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NASA NTRS1991

Computational aspects of sensitivity calculations in linear transient structural analysis

The calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, and transient response problems is studied. Several existing sensitivity calculation methods and two new methods are compared for three example problems. Approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite model. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models. This was found to result in poor convergence of stress sensitivities in several cases. Two semianalytical techniques are developed to overcome this poor convergence. Both new methods result in very good convergence of the stress sensitivities; the computational cost is much less than would result if the vibration modes were recalculated and then used in an overall finite difference method.

Greene, W. H.↗

NASA NTRS1981

On adaptive regulation of flexible spacecraft

It is pointed out that the regulation of shape and attitude disturbances in large space structures (LSS) using adaptive control remains an actively studied, yet controversial approach, just as adapative control itself. The controversy arises because the utility of many methods of adapatively controlling distributed parameter systems (DPS) is unsubstantiated. However, it appears that adaptive control can be applied to solve problems in LSS control which are not amenable to more common control methods. The present investigation has the objective to clarify the application of adaptive control to LSS. Attention is given to the characteristics of adaptive model control, aspects of simultaneous mode shape adaption, questions of multivariable simultaneous identification and control, and direct adaptive multivariable control.

Lawrence, D. A.↗

NASA NTRS1990

An experimental study of tip shape effects on the flutter of aft-swept, flat-plate wings

The effects of tip chord orientation on wing flutter are investigated experimentally using six cantilever-mounted, flat-plate wing models. Experimentally determined flutter characteristics of the six models are presented covering both the subsonic and transonic Mach number ranges. While all models have a 60 degree leading edge sweep, a 40.97 degree trailing edge sweep, and a root chord of 34.75 inches, they are subdivided into two series characterized by a higher aspect ratio and a lower aspect ratio. Each series is made up of three models with tip chord orientations which are parallel to the free-stream flow, perpendicular to the model mid-chord line, and perpendicular to the free-stream flow. Although planform characteristics within each series of models are held constant, structural characteristics such as mode shapes and natural frequencies are allowed to vary.

Dansberry, Bryan E.↗

NASA NTRSDate not supplied

Finite Element Modeling for Compression Strength Prediction of Honeycomb Cores with Geometric Imperfections Measured using X-ray CT Imaging

Aluminum honeycomb cores have been used extensively in composite sandwich panels due to having high bending rigidity while maintaining low density. During manufacturing of the aluminum honeycomb, the thin metal walls are susceptible to imperfections that deviate from an ideal honeycomb shape. Computational tools to quantify imperfections and investigate their effects on quasi-static compression and impact response can inform design criteria to construct safer and lighter launch vehicle structures. This paper presents the results of a study on finite element modeling of metallic honeycomb cores (HCC) with geometric imperfections measured using X-ray Computer Tomography (CT), to predict the compression response. Finite element (FE) models are constructed with measured imperfections with appropriate boundary conditions. It is shown that the average behavior of larger 10x11 cell models can be predicted by sampling single cell models from the larger domain. Amplification of imperfections for cells at the center of sampled specimens are mode switched from the larger out-of-plane imperfection to the mode shape of the adjacent cells resulting in strengthening of the center specimens.

aluminum honeycomb↗

NASA NTRS1988

Frequency based localization of structural discrepancies

The intent of modal analysis is to develop a reliable model of a structure by working with the analytical and experimental modal properties of frequency, damping and mode shape. In addition to identifying these modal properties, it would be desirable to determine spatially which parts of the structure are modelled poorly or well. It is shown how the pattern of discrepancies in the analytical and experimental test values for the pole and the driving point zero frequencies of a structure can be linked to discrepancies in the mass or stiffness of the structural elements. The success of the procedure depends on the numerical conditioning of a modal reference matrix. Strategies to insure adequate numerical conditioning require a formulation which avoids geometric and energy storage symmetries of the structure, and ignores structural elements which contribute negligibly small potential or kinetic energy to the excited modes. Physical insight into the numerical conditioning problem is provided by a numerical example and by localization of a mass discrepancy in a real structure based on lab tests.

Shepard, G. D.↗

DOE OSTI2024

Three-dimensional reconstruction of laser-direct-drive inertial confinement fusion hot-spot plasma from x-ray diagnostics on the OMEGA laser facility (invited)

A deep-learning convolutional neural network (CNN) is used to infer, from x-ray images along multiple lines of sight, the low-mode shape of the hot-spot emission of deuterium–tritium (DT) laser-direct-drive cryogenic implosions on OMEGA. The motivation of this approach is to develop a physics-informed 3-D reconstruction technique that can be performed within minutes to facilitate the use of the results to inform changes to the initial target and laser conditions for the subsequent implosion. The CNN is trained on a 3D radiation-hydrodynamic simulation database to relate 2D x-ray images to 3D emissivity at stagnation. The CNN accounts for the lack of an absolute spatial reference and the different bands of photon energies in the x-ray images. While previous works studied the effect of mode-1 asymmetries on implosion performance using nuclear diagnostics, this work focuses on the effect of mode 2 inferred from x-ray diagnostics on implosion performance. A current analysis of 19 DT cryogenic implosions indicates there is an upper limit of ~20% reduction in the neutron yield caused by an ℓ = 2 amplitude for ℓ 2 /ℓ 0 ≤ 0.32. Here, these conclusions are supported by 2D simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1990

Computational aspects of sensitivity calculations in linear transient structural analysis

A study was performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal of the study was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semi-analytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models. In several cases this fixed mode approach resulted in very poor approximations of the stress sensitivities. Almost all of the original modes were required for an accurate sensitivity and for small numbers of modes, the accuracy was extremely poor. To overcome this poor accuracy, two semi-analytical techniques were developed. The first technique accounts for the change in eigenvectors through approximate eigenvector derivatives. The second technique applies the mode acceleration method of transient analysis to the sensitivity calculations. Both result in accurate values of the stress sensitivities with a small number of modes and much lower computational costs than if the vibration modes were recalculated and then used in an overall finite difference method.

Greene, William H.↗

NASA NTRS1985

Application of a personal computer for the uncoupled vibration analysis of wind turbine blade and counterweight assemblies

A research effort was undertaken to develop personal computer based software for vibrational analysis. The software was developed to analytically determine the natural frequencies and mode shapes for the uncoupled lateral vibrations of the blade and counterweight assemblies used in a single bladed wind turbine. The uncoupled vibration analysis was performed in both the flapwise and chordwise directions for static rotor conditions. The effects of rotation on the uncoupled flapwise vibration of the blade and counterweight assemblies were evaluated for various rotor speeds up to 90 rpm. The theory, used in the vibration analysis codes, is based on a lumped mass formulation for the blade and counterweight assemblies. The codes are general so that other designs can be readily analyzed. The input for the codes is generally interactive to facilitate usage. The output of the codes is both tabular and graphical. Listings of the codes are provided. Predicted natural frequencies of the first several modes show reasonable agreement with experimental results. The analysis codes were originally developed on a DEC PDP 11/34 minicomputer and then downloaded and modified to run on an ITT XTRA personal computer. Studies conducted to evaluate the efficiency of running the programs on a personal computer as compared with the minicomputer indicated that, with the proper combination of hardware and software options, the efficiency of using a personal computer exceeds that of a minicomputer.

White, P. R.↗

NASA NTRS2004

Optics-Only Calibration of a Neural-Net Based Optical NDE Method for Structural Health Monitoring

A calibration process is presented that uses optical measurements alone to calibrate a neural-net based NDE method. The method itself detects small changes in the vibration mode shapes of structures. The optics-only calibration process confirms previous work that the sensitivity to vibration-amplitude changes can be as small as 10 nanometers. A more practical value in an NDE service laboratory is shown to be 50 nanometers. Both model-generated and experimental calibrations are demonstrated using two implementations of the calibration technique. The implementations are based on previously published demonstrations of the NDE method and an alternative calibration procedure that depends on comparing neural-net and point sensor measurements. The optics-only calibration method, unlike the alternative method, does not require modifications of the structure being tested or the creation of calibration objects. The calibration process can be used to test improvements in the NDE process and to develop a vibration-mode-independence of damagedetection sensitivity. The calibration effort was intended to support NASA s objective to promote safety in the operations of ground test facilities or aviation safety, in general, by allowing the detection of the gradual onset of structural changes and damage.

Decker, Arthur J.↗

NASA NTRS1989

Mobility power flow analysis of an L-shaped plate structure subjected to acoustic excitation

An analytical investigation based on the Mobility Power Flow method is presented for the determination of the vibrational response and power flow for two coupled flat plate structures in an L-shaped configuration, subjected to acoustical excitation. The principle of the mobility power flow method consists of dividing the global structure into a series of subsystems coupled together using mobility functions. Each separate subsystem is analyzed independently to determine the structural mobility functions for the junction and excitation locations. The mobility functions, together with the characteristics of the junction between the subsystems, are then used to determine the response of the global structure and the power flow. In the coupled plate structure considered here, mobility power flow expressions are derived for excitation by an incident acoustic plane wave. In this case, the forces (acoustic pressures) acting on the structure are dependent on the response of the structure because of the scattered pressure component. The interaction between the structure and the fluid leads to the derivation of a corrected mode shape for the plates' normal surface velocity and also for the structure mobility functions. The determination of the scattered pressure components in the expressions for the power flow represents an additional component in the power flow balance for the source plate and the receiver plate. This component represents the radiated acoustical power from the plate structure.

Cuschieri, J. M.↗

NASA NTRS1992

A new pre-loaded beam geometric stiffness matrix with full rigid body capabilities

Space structures, such as the Space Station solar arrays, must be extremely light-weight, flexible structures. Accurate prediction of the natural frequencies and mode shapes is essential for determining the structural adequacy of components, and designing a controls system. The tension pre-load in the 'blanket' of photovoltaic solar collectors, and the free/free boundary conditions of a structure in space, causes serious reservations on the use of standard finite element techniques of solution. In particular, a phenomenon known as 'grounding', or false stiffening, of the stiffness matrix occurs during rigid body rotation. The authors have previously shown that the grounding phenomenon is caused by a lack of rigid body rotational capability, and is typical in beam geometric stiffness matrices formulated by others, including those which contain higher order effects. The cause of the problem was identified as the force imbalance inherent in the formulations. In this paper, the authors develop a beam geometric stiffness matrix for a directed force problem, and show that the resultant global stiffness matrix contains complete rigid body mode capabilities, and performs very well in the diagonalization methodology customarily used in dynamic analysis.

Bosela, P. A.↗

NASA NTRS2007

Nonlinear Structural Analysis Methodology and Dynamics Scaling of Inflatable Parabolic Reflector Antenna Concepts

Ultra-light weight and ultra-thin membrane inflatable antenna concepts are fast evolving to become the state-of-the-art antenna concepts for deep-space applications. NASA Langley Research Center has been involved in the structural dynamics research on antenna structures. One of the goals of the research is to develop structural analysis methodology for prediction of the static and dynamic response characteristics of the inflatable antenna concepts. This research is focused on the computational studies to use nonlinear large deformation finite element analysis to characterize the ultra-thin membrane responses of the antennas. Recently, structural analyses have been performed on a few parabolic reflector antennas of varying size and shape, which are referred in the paper as 0.3 meters subscale, 2 meters half-scale, and 4 meters full-scale antenna. The various aspects studied included nonlinear analysis methodology and solution techniques, ways to speed convergence in iterative methods, the sensitivities of responses with respect to structural loads, such as inflation pressure, gravity, and pretension loads in the ground and in-space conditions, and the ultra-thin membrane wrinkling characteristics. Several such intrinsic aspects studied have provided valuable insight into evaluation of structural characteristics of such antennas. While analyzing these structural characteristics, a quick study was also made to assess the applicability of dynamics scaling of the half-scale antenna. This paper presents the details of the nonlinear structural analysis results, and discusses the insight gained from the studies on the various intrinsic aspects of the analysis methodology. The predicted reflector surface characteristics of the three inflatable ultra-thin membrane parabolic reflector antenna concepts are presented as easily observable displacement fringe patterns with associated maximum values, and normal mode shapes and associated frequencies. Wrinkling patterns are presented to show how surface wrinkle progress with increasing tension loads. Antenna reflector surface accuracies were found to be very much dependent on the type and size of the antenna, the reflector surface curvature, reflector membrane supports in terms of spacing of catenaries, as well as the amount of applied load.

Sreekantamurthy, Tham↗

NASA NTRS1995

System Identification of Damped Truss-Like Space Structures

A spacecraft payload flown on a launch vehicle experiences dynamic loads. The dynamic loads are caused by various phenomena ranging from the start-up of the launch vehicle engine to wind gusts. A spacecraft payload should be designed to meet launch vehicle dynamic loads. One of the major steps taken towards determining the dynamic loads is to correlate the finite element model of the spacecraft with the test results of a modal survey test. A test-verified finite element model of the spacecraft should possess the same spatial properties (stiffness, mass, and damping) and modal properties (frequencies and mode shapes) as the test hardware representing the spacecraft. The test-verified and correlated finite element model of the spacecraft is then coupled with the finite element model of the launch vehicle for analysis of loads and stress. Modal survey testing, verification of a finite element model, and modification of the finite element model to match the modal survey test results can easily be accomplished if the spacecraft structure is simple. However, this is rarely the case. A simple structure here is defined as a structure where the influence of nonlinearity between force and displacement (uncertainty in a test, for example, with errors in input and output), and the influence of damping (structural, coulomb, and viscous) are not pronounced. The objective of this study is to develop system identification and correlation methods with the focus on the structural systems that possess nonproportional damping. Two approaches to correct the nonproportional damping matrix of a truss structure were studied, and have been implemented on truss-like structures such as the National Aeronautics and Space Administration's space station truss. The results of this study showed nearly 100 percent improvement of the correlated eigensystem over the analytical eigensystem. The first method showed excellent results with up to three modes used in the system identification process. The second method could handle more modes, but required more computer usage time, and the results were less accurate than those of the first method.

Armand, Sasan↗

DOE OSTI2025

Insights on the Influence of the Central-Cut Width of the Box Assembly with Removable Component on Its Dynamical Responses

This investigation focuses on the dynamical effects caused by varying the central-cut width within the Box Assembly with Removable Component (BARC) system. The central-cut widths included in this study are a 0.5″ cut, a 0.25″ cut, a thin 0.1″ cut, and a structure that did not have a cut at all. Finite element analysis was conducted to determine the mode shapes and natural frequencies of each of the BARC structures. Structural dynamics experiments were run to examine the effects of the central-cut width on the dynamical responses and nonlinear characteristics of the BARC system. Free vibration testing with an impact hammer was carried out to excite the system and extract the dominant frequencies and directions of the significant responses. A pseudorandom vibration test that allows for the qualitative determination of any nonlinear behavior within the system was performed. This type of behavior can include nonlinear softening, nonlinear hardening, and the most common, nonlinear damping due to the presence of several bolted-joint connections and the possible activation of geometric and inertia nonlinearities. To quantitatively investigate the impacts of the central-cut width on the dynamics of the system, swept sinusoidal testing was conducted. It is determined that almost all systems with central cuts demonstrate the presence of nonlinear softening, but at times, nonlinear hardening trends are seen, particularly in the 0.1″ cut and no-cut systems when testing harmonically. Each of the central-cut systems displays nonlinear damping, with the amount of damping generally increasing as the central cut decreases in size. The effect of the central cut of the BARC system on the mode-switching ability of the system is negligible; however, mode switching takes place when comparing the central-cut configurations to the no-cut one. These results show the significance of accurately measuring the central-cut width and how geometric uncertainty may change the dynamical responses and nonlinear properties of the system.

Padilla, Christopher (ORCID:000900033446732X)↗

NASA NTRS2018

Comparing Free-Free and Shaker Table Model Correlation Methods Using Jim Beam

Finite element model correlation as part of a spacecraft program has always been a challenge. For any NASA mission, the coupled system response of the spacecraft and launch vehicle can be determined analytically through a Coupled Loads Analysis (CLA), as it is not possible to test the spacecraft and launch vehicle coupled system before launch. The value of the CLA is highly dependent on the accuracy of the frequencies and mode shapes extracted from the spacecraft model. NASA standards require the spacecraft model used in the final Verification Loads Cycle to be correlated by either a modal test or by comparison of the model with Frequency Response Functions (FRFs) obtained during the environmental qualification test. Due to budgetary and time constraints, most programs opt to correlate the spacecraft dynamic model during the environmental qualification test, conducted on a large shaker table. For any model correlation effort, the key has always been finding a proper definition of the boundary conditions. This paper is a correlation case study to investigate the difference in responses of a simple structure using a free-free boundary, a fixed boundary on the shaker table, and a base-drive vibration test, all using identical instrumentation. The NAVCON Jim Beam test structure, featured in the IMAC round robin modal test of 2009, was selected as a simple, well recognized and well characterized structure to conduct this investigation. First, a free-free impact modal test of the Jim Beam was done as an experimental control. Second, the Jim Beam was mounted to a large 20,000 lbf shaker, and an impact modal test in this fixed configuration was conducted. Lastly, a vibration test of the Jim Beam was conducted on the shaker table. The free-free impact test, the fixed impact test, and the base-drive test were used to assess the effect of the shaker modes, evaluate the validity of fixed-base modeling assumptions, and compare final model correlation results between these boundary conditions.

Modal Test↗

NASA NTRS2015

Oxide_Oxide Ceramic Matrix Composite (CMC) Exhaust Mixer Development in the NASA Environmentally Responsible Aviation (ERA) Project

Rolls-Royce North American Technologies, Inc. (LibertyWorksLW) began considering the development of CMC exhaust forced mixers in 2008, as a means of obtaining reduced weight and hotter operating temperature capability, while minimizing shape distortion during operation, which would improve mixing efficiency and reduce fuel burn. Increased component durability, enhanced ability to fabricate complex-shaped components, and engine noise reduction are other potential advantages of CMC mixers (compared to metallic mixers). In 2010, NASA was pursuing the reduction of NOx emissions, fuel burn, and noise from turbine engines in Phase I of the Environmentally Responsible Aviation (ERA) Project. ERA subtasks, including those focused on CMC components, were formulated with the goal of maturing technology from proof of concept validation (TRL 3) to a systemsubsystem or prototype demonstration in a relevant environment (TRL 6). In April 2010, the NASA Glenn Research Center (GRC) and LibertyWorks jointly initiated a CMC Exhaust System Validation Program within the ERA Project, teaming on CMC exhaust mixer development for subsonic jet engines capable of operating with increased performance. Our initial focus was on designing, fabricating, and characterizing the thrust and acoustic performance of a roughly quarter-scale 16-lobe oxide oxide CMC mixer and tail cone along with a conventional low bypass exhaust nozzle. Support Services, LLC (Allendale, MI) and ATK COI Ceramics, Inc. (COIC, in San Diego, CA) supported the design of a subscale nozzle assembly that consisted of an oxide oxide CMC mixer and center body, with each component mounted on a metallic attachment ring. That design was based upon the operating conditions a mixer would experience in a turbofan engine. Validation of the aerodynamic and acoustic performance of the subscale mixer via testing and the achievement of TRL 4 encouraged the NASALWCOIC team to move to the next phase where a full scale CMC mixer sized for a RR AE3007 engine and a compatible attachment flange were designed, followed by CMC component fabrication by COIC, and vibration testing at GRC under conditions simulating the structural and dynamic environment encountered during engine operation. AFRL (WPAFB) supported this testing by performing 3D laser vibrometry to identify the mixer mode shapes and modal frequencies. The successful fabrication and testing of such a component has been achieved. The CMC mixer demonstrated good durability during vibration testing at room and elevated temperature (TRL5). This has cleared the article for a ground-based test on a Rolls-Royce AE3007 engine, where the performance and benefits of the component can be further assessed.

exhaust nozzles↗

NASA NTRSDate not supplied

SLS Integrated Modal Test Uncertainty Quantification using the Hybrid Parametric Variation Method

Uncertainty in structural loading during launch is a significant concern in the development of spacecraft and launch vehicles. Small variations in launch vehicle and payload mode shapes and their interaction can result in significant variation in system loads. In many cases involving large aerospace systems it is difficult, not economical, or impossible to perform a system modal test. However, it is still vital to obtain test results that can be compared with analytical predictions to validate models. Instead, the “Building Block Approach” is used in which system components are tested individually. Component models are correlated and updated to agree as best they can with test results. The Space Launch System consists of a number of components that are assembled into a launch vehicle. Finite element models of the components are developed, reduced to Hurty/Craig-Bampton models and assembled to represent different phases of flight. The only opportunity to obtain modal test data from an assembled Space Launch System will be during the Integrated Modal Test. There is always uncertainty in every model, which flows into uncertainty in predicted system results. Uncertainty Quantification is used to determine statistical bounds on prediction accuracy based on model uncertainty. For the Space Launch System, model uncertainty is at the Hurty/Craig-Bampton component level. Uncertainty in the Hurty/Craig-Bampton components is quantified using the hybrid parametric variation approach that combines parametric and nonparametric uncertainty. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. This type of uncertainty cannot be represented by variations infinite element model input parameters and thus cannot be included in a parametric approach. However, model-form uncertainty can be modeled using a nonparametric approach based on random matrix theory. The hybrid parametric variation method requires the selection of dispersion values for the Hurty/Craig-Bampton fixed-interface eigenvalues, and the Hurty/Craig-Bampton stiffness matrices. Component test/analysis frequency error is used to identify the fixed-interface eigenvalue dispersions, while test/analysis cross-orthogonality is used to identify stiffness dispersion values. The hybrid parametric variation uncertainty quantification approach is applied to the Space Launch System Integrated Modal Test configuration. Monte Carlo analysis is performed, and statistics are determined for modal correlation metrics, frequency response from Integrated Modal Test shakers to selected accelerometers, as well as other metrics for determining how well target modes are excited and identified. If the predicted uncertainty envelopes future Integrated Modal Test results, then there will be increased confidence in the utility of the component-based hybrid parametric variation uncertainty quantification approach.

Uncertainty Quantification↗

DOE OSTI2020

Method for Selecting Rotor Suspension Design Criteria

A method for selecting rotor suspension design criteria that allow rotors with internal friction to negotiate critical speeds and avoid subsynchronous internal friction instabilities is described. A rotor model of a test rotor with internal friction is created and used to calculate the test rotor’s critical speeds, mode shapes, Campbell plots, and the rotational speed corresponding to the stability boundary for a nominal set of suspension parameters. The test rotor model is then used to demonstrate the suspension design criteria selection method.

Damiano, Brian↗