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NASA NTRS1977

NASTRAN hydroelastic modal studies. Volume 1: Introduction, theory, and results

The implementation of a general three-dimensional hydroelastic capability in the NASTRAN computer program is described. A method for analyzing the combined mode shapes of arbitrary fluid and structure finite element models was developed. The fluid was modeled with three-dimensional solid elements with options for tetrahedron, wedge, and hexahedron shapes. The elements were then connected to fluid grid points which defined the pressure in the fluid at the specified location. Matrices were formulated to provide efficient solutions for large-order problems. The structure matrices were processed separately and could be reduced using matrix condensation procedures or through a modal formulation using the normal modes of the empty structure as solution coordinates. The fluid/structure interface and the free surface were defined by the user with special NASTRAN boundary elements. A special purpose mesh generator program was provided to generate the actual NASTRAN data cards for the fluid, the structure, and the boundary elements for typical tank-type models.

Source record↗

NASA NTRS1990

Calculation of flight vibration levels of the AH-1G helicopter and correlation with existing flight vibration measurements

NASA-Langley is sponsoring a rotorcraft structural dynamics program with the objective to establish in the U.S. a superior capability to utilize finite element analysis models for calculations to support industrial design of helicopter airframe structures. In the initial phase of the program, teams from the major U.S. manufacturers of helicopter airframes will apply extant finite element analysis methods to calculate loads and vibrations of helicopter airframes, and perform correlations between analysis and measurements. The aforementioned rotorcraft structural dynamics program was given the acronym DAMVIBS (Design Analysis Method for Vibrations). Sikorsky's RDYNE Rotorcraft Dynamics Analysis used for the correlation study, the specifics of the application of RDYNE to the AH-1G, and comparisons of the predictions of the method with flight data for loads and vibrations on the AH-1G are described. RDYNE was able to predict trends of variations of loads and vibrations with airspeed, but in some instances magnitudes differed from measured results by factors of two or three to one. Sensitivities were studied of predictions to rotor inflow modeling, effects of torsional modes, number of blade bending modes, fuselage structural damping, and hub modal content.

Sopher, R.↗

NASA NTRS1989

Evaluation of analysis techniques for low frequency interior noise and vibration of commercial aircraft

The application of selected analysis techniques to low frequency cabin noise associated with advanced propeller engine installations is evaluated. Three design analysis techniques were chosen for evaluation including finite element analysis, statistical energy analysis (SEA), and a power flow method using element of SEA (computer program Propeller Aircraft Interior Noise). An overview of the three procedures is provided. Data from tests of a 727 airplane (modified to accept a propeller engine) were used to compare with predictions. Comparisons of predicted and measured levels at the end of the first year's effort showed reasonable agreement leading to the conclusion that each technique had value for propeller engine noise predictions on large commercial transports. However, variations in agreement were large enough to remain cautious and to lead to recommendations for further work with each technique. Assessment of the second year's results leads to the conclusion that the selected techniques can accurately predict trends and can be useful to a designer, but that absolute level predictions remain unreliable due to complexity of the aircraft structure and low modal densities.

Landmann, A. E.↗

NASA NTRS1994

Sensitivity of lag-damping correlations to structural and aerodynamic approximations of isolated experimental rotors in forward flight

The predictions of regressive lag-mode damping levels are correlated with the database of an isolated, soft-inplane, three-blade rotor operated untrimmed. The database was generated at the Army Aeroflightdynamics Directorate at Ames. The correlation covers a broad range of data, from near-zero thrust conditions in hover to high-thrust and highly stalled conditions in forward flight with advance ratio as high as 0.55 and shaft angle as high as 20 degrees. In the experimental rotor, the airfoil or blade portion has essentially uniform mass and stiffness distributions, but the root flexure has highly nonuniform mass and stiffness distributions. Accordingly, the structural approximations refer to four models of root-flexure-blade assembly. They range from a rigid flap-lag model to three elastic flap-lag-torsion models, which differ in modeling the root flexure. The three models of root-flexure are: three root springs in which the bending-torsion couplings are fully accounted for; a finite-length beam element with some average mass and stiffness distributions such that the fundamental frequencies match those of the experimental model; and accurate modal representation in which the actual mass and stiffness distributions of the experimental root-flexure-blade assembly are used in calculating the nonrotating mode shapes. The four models of root-flexure-blade assembly are referred to as the rigid flap-lag model, spring model, modified model and modal model. For each of these four models of the root-flexure-blade assembly, the predictions are based on the following five aerodynamic theories: ear theory, which accounts for large angle-of-attack and reverse-flow effects on lift, and has constant drag and pitching moment; quasisteady stall theory, which includes quasisteady stall lift, drag and pitching moment characteristics of the airfoil section, dynamics stall theory, which uses the ONERA dynamic stall models of lift, drag and pitching moment; dynamic wake theory, which is based on a finite-state three-dimensional wake model and includes all wake effects including both shed and trailing vorticity; and dynamics and wake theory, which combines both dynamic stall theory and dynamic wake theory and is a relatively complete aerodynamic representation.

Gaonkar, G. H.↗

NASA NTRS2014

Impact Testing and Simulation of Composite Airframe Structures

Dynamic tests were performed at NASA Langley Research Center on composite airframe structural components of increasing complexity to evaluate their energy absorption behavior when subjected to impact loading. A second objective was to assess the capabilities of predicting the dynamic response of composite airframe structures, including damage initiation and progression, using a state-of-the-art nonlinear, explicit transient dynamic finite element code, LS-DYNA. The test specimens were extracted from a previously tested composite prototype fuselage section developed and manufactured by Sikorsky Aircraft Corporation under the US Army's Survivable Affordable Repairable Airframe Program (SARAP). Laminate characterization testing was conducted in tension and compression. In addition, dynamic impact tests were performed on several components, including I-beams, T-sections, and cruciform sections. Finally, tests were conducted on two full-scale components including a subfloor section and a framed fuselage section. These tests included a modal vibration and longitudinal impact test of the subfloor section and a quasi-static, modal vibration, and vertical drop test of the framed fuselage section. Most of the test articles were manufactured of graphite unidirectional tape composite with a thermoplastic resin system. However, the framed fuselage section was constructed primarily of a plain weave graphite fabric material with a thermoset resin system. Test data were collected from instrumentation such as accelerometers and strain gages and from full-field photogrammetry.

Jackson, Karen E.↗

NASA NTRS2008

Optimized Non-Obstructive Particle Damping (NOPD) Treatment for Composite Honeycomb Structures

Non-Obstructive Particle Damping (NOPD) technology is a passive vibration damping approach whereby metallic or non-metallic particles in spherical or irregular shapes, of heavy or light consistency, and even liquid particles are placed inside cavities or attached to structures by an appropriate means at strategic locations, to absorb vibration energy. The objective of the work described herein is the development of a design optimization procedure and discussion of test results for such a NOPD treatment on honeycomb (HC) composite structures, based on finite element modeling (FEM) analyses, optimization and tests. Modeling and predictions were performed and tests were carried out to correlate the test data with the FEM. The optimization procedure consisted of defining a global objective function, using finite difference methods, to determine the optimal values of the design variables through quadratic linear programming. The optimization process was carried out by targeting the highest dynamic displacements of several vibration modes of the structure and finding an optimal treatment configuration that will minimize them. An optimal design was thus derived and laboratory tests were conducted to evaluate its performance under different vibration environments. Three honeycomb composite beams, with Nomex core and aluminum face sheets, empty (untreated), uniformly treated with NOPD, and optimally treated with NOPD, according to the analytically predicted optimal design configuration, were tested in the laboratory. It is shown that the beam with optimal treatment has the lowest response amplitude. Described below are results of modal vibration tests and FEM analyses from predictions of the modal characteristics of honeycomb beams under zero, 50% uniform treatment and an optimal NOPD treatment design configuration and verification with test data.

Panossian, H.↗

NASA NTRS1993

The NASA/industry Design Analysis Methods for Vibrations (DAMVIBS) program: Boeing Helicopters airframe finite element modeling

Mathematical models based on the finite element method of structural analysis, as embodied in the NASTRAN computer code, are routinely used by the helicopter industry to calculate airframe static internal loads used for sizing structural members. Historically, less reliance has been placed on the vibration predictions based on these models. Beginning in the early 1980's NASA's Langley Research Center initiated an industry wide program with the objective of engendering the needed trust in vibration predictions using these models and establishing a body of modeling guides which would enable confident future prediction of airframe vibration as part of the regular design process. Emphasis in this paper is placed on the successful modeling of the Army/Boeing CH-47D which showed reasonable correlation with test data. A principal finding indicates that improved dynamic analysis requires greater attention to detail and perhaps a finer mesh, especially the mass distribution, than the usual stress model. Post program modeling efforts show improved correlation placing key modal frequencies in the b/rev range with 4 percent of the test frequencies.

Gabel, R.↗

NASA NTRS2011

Ice Shape Characterization Using Self-Organizing Maps

A method for characterizing ice shapes using a self-organizing map (SOM) technique is presented. Self-organizing maps are neural-network techniques for representing noisy, multi-dimensional data aligned along a lower-dimensional and possibly nonlinear manifold. For a large set of noisy data, each element of a finite set of codebook vectors is iteratively moved in the direction of the data closest to the winner codebook vector. Through successive iterations, the codebook vectors begin to align with the trends of the higher-dimensional data. In information processing, the intent of SOM methods is to transmit the codebook vectors, which contains far fewer elements and requires much less memory or bandwidth, than the original noisy data set. When applied to airfoil ice accretion shapes, the properties of the codebook vectors and the statistical nature of the SOM methods allows for a quantitative comparison of experimentally measured mean or average ice shapes to ice shapes predicted using computer codes such as LEWICE. The nature of the codebook vectors also enables grid generation and surface roughness descriptions for use with the discrete-element roughness approach. In the present study, SOM characterizations are applied to a rime ice shape, a glaze ice shape at an angle of attack, a bi-modal glaze ice shape, and a multi-horn glaze ice shape. Improvements and future explorations will be discussed.

McClain, Stephen T.↗

NASA NTRS1991

Basic research on design analysis methods for rotorcraft vibrations

The objective of the present work was to develop a method for identifying physically plausible finite element system models of airframe structures from test data. The assumed models were based on linear elastic behavior with general (nonproportional) damping. Physical plausibility of the identified system matrices was insured by restricting the identification process to designated physical parameters only and not simply to the elements of the system matrices themselves. For example, in a large finite element model the identified parameters might be restricted to the moduli for each of the different materials used in the structure. In the case of damping, a restricted set of damping values might be assigned to finite elements based on the material type and on the fabrication processes used. In this case, different damping values might be associated with riveted, bolted and bonded elements. The method itself is developed first, and several approaches are outlined for computing the identified parameter values. The method is applied first to a simple structure for which the 'measured' response is actually synthesized from an assumed model. Both stiffness and damping parameter values are accurately identified. The true test, however, is the application to a full-scale airframe structure. In this case, a NASTRAN model and actual measured modal parameters formed the basis for the identification of a restricted set of physically plausible stiffness and damping parameters.

Hanagud, S.↗

NASA NTRS1998

Development of a Probabilistic Dynamic Synthesis Method for the Analysis of Nondeterministic Structures

Accounting for the statistical geometric and material variability of structures in analysis has been a topic of considerable research for the last 30 years. The determination of quantifiable measures of statistical probability of a desired response variable, such as natural frequency, maximum displacement, or stress, to replace experience-based "safety factors" has been a primary goal of these studies. There are, however, several problems associated with their satisfactory application to realistic structures, such as bladed disks in turbomachinery. These include the accurate definition of the input random variables (rv's), the large size of the finite element models frequently used to simulate these structures, which makes even a single deterministic analysis expensive, and accurate generation of the cumulative distribution function (CDF) necessary to obtain the probability of the desired response variables. The research presented here applies a methodology called probabilistic dynamic synthesis (PDS) to solve these problems. The PDS method uses dynamic characteristics of substructures measured from modal test as the input rv's, rather than "primitive" rv's such as material or geometric uncertainties. These dynamic characteristics, which are the free-free eigenvalues, eigenvectors, and residual flexibility (RF), are readily measured and for many substructures, a reasonable sample set of these measurements can be obtained. The statistics for these rv's accurately account for the entire random character of the substructure. Using the RF method of component mode synthesis, these dynamic characteristics are used to generate reduced-size sample models of the substructures, which are then coupled to form system models. These sample models are used to obtain the CDF of the response variable by either applying Monte Carlo simulation or by generating data points for use in the response surface reliability method, which can perform the probabilistic analysis with an order of magnitude less computational effort. Both free- and forced-response analyses have been performed, and the results indicate that, while there is considerable room for improvement, the method produces usable and more representative solutions for the design of realistic structures with a substantial savings in computer time.

Brown, A. M.↗

NASA NTRS2016

Unsteady Aerodynamic Force Sensing from Measured Strain

A simple approach for computing unsteady aerodynamic forces from simulated measured strain data is proposed in this study. First, the deflection and slope of the structure are computed from the unsteady strain using the two-step approach. Velocities and accelerations of the structure are computed using the autoregressive moving average model, on-line parameter estimator, low-pass filter, and a least-squares curve fitting method together with analytical derivatives with respect to time. Finally, aerodynamic forces over the wing are computed using modal aerodynamic influence coefficient matrices, a rational function approximation, and a time-marching algorithm. A cantilevered rectangular wing built and tested at the NASA Langley Research Center (Hampton, Virginia, USA) in 1959 is used to validate the simple approach. Unsteady aerodynamic forces as well as wing deflections, velocities, accelerations, and strains are computed using the CFL3D computational fluid dynamics (CFD) code and an MSC/NASTRAN code (MSC Software Corporation, Newport Beach, California, USA), and these CFL3D-based results are assumed as measured quantities. Based on the measured strains, wing deflections, velocities, accelerations, and aerodynamic forces are computed using the proposed approach. These computed deflections, velocities, accelerations, and unsteady aerodynamic forces are compared with the CFL3D/NASTRAN-based results. In general, computed aerodynamic forces based on the lifting surface theory in subsonic speeds are in good agreement with the target aerodynamic forces generated using CFL3D code with the Euler equation. Excellent aeroelastic responses are obtained even with unsteady strain data under the signal to noise ratio of -9.8dB. The deflections, velocities, and accelerations at each sensor location are independent of structural and aerodynamic models. Therefore, the distributed strain data together with the current proposed approaches can be used as distributed deflection, velocity, and acceleration sensors. This research demonstrates the feasibility of obtaining induced drag and lift forces through the use of distributed sensor technology with measured strain data. An active induced drag control system thus can be designed using the two computed aerodynamic forces, induced drag and lift, to improve the fuel efficiency of an aircraft. Interpolation elements between structural finite element grids and the CFD grids and centroids are successfully incorporated with the unsteady aeroelastic computation scheme. The most critical technology for the success of the proposed approach is the robust on-line parameter estimator, since the least-squares curve fitting method depends heavily on aeroelastic system frequencies and damping factors.

shape sensing↗

NASA NTRSDate not supplied

Error Localization Examples: Looking for a Needle in a Hay-stack

Finite element models (FEM) are routinely developed and used during fabrication of high dollar-value hardware. NASA as part of the pre-flight certification of launch vehicles routinely conducts vibration and static tests to calibrate models used for flight-risk assessments. As part of the calibration process, certain areas in the model are modified, using engineering judgment and sensitivity analysis, to match the test results. Unfortunately, tools to identify problem areas in the FEM using test data directly are scarce. Over the years, Error Localization Algorithms (ELA) have been proposed with very limited success. Recently, the Analytical Dynamics Model Improvement (ADMI) algorithm, which computes closed-form mass and stiffness corrections to match the test data exactly, have been shown to be effective for error localization. The paper will present several FEM example problems where ELA is used with simulated test data to determine FEM problem areas. For each example, the correct answer is shown along with ELA results. It is shown that the ELA process is able to identify general problem areas in the FEM, which are consistent with known model perturbations. However, in most cases the ELA identified area of improvement is larger than the true answer. Nonetheless, with proper optimization tools, calibration results using the ELA identified areas provide excellent results.

error localization↗

NASA NTRSDate not supplied

Probability Bounds Analysis Applied to Multi-Purpose Crew Vehicle Nonlinearity

The Multi-Purpose Crew Vehicle (MPCV) Program Orion vehicle finite element model (FEM) was updated based on a modal test performed by Lockheed Martin. Due to nonlinearity observed in the test results, linear low force level (LL) and high force level (HL) FEMs were developed for use during various Space Launch System (SLS) flight regimes depending on expected forcing levels. Uncertainty models were derived for the combined MPCV and MPCV Stage Adaptor LL and HL Hurty/Craig-Bampton (HCB) components based on the MPCV structural test article Configuration 4 modal test-analysis correlation results. Subsequently, system-level uncertainty quantification analyses were performed using both models for various SLS flight configurations to determine the impact of the nonlinearity on important system metrics. The system metrics included both transfer functions associated with attitude control and dynamic loads associated with aerodynamic buffeting during ascent. In each case, an independent Monte Carlo (MC) analysis was performed, and no attempt was made to combine the results. The Hybrid Parametric Variation (HPV) method was used to develop the LL and HL MPCV HCB uncertainty models. The HPV method provides both parametric and non-parametric components of uncertainty. The non-parametric uncertainty accounts for the difference in model-form between the linearized analytical model and the corresponding linearized component test results in the form of mode shapes and frequencies at that force level. This linear model-form uncertainty is implemented in the HPV method using random matrix theory. However, the HPV uncertainty models developed for the linear LL and HL MPCV components do not account for the nonlinearity in the MPCV. With respect to the linearized models, this nonlinearity is also an uncertainty in model form, but in this case, it must be treated independently as an epistemic uncertainty. It represents a lack of knowledge, in contrast to an aleatory uncertainty due to the randomness of a variable. In the case of an epistemic variable, the true value is unknown, only the interval within which it lies is known. Epistemic uncertainty can be reduced with increased knowledge, while in general, aleatory uncertainty cannot. This work combines the epistemic uncertainty due to the MPCV nonlinearity with the parametric and non-parametric uncertainty within the HPV method using a second order propagation approach. The LL and HL test data is augmented with surrogate test data derived from a nonlinear MPCV representation. The impact of the MPCV nonlinearity on system response statistics is determined using a series of cumulative distribution functions in the form of a horsetail plot, or p-box. This results in an interval of probabilities for a specific response value, or an interval of response values at a specific probability.

Daniel C Kammer↗

NASA NTRS2022

Uncertainty Models for the Hybrid Parametric Variation Method of Uncertainty Quantification; Analysis

There is some level of uncertainty in every finite element model (FEM), which flows to a level of uncertainty in predicted results. The purpose of uncertainty quantification (UQ) is to provide statistical bounds on prediction accuracy based on model uncertainty. This is distinct from model updating, which attempts to modify models to improve their accuracy. UQ does not improve the accuracy of models, but accepts that the models are inherently inaccurate and attempts to quantify the impact of that inaccuracy on predicted results. Previously, an alternate method for UQ, called the Hybrid Parametric Variation (HPV) method, was applied to Space Launch System (SLS) Hurty/Craig-Bampton (HCB) components to predict system-level statistics for launch vehicle attitude control transfer functions and core stage section loads due to buffet. The HPV method combines a parametric variation of the HCB fixed-interface (FI) modal frequencies with a nonparametric variation (NPV) method that randomly varies the HCB mass and stiffness matrices as Wishart random matrix distributions using random matrix theory (RMT). Alternatively, the most common method for modeling uncertainty in the structural dynamics community is a parametric approach, which varies physical parameters in the model. However, there are several disadvantages associated with the parametric method. Determining a reduced set of parameters that have a significant impact on the system response can be time consuming, and the selected parameter probability distributions are rarely reliably known. Therefore, in practice, the parameters are surrogates for the actual errors, and the link to parameter uncertainty is unknown. Another major drawback is that the uncertainty that can be represented is limited to the form of the nominal FEM. It is the experience of the authors that based on numerous aerospace programs, almost all FEM errors are in form rather than parameter values. This hypothesis is supported by the observation of the authors that it is almost never possible to ‘tune’ a FEM to match modal test results by only modifying model parameters. Model-form uncertainty cannot be directly represented by FEM input parameters nor included in a parametric approach. However, model-form uncertainty can be modeled using RMT, where a probability distribution is developed for the matrix ensemble of interest. The major advantage of the NPV method is that it covers errors in model form. The HPV method anchors uncertainty at the HCB component level to component modal test results by matching the HCB and test modes based on mode descriptions or other methods, and then applying differing levels of frequency variation. The specific variations depend on the confidence to which a component FEM has been validated through modal testing. The NPV method is layered on the frequency variation to match modal test self-orthogonality and cross-orthogonality (XO) results. Once the component uncertainty models are identified, they are assembled, and the uncertainty is propagated to the system level using a Monte Carlo (MC) analysis approach that generates statistics for system-level predictions This provides a UQ method that can be traced to test data, which can be updated as additional data and improved correlated models become available. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The second example is an application to a component that is design specific to the SLS. Based on this work and other assessments, the HPV method provides another tool to the toolset used for complex system UQ analysis. From experience gathered to date using the HPV method, additional design specific applications must be investigated to provide further confidence in the validity of the HPV method of UQ analysis.

Uncertainty quantification↗