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At least 325 records · Page 18

Estimating modal abundances from the spectra of natural and laboratory pyroxene mixtures using the modified Gaussian model

The modified Gaussian model (MGM) is used to explore spectra of samples containing multiple pyroxene components as a function of modal abundance. The MGM allows spectra to be analyzed directly, without the use of actual or assumed end-member spectra and therefore holds great promise for remote applications. A series of mass fraction mixtures created from several different particle size fractions are analyzed with the MGM to quantify the properties of pyroxene mixtures as a function of both modal abundance and grain size. Band centers, band widths, and relative band strengths of absorptions from individual pyroxenes in mixture spectra are found to be largely independent of particle size. Spectral properties of both zoned and exsolved pyroxene components are resolved in exsolved samples using the MGM, and modal abundances are accurately estimated to within 5-10 percent without predetermined knowledge of the end-member spectra.

Sunshine, Jessica M.↗

Integrated system identification and modal state estimation for control of flexible space structures

A novel approach of integrated system identification and modal state estimation is proposed for control of linear dynamical systems including flexible space structures. There are four steps involved in this approach. First, the relation between a stochastic state space model of a dynamical system and the coefficients of its autoregressive model with exogenous input is derived. Second, an adaptive least-squares transversal predictor is used to estimate the coefficients of the model. Third, a state space model and a steady state Kalman filter gain of the dynamical system are then identified from the coefficients of the model by using the eigensystem realization algorithm. Fourth, a modal state estimator is constructed using the modal parameters of the identified model. On-line implementation of this algorithm can continually improve the modal parameters and the filter gain. It can also gradually update the system model when the system characteristics are slowly changing. A numerical example is used to illustrate the feasibility of the new approach.

Chen, Chung-Wen↗

Static shape determination and control for a large space antenna

An integral operator approach is used to derive solutions to static shape determination and control problems associated with large space structures. Problem assumptions include a linear self-adjoint system model, observations and control forces at discrete points, and quadratic performance criteria for the comparison of estimates or control forces. Results are illustrated by simulations with a finite element model of a large space antenna. Modal expansions for terms in the solution algorithms are presented, using modes from the static or associated dynamic model. These expansions provide approximate solutions in the event that a closed form analytical solution to the system boundary value problem is not available.

Weeks, C.↗

Model reduction for flexible structures

Several conditions for a near-optimal reduction of general dynamic systems are presented focusing on the reduction in balanced and modal coordinates. It is shown that model and balanced reductions give very different results for the flexible structure with closely-spaced natural frequencies. In general, balanced reduction is found to give better results. A robust model reduction technique was developed to study the sensitivity of modeling error to variations in the damping of a structure. New concepts of grammians defined over a finite time and/or a frequency interval are proposed including computational procedures for evaluating them. Application of the model reduction technique to these grammians is considered to lead to a near-optimal reduced model which closely reproduces the full system output in the time and/or frequency interval.

Gawronski, Wodek↗

The effect of inertial coupling in the dynamics and control of flexible robotic manipulators

A general model of the dynamics of flexible robotic manipulators is presented, including the gross motion of the links, the vibrations of the links and joints, and the dynamic coupling between the gross motions and vibrations. The vibrations in the links may be modeled using lumped parameters, truncated modal summation, a component mode synthesis method, or a mixture of these methods. The local link inertia matrix is derived to obtain the coupling terms between the gross motion of the link and the vibrations of the link. Coupling between the motions of the links results from the kinematic model, which utilizes the method of kinematic influence. The model is used to simulate the dynamics of a flexible space-based robotic manipulator which is attached to a spacecraft, and is free to move with respect to the inertial reference frame. This model may be used to study the dynamic response of the manipulator to the motions of its joints, or to externally applied disturbances.

Tesar, Delbert↗

Damage detection in elastic structures using vibratory residual forces and weighted sensitivity

A methodology is presented for detecting structural damage in elastic structures by nondestructive means. Measured modal test data along with a correlated analytical structural model are used to locate potentially damaged regions using residual modal force vectors and to conduct a weighted sensitivity analysis to assess the extent of mass and/or stiffness variations, where damage is characterized as a stiffness reduction. The current approach is unique among other approaches in that it accounts for (1) variations in system mass, system stiffness, and mass center (locations), (2) perturbations of both the natural frequencies and modal vectors, and (3) statistical confidence factors for the structural parameters and potential experimental instrumentation error. Moreover, this procedure can be used with either full or reduced models. A wide variety of numerical examples are presented that show that the current method provides a precise indication of both the location and the extent of structural damage.

Ricles, J. M.↗

Parameter identification of material constants in a composite shell structure

One of the basic requirements in engineering analysis is the development of a mathematical model describing the system. Frequently comparisons with test data are used as a measurement of the adequacy of the model. An attempt is typically made to update or improve the model to provide a test verified analysis tool. System identification provides a systematic procedure for accomplishing this task. The terms system identification, parameter estimation, and model correlation all refer to techniques that use test information to update or verify mathematical models. The goal of system identification is to improve the correlation of model predictions with measured test data, and produce accurate, predictive models. For nonmetallic structures the modeling task is often difficult due to uncertainties in the elastic constants. A finite element model of the shell was created, which included uncertain orthotropic elastic constants. A modal survey test was then performed on the shell. The resulting modal data, along with the finite element model of the shell, were used in a Bayes estimation algorithm. This permitted the use of covariance matrices to weight the confidence in the initial parameter values as well as confidence in the measured test data. The estimation procedure also employed the concept of successive linearization to obtain an approximate solution to the original nonlinear estimation problem.

Martinez, David R.↗

Modal forced response of propfans in yawed flow

A modal forced response method for propfans in yawed flow is presented. This capability exists in the Aeroelastic Stability and Response of Propfan (ASTROP3) code developed at the Lewis Research Center. The code uses three-dimensional steady and unsteady cascade aerodynamics by Williams and Hwang (1986) and a NASTRAN finite element model to represent the blade structure. In addition, many utility programs exist in ASTROP3 that help in both the preprocessing of the NASTRAN model and the postprocessing of modal response results. The postprocessing work that computes the blade vibratory displacements and stresses in yawed flow are highlighted here.

Narayanan, G. V.↗

Experimental validation of finite element and boundary element methods for predicting structural vibration and radiated noise

This research report is presented in three parts. In the first part, acoustical analyses were performed on modes of vibration of the housing of a transmission of a gear test rig developed by NASA. The modes of vibration of the transmission housing were measured using experimental modal analysis. The boundary element method (BEM) was used to calculate the sound pressure and sound intensity on the surface of the housing and the radiation efficiency of each mode. The radiation efficiency of each of the transmission housing modes was then compared to theoretical results for a finite baffled plate. In the second part, analytical and experimental validation of methods to predict structural vibration and radiated noise are presented. A rectangular box excited by a mechanical shaker was used as a vibrating structure. Combined finite element method (FEM) and boundary element method (BEM) models of the apparatus were used to predict the noise level radiated from the box. The FEM was used to predict the vibration, while the BEM was used to predict the sound intensity and total radiated sound power using surface vibration as the input data. Vibration predicted by the FEM model was validated by experimental modal analysis; noise predicted by the BEM was validated by measurements of sound intensity. Three types of results are presented for the total radiated sound power: sound power predicted by the BEM model using vibration data measured on the surface of the box; sound power predicted by the FEM/BEM model; and sound power measured by an acoustic intensity scan. In the third part, the structure used in part two was modified. A rib was attached to the top plate of the structure. The FEM and BEM were then used to predict structural vibration and radiated noise respectively. The predicted vibration and radiated noise were then validated through experimentation.

Seybert, A. F.↗

Performing a Large-Scale Modal Test on the B2 Stand Crane at NASA's Stennis Space Center

A modal test of NASA's Space Launch System (SLS) Core Stage is scheduled to occur at the Stennis Space Center B2 test stand. A derrick crane with a 150-ft long boom, located at the top of the stand, will be used to suspend the Core Stage in order to achieve defined boundary conditions. During this suspended modal test, it is expected that dynamic coupling will occur between the crane and the Core Stage. Therefore, a separate modal test was performed on the B2 crane itself, in order to evaluate the varying dynamic characteristics and correlate math models of the crane. Performing a modal test on such a massive structure was challenging and required creative test setup and procedures, including implementing both AC and DC accelerometers, and performing both classical hammer and operational modal analysis. This paper describes the logistics required to perform this large-scale test, as well as details of the test setup, the modal test methods used, and an overview and application of the results.

Stasiunas, Eric C.↗

Performing a Large-Scale Modal Test on the B2 Stand Crane at NASA's Stennis Space Center

A modal test of NASA’s Space Launch System (SLS) Core Stage is scheduled to occur prior to propulsion system verification testing at the Stennis Space Center B2 test stand. A derrick crane with a 180-ft long boom, located at the top of the stand, will be used to suspend the Core Stage in order to achieve defined boundary conditions. During this suspended modal test, it is expected that dynamic coupling will occur between the crane and the Core Stage. Therefore, a separate modal test was performed on the B2 crane itself, in order to evaluate the varying dynamic characteristics and correlate math models of the crane. Performing a modal test on such a massive structure was challenging and required creative test setup and procedures, including implementing both AC and DC accelerometers, and performing both classical hammer and operational modal analysis. This paper describes the logistics required to perform this large-scale test, as well as details of the test setup, the modal test methods used, and an overview of the results.

Stasiunas, Eric C.↗

A hybrid approach to test-analysis-model development for large space structures

The present FEM reduction method for the generation of test-analysis-models (TAMs) in test-analysis correlation addresses contentions that the current modal TAM is hypersensitive to differences between test model shapes and analysis mode shapes, thereby generating large off-diagonal terms within the orthogonality and cross-orthogonality matrices employed in test-analysis mode-shape correlation. A hybrid TAM methodology is accordingly developed which combines the exact representation of the FEM target modes from the modal TAM with the more accurate TAM representation of the residual modes; the superior residual dynamics representation of the hybrid TAM is demonstrated for a detailed representation of a large space structure.

Kammer, D. C.↗

Time-domain approach for the transient responses in stratified viscoelastic Earth models

We have developed the numerical algorithm for the computation of transient viscoelastic responses in the time domain for a radially stratified Earth model. Stratifications in both the elastic parameters and the viscosity profile have been considered. The particular viscosity profile employed has a viscosity maximum with a constrast of O(100) in the mid lower mantle. The distribution of relaxation times reveals the presence of a continuous spectrum situated between O(100) and O(exp 4) years. The principal mode is embedded within this continuous spectrum. From this initial-value approach we have found that for the low degree harmonics the non-modal contributions are comparable to the modal contributions. For this viscosity model the differences between the time-domain and normal-mode results are found to decrease strongly with increasing angular order. These calculations also show that a time-dependent effective relaxation time can be defined, which can be bounded by the relaxation times of the principal modes.

Hanyk, L.↗

Distributed parameter estimation for NASA Mini-Mast truss through displacement measurements

Most methods of system identification of large flexible structures by far are based on the lumped parameter approach. Because of the considerable computational burden due to the large number of unknown parameters, distributed parameter approach, which greatly decreases the number of unknowns, has being investigated. In this paper a distributed parameter model for the estimation of modal characteristics of NASA Mini-Mast truss has been formulated. Both Bernoulli-Euler beam and Timoshenko beam equations are used to characterize the lateral bending vibrations of the truss. The measurement of the lateral displacement at the tip of the truss is provided to the maximum likelihood estimator. Closed-form solutions of the partial differential equations and closed-form expressions of the sensitivity functions are derived so that the estimation algorithm is highly efficient. The resulting estimates from test data by using Timoshenko beam model are found to be comparable to those derived from finite element analysis.

Huang, Jen-Kuang↗

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

Gibson, J. S.↗

Model reduction for flexible space structures

This paper presents the conditions under which modal truncation yields a near-optimal reduced-order model for a flexible structure. Next, a robust model reduction technique to cope with the damping uncertainties typical of flexible space structure is developed. Finally, a flexible truss and the COFS-1 structure are used to give realistic applications for the model reduction techniques studied in the paper.

Gawronski, Wodek↗

Calculating Nozzle Side Loads using Acceleration Measurements of Test-Based Models

As part of a NASA/MSFC research program to evaluate the effect of different nozzle contours on the well-known but poorly characterized "side load" phenomena, we attempt to back out the net force on a sub-scale nozzle during cold-flow testing using acceleration measurements. Because modeling the test facility dynamics is problematic, new techniques for creating a "pseudo-model" of the facility and nozzle directly from modal test results are applied. Extensive verification procedures were undertaken, resulting in a loading scale factor necessary for agreement between test and model based frequency response functions. Side loads are then obtained by applying a wide-band random load onto the system model, obtaining nozzle response PSD's, and iterating both the amplitude and frequency of the input until a good comparison of the response with the measured response PSD for a specific time point is obtained. The final calculated loading can be used to compare different nozzle profiles for assessment during rocket engine nozzle development and as a basis for accurate design of the nozzle and engine structure to withstand these loads. The techniques applied within this procedure have extensive applicability to timely and accurate characterization of all test fixtures used for modal test.A viewgraph presentation on a model-test based pseudo-model used to calculate side loads on rocket engine nozzles is included. The topics include: 1) Side Loads in Rocket Nozzles; 2) Present Side Loads Research at NASA/MSFC; 3) Structural Dynamic Model Generation; 4) Pseudo-Model Generation; 5) Implementation; 6) Calibration of Pseudo-Model Response; 7) Pseudo-Model Response Verification; 8) Inverse Force Determination; 9) Results; and 10) Recent Work.

Brown, Andrew M.↗

Decentralized control experiments on NASA's flexible grid

Methods arising from the area of decentralized control are emerging for analysis and control synthesis for large flexible structures. In this paper the control strategy involves a decentralized model reference adaptive approach using a variable structure control. Local models are formulated based on desired damping and response time in a model-following scheme for various modal configurations. Variable structure controllers are then designed employing co-located angular rate and position feedback. In this scheme local control forces the system to move on a local sliding mode in some local error space. An important feature of this approach is that the local subsystem is made insensitive to dynamical interactions with other subsystems once the sliding surface is reached. Experiments based on the above have been performed for NASA's flexible grid experimental apparatus. The grid is designed to admit appreciable low-frequency structural dynamics, and allows for implementation of distributed computing components, inertial sensors, and actuation devices. A finite-element analysis of the grid provides the model for control system design and simulation; results of several simulations are reported on here, and a discussion of application experiments on the apparatus is presented.

Ozguner, U.↗