design framework that effectively and efficiently generates FRPCs with targeted nonlinear stress-strain responses. We introduce a physically constrained diffusion model (PC3D_Diffusion) capable of managing the complexities of composite materials and producing detailed, high-quality designs. We propose a loss-guided, learning-free approach to generate physically feasible microstructure designs by explicitly enforcing physical constraints during the generation process. For training purposes, 1.35 million FRPC samples were created, and their corresponding stress-strain curves were computed using established physics-based computational models. The results show that PC3D_Diffusion consistently generates high-quality designs with tailored mechanical behaviors, while guaranteeing compliance with the physical constraints. PC3D_Diffusion advances FRPC inverse design and may facilitate the inverse design of other 3D materials, offering potential applications in industries reliant on materials with custom mechanical properties.
Xu, Pei [Clemson Univ., SC (United States)]↗
Pilot-aircraft system response to wind shear
The nonlinear aircraft motion and automatic control computer model of Frost and Reddy has been expanded to incorporate the human pilot into simulations of aircraft response to wind shear. Fixed-stick, autopilot, and manned computer simulations are made with an aircraft having characteristics of a Queen Air (small commuter-type aircraft) flown through longitudinal winds measured by a Doppler radar beamed along the glide slope during the SESAME '79 experiments in Oklahoma. Simulations are also made flying a model Boeing 727 through sinusoidal head wind to tail wind shears at the phugoid frequency to evaluate the response of manned aircraft in thunderstorm wind environments.
Turkel, B. S.↗
Analyses of Multishaft Rotor-Bearing Response
Method works for linear and nonlinear systems. Finite-element-based computer program developed to analyze free and forced response of multishaft rotor-bearing systems. Acronym, ARDS, denotes Analysis of Rotor Dynamic Systems. Systems with nonlinear interconnection or support bearings or both analyzed by numerically integrating reduced set of coupledsystem equations. Linear systems analyzed in closed form for steady excitations and treated as equivalent to nonlinear systems for transient excitation. ARDS is FORTRAN program developed on an Amdahl 470 (similar to IBM 370).
Nelson, H. D.↗
Theoretical considerations of some nonlinear aspects of hypersonic panel flutter Annual report, 1 Sep. 1966 - 31 Aug. 1967
Systematic investigation of effects on panel response and stability of nonlinear aerodynamic loading at hypersonic speeds
Mc Intosh, S. C.↗
Nonlinear rotordynamics analysis
Effective analysis tools were developed for predicting the nonlinear rotordynamic behavior of the Space Shuttle Main Engine (SSME) turbopumps under steady and transient operating conditions. Using these methods, preliminary parametric studies were conducted on both generic and actual HPOTP (high pressure oxygen turbopump) models. In particular, a novel modified harmonic balance/alternating Fourier transform (HB/AFT) method was developed and used to conduct a preliminary study of the effects of fluid, bearing and seal forces on the unbalanced response of a multi-disk rotor in the presence of bearing clearances. The method makes it possible to determine periodic, sub-, super-synchronous and chaotic responses of a rotor system. The method also yields information about the stability of the obtained response, thus allowing bifurcation analyses. This provides a more effective capability for predicting the response under transient conditions by searching in proximity of resonance peaks. Preliminary results were also obtained for the nonlinear transient response of an actual HPOTP model using an efficient, newly developed numerical method based on convolution integration. Currently, the HB/AFT is being extended for determining the aperiodic response of nonlinear systems. Initial results show the method to be promising.
Noah, Sherif T.↗
Structurally-Tailorable, Nonlinear, Snap-Through Spring
Abrupt change in load/deflection response controllable and predictable. Structurally-tailorable, nonlinear, snap-through spring (STNSTS) exhibits controllable and predictable abrupt change in load/deflection response and based upon known phenomenon of snap-through structural response. Composed of pin-connected two-bar linkage which depicts combined tension/compression springs. As load applied to STNSTS, stiffness is function of internal spring and bending stiffness of pin-connected bars. As load increases, bars deform laterally until they collapse and snap through. Has application in passively-tailored rotor-blade flap, pitch, and lag response, to improve aerodynamic performance and stability characteristics of rotors; in aerodynamically- and aeroelastically-tailored wing spars and ribs, to produce tailored deformation state for improved effectiveness in maneuvering, aerodynamic performance, and stability characteristics; and in energy absorbers for automobile bumpers and aircraft land
Starnes, James H., Jr.↗
Strain Measurement Using FBG on COPV in Stress Rupture Test
White Sands Test Facility (WSTF) was requested to perform ambient temperature hydrostatic pressurization testing of a Space Transportation System (STS) 40-in. Kevlar Composite Overwrapped Pressure Vessel (COPV). The 40-in. vessel was of the same design and approximate age as the STS Main Propulsion System (MPS) and Orbiter Maneuvering System (OMS) vessels. The NASA Engineering Safety Center (NESC) assembled a team of experts and conducted an assessment that involved a review of national Kevlar COPY data. During the review, the STS COPVs were found to be beyond their original certification of ten years. The team observed that the likelihood of STS COPV Stress rupture, a catastrophic burst before leak failure mode, was greater than previously believed. Consequently, a detailed assessment of remaining stress rupture life became necessary. Prior to STS-114, a certification deviation was written for two flights of OV-103 (Discovery) and OV-104 (Atlantis) per rationale that was based on an extensive review of the Lawrence Livermore National Laboratories, COPV data, and revisions to the STS COPV stress levels. In order to obtain flight rationale to extend the certification deviation through the end of the Program, the Orbiter Project Office has directed an interagency COPV team to conduct further testing and analysis to investigate conservatism in the stress rupture model and evaluate material age degradation. Additional analysis of stress rupture life requires understanding the fiber stresses including stress that occurs due to thru-wall composite compression in COPV components. Data must be obtained at both zero gauge pressure (pre-stress) and at the component operating pressure so that this phenomenon can be properly evaluated. The zero gauge pressure stresses are predominantly a result of the autofrettage process used during vessel manufacture. Determining these pre-stresses and the constitutive behavior of the overwrap at pressure will provide necessary information to better predict the remaining life of the STS COPVs. The primary test objective is obtaining data to verify the hypothesis of a radially oriented thru-thickness stress-riser in the COPV composite whose magnitude is a function of the applied pressure and the load history. The anticipated load dependent response follows from the constitutive behavior of the composite overwrap so data to quantify its nonlinear and time dependent response will be sought. The objective of the Fiber Braggs Gratings (FBGs) were to advance the state-of-the-art by developing techniques using FBG sensors that are capable of assessing stress-rupture degradation in Kevlar COPVs in a health monitoring mode (1). Moreover, they sought to answer questions of how embedded sensors affect overall integrity of the structure. And lastly, they sought to provide an important link in the overall stress rupture study that will help close the loop on the COPV fabrication process. NDE inspection methods will be used from start to finish and FBG will be an integral link within the overall chain.
Banks, Curtis↗
Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, $\mathcal{PT}$- and supersymmetric potential
In this work, we present trapped solitary wave solutions of a coupled nonlinear Schrödinger (NLS) system in 1 + 1 dimensions in the presence of an external, supersymmetric and complex $\mathcal{PT}$-symmetric potential. The Schrödinger system this work focuses on possesses exact solutions whose existence, stability, and spatio-temporal dynamics are investigated by means of analytical and numerical methods. Two different variational approximations are considered where the stability and dynamics of the solitary waves are explored in terms of eight and twelve time-dependent collective coordinates (CCs). We find regions of stability for specific potential choices as well as analytic expressions for the small oscillation frequencies in the CC approximation. Our findings are further supported by performing systematic numerical simulations of the NLS system.
97 MATHEMATICS AND COMPUTING↗
Dynamic Response of a Semiactive Suspension System with Hysteretic Nonlinear Energy Sink Based on Random Excitation by means of Computer Simulation
This paper aims to investigate the property and behavior of the hysteretic nonlinear energy sink (HNES) coupled to a half vehicle system which is a nine-degree-of-freedom, nonlinear, and semiactive suspension system in order to improve the ride comfort and increase the stability in shock mitigation by using the computer simulation method. The HNES model is a semiactive suspension device, which comprises the famous Bouc–Wen (B-W) model employed to describe the force produced by both the purely hysteretic spring and linear elastic spring of potentially negative stiffness connected in parallel, for the half vehicle system. Nine nonlinear motion equations of the half vehicle system are derived in terms of the seven displacements and the two dimensionless hysteretic variables, which are integrated numerically by employing the direct time integration method for studying both the variables of vertical displacements, velocities, accelerations, chassis pitch angle, and the ride comfort and driver safety, respectively, based on the bump and random road inputs of the pseudoexcitation method as excitation signal. Simulation results show that, compared with the HNES model and the magnetorheological (MR) model coupled to the half vehicle system, the ride comfort and stability have been evidently improved. A successful validation process has been performed, which indicated that both the ride comfort and driver safety properties of the HNES model coupled to half vehicle significantly improved.
Chen, Hui↗
Nonlinear Analysis of the Space Shuttle Superlightweight LO2 Tank: Behavior Under 3g End-of-Flight Loads - Part 2
Results of linear bifurcation and nonlinear analyses of the Space Shuttle super lightweight (SLWT) external liquid-oxygen (LO2) tank are presented for an important end-of-flight loading condition. These results illustrate an important type of response mode for thin-walled shells, that are subjected to combined mechanical and thermal loads, that may be encountered in the design of other liquid-fuel launch vehicles. Linear bifurcation analyses are presented that predict several nearly equal eigenvalues that correspond to local buckling modes in the aft dome of the LO2 tank. In contrast, the nonlinear response phenomenon is shown to consist of a short-wavelength bending deformation in the aft elliptical dome of the LO2 tank that grows in amplitude in a stable manner with increasing load. Imperfection sensitivity analyses are presented that show that the presence of several nearly equal eigenvalues does not lead to a premature general instability mode for the aft dome. For the linear bifurcation and nonlinear analyses, the results show that accurate predictions of the response of the shell generally require a large-scale, high fidelity finite-element model. Results are also presented that show that the SLWT LO2 tank can support loads in excess of approximately 1.9 times the values of the operational loads considered.
Nemeth, Michael P.↗
Composite fuselage shell structures research at NASA Langley Research Center
Fuselage structures for transport aircraft represent a significant percentage of both the weight and the cost of these aircraft primary structures. Composite materials offer the potential for reducing both the weight and the cost of transport fuselage structures, but only limited studies of the response and failure of composite fuselage structures have been conducted for transport aircraft. The behavior of these important primary structures must be understood, and the structural mechanics methodology for analyzing and designing these complex stiffened shell structures must be validated in the laboratory. The effects of local gradients and discontinuities on fuselage shell behavior and the effects of local damage on pressure containment must be thoroughly understood before composite fuselage structures can be used for commercial aircraft. This paper describes the research being conducted and planned at NASA LaRC to help understand the critical behavior or composite fuselage structures and to validate the structural mechanics methodology being developed for stiffened composite fuselage shell structure subjected to combined internal pressure and mechanical loads. Stiffened shell and curved stiffened panel designs are currently being developed and analyzed, and these designs will be fabricated and then tested at Langley to study critical fuselage shell behavior and to validate structural analysis and design methodology. The research includes studies of the effects of combined internal pressure and mechanical loads on nonlinear stiffened panel and shell behavior, the effects of cutouts and other gradient-producing discontinuities on composite shell response, and the effects of local damage on pressure containment and residual strength. Scaling laws are being developed that relate full-scale and subscale behavior of composite fuselage shells. Failure mechanisms are being identified and advanced designs will be developed based on what is learned from early results from the LaRC research activities. Results from combined load tests will be used to validate analytical models of critical nonlinear response mechanisms as well as shell scaling laws.
Starnes, James H., Jr.↗
A numerical procedure for predicting creep and delayed failures in laminated composites
A numerical procedure is described for predicting the viscoelastic response of general laminates. A nonlinear compliance model is used to predict the creep response of the individual laminae. A biaxial delayed failure model predicts ply failure. The numerical procedure, based on lamination theory, increases by increments through time to predict creep compliance and delayed failures in laminates. Numerical stability problems and experimental verification are discussed. Although the program has been quite successful in predicting creep of general laminates, the assumptions associated with lamination theory have resulted in erroneous bounds on the predicted material response. Delayed failure predictions have been conservative. Several improvements are suggested to increase the accuracy of the procedure.
Dillard, D. A.↗
Theoretical and Analog Studies of the Effects of Nonlinear Stability Derivatives on the Longitudinal Motions of an Aircraft in Response to Step Control Deflections and to the Influence of Proportional Automatic Control
Through theoretical and analog results the effects of two nonlinear stability derivatives on the longitudinal motions of an aircraft have been investigated. Nonlinear functions of pitching-moment and lift coefficients with angle of attack were considered. Analog results of aircraft motions in response to step elevator deflections and to the action of the proportional control systems are presented. The occurrence of continuous hunting oscillations was predicted and demonstrated for the attitude stabilization system with proportional control for certain nonlinear pitching-moment variations and autopilot adjustments.
Curfman, Howard J , Jr↗
The STAGS computer code
Basic information about the computer code STAGS (Structural Analysis of General Shells) is presented to describe to potential users the scope of the code and the solution procedures that are incorporated. Primarily, STAGS is intended for analysis of shell structures, although it has been extended to more complex shell configurations through the inclusion of springs and beam elements. The formulation is based on a variational approach in combination with local two dimensional power series representations of the displacement components. The computer code includes options for analysis of linear or nonlinear static stress, stability, vibrations, and transient response. Material as well as geometric nonlinearities are included. A few examples of applications of the code are presented for further illustration of its scope.
Almroth, B. O.↗
Nonlinear Analysis of the Space Shuttle Superlightweight LO2 Tank: Bahavior Under Booster Ascent Loads - Part 1
Results of linear bifurcation and nonlinear analyses of the Space Shuttle superlightweight (SLWT) external liquid-oxygen (LO2) tank for an important early booster ascent loading condition are presented. These results for thin-walled linear elastic shells that are subjected to combined mechanical and thermal loads illustrate an important type of response mode that may be encountered in the design of other liquid-fuel launch vehicles. Linear bifurcation analyses are presented that predict several nearly equal eigenvalues that correspond to local buckling modes in the forward ogive section of the LO2 tank. In contrast, the nonlinear response phenomenon is shown to consist of short-wavelength bending deformations in the forward ogive and barrel sections of the LO2 tank that growing amplitude in a stable manner increasing load. Imperfection sensitivity analyses are presented that show that the presence of several nearly equal eigenvalues does not lead to a premature general instability mode for the forward ogive section. For the linear bifurcation and nonlinear analyses, the results show that accurate predictions of the response of the shield generally require a large-scale, high-fidelity finite-element model. Results are also presented that show that the SLWT LO2 tank can support loads in excess of approximately 2.6 times the values of the operational loads considered.
Young, Richard D.↗
Modeling the Yaw Behavior of Tail Fins for Small Wind Turbines: November 22, 2021 - May 21, 2024
This report describes the aerodynamic modelling of the yaw behavior of tail fins for small wind turbines (SWTs). The analysis is based on unsteady slender body theory (USBT) and is formulated to be used with the proposed tail fin module to be added to OpenFAST. Linearized USBT, which has been applied in the past to SWT tail fins, is developed in three main ways. First, USBT is extended to high yaw angles and aspect ratios by modelling the associated nonlinear vortex dynamics and the chordwise load distribution respectively. Second, we consider the effect of time-varying wind speed. The extended theory is compared to recent unpublished measurements at the University of Perugia, Italy, for the yaw behavior of delta, elliptical, and rectangular tail fins without a rotor and nacelle. The fins were released from initial yaw angles of -40 degrees and -80 degrees ; the latter is of sufficient magnitude to show the importance of the nonlinear yaw dynamics. Further, the friction in the model tail fin bearings was measured and modelled. The constants in the aerodynamic models were taken from the literature but significant improvement in accuracy is achieved by using system identification techniques to optimize the values. This leads to the third main finding: extended USBT is accurate for all generic tail fin shapes that we considered and is, therefore, very suitable for inclusion in aeroelastic codes for SWTs. The final development is of a general nonlinear equation for yaw response that is simpler than the extended USBT and is also suitable for inclusion in OpenFAST. The two nonlinear models are used to highlight the geometric requirements for good tail fin design.
distributed wind↗