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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS2015

Subharmonic Oscillations and Chaos in Dynamic Atomic Force Microscopy

The increasing use of dynamic atomic force microscopy (d-AFM) for nanoscale materials characterization calls for a deeper understanding of the cantilever dynamics influencing scan stability, predictability, and image quality. Model development is critical to such understanding. Renormalization of the equations governing d- AFM provides a simple interpretation of cantilever dynamics as a single spring and mass system with frequency dependent cantilever stiffness and damping parameters. The renormalized model is sufficiently robust to predict the experimentally observed splitting of the free-space cantilever resonance into multiple resonances upon cantilever-sample contact. Central to the model is the representation of the cantilever sample interaction force as a polynomial expansion with coefficients F(sub ij) (i,j = 0, 1, 2) that account for the effective interaction stiffness parameter, the cantilever-to-sample energy transfer, and the amplitude of cantilever oscillation. Application of the Melnikov method to the model equation is shown to predict a homoclinic bifurcation of the Smale horseshoe type leading to a cascade of period doublings with increasing drive displacement amplitude culminating in chaos and loss of image quality. The threshold value of the drive displacement amplitude necessary to initiate subharmonic generation depends on the acoustic drive frequency, the effective damping coefficient, and the nonlinearity of the cantilever-sample interaction force. For parameter values leading to displacement amplitudes below threshold for homoclinic bifurcation other bifurcation scenarios can occur, some of which lead to chaos.

Cantrell, John H.↗
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

Error Localization Examples: Looking for a Needle in a Haystack

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. During model calibration, certain areas of 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 and infrequently applied. Over the years, error localization algorithms 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 an effective Error Localization Algorithm (ELA). The paper discusses three examples where ELA is used with simulated test data to locate problem areas. To gain confidence in the approach, the exact answer is shown along with ELA results. Results show that ELA is able to identify general problem areas consistent with known problem areas. In all examples, the ELA identified area is larger than the exact problem area. Nonetheless, with proper optimization tools, calibration results using the ELA identified areas provide excellent results.

model calibration↗
NASA NTRS1996

Steady-State Dynamic Behavior of a Flexible Rotor With Auxiliary Support From a Clearance Bearing

This paper investigates the steady-state responses of a rotor system supported by auxiliary bearings in which there is a clearance between the rotor and the inner race of the bearing. A simulation model based upon the rotor of a production jet engine is developed and its steady-state behavior is explored over a wide range of operating conditions for various parametric configurations. Specifically, the influence of rotor imbalance, clearance, support stiffness and damping is studied. Bifurcation diagrams are used as a tool to examine the dynamic behavior of this system as a function of the afore mentioned parameters. The harmonic balance method is also employed for synchronous response cases. The observed dynamical responses is discussed and some insights into the behavior of such systems are presented.

Xie, Huajun↗
NASA NTRS1995

NASA-GRA--Geared-Rotor Analyzer

NASA-GRA computer program designed to solve for steady-state dynamic responses of multigeared rotor systems. Based on transfer-matrix method combined with harmonic-balance method. Includes accurate gear-mesh model for spur and helical gears, containing time-varying mesh stiffnesses, gear-mounting errors, and gear-profile errors. Also includes accurate disk model containing inertia-based dynamic coupling terms due to mass and skew unbalances and massless-elastic-shaft model and linearly coupled fluid-film bearing model. Written in FORTRAN 77.

Park, N.↗
NASA NTRS1989

Results of a parametric aeroelastic stability analysis of a generic X-wing aircraft

This paper discusses the trends in longitudinal dynamic aeroelastic stability of a generic x-wing aircraft model with design parameter variations. X-wing rotor blade sweep angle, ratio of blade mass to total vehicle mass, blade structural stiffness cross-coupling and vehicle center-of-gravity location were parameters considered. The typical instability encountered is body-freedom flutter involving a low frequency interaction of the first elastic mode and the aircraft short period mode. Parametric cases with the lowest static margin consistently demonstrated the highest flutter dynamic pressures. As mass ratio was increased, the flutter boundary decreased. The decrease was emphasized as center-of-gravity location was moved forward. As sweep angle varied, it was observed that the resulting increase in forward-swept blade bending amplitude relative to aft blade bending amplitude in the first elastic mode had a stabilizing effect on the flutter boundary. Finally, small amounts of stiffness cross-coupling in the aft blades increased flutter dynamic pressure.

Woods, Jessica A.↗
NASA NTRS1989

Results of a parametric aeroelastic stability analysis of a generic X-wing aircraft

This paper discusses the trend in longitudinal dynamic aeroelastic stability of a generic X-Wing aircraft model with design parameter variations. X-Wing rotor blade sweep angle, ratio of blade mass to total vehicle mass, blade structural stiffness cross-coupling and vehicle center-of-gravity location were parameters considered. The typical instability encountered is body-freedom flutter involving a low frequency interaction of the first elastic mode and the aircraft short period mode. Parametric cases with the lowest static margin consistently demonstrated the highest flutter dynamic pressures. As mass ratio was increased, the flutter boundary decreased. The decrease was emphasized as center-of-gravity location was moved forward. As sweep angle varied, it was observed that the resulting increase in forward-swept blade bending amplitude relative to aft blade bending amplitude in the first elastic mode had a stabilizing effect on the flutter boundary. Finally, small amounts of stiffness cross-coupling in the aft blades increased flutter dynamic pressure.

Woods, Jessica A.↗
NASA NTRS1973

Reduction of truncation errors in modal analysis

A condensation method and computer program are described for large discrete parameter vibration analysis of complex structures that greatly reduces truncation errors and provides accurate definition of modes in a selected frequency range. A dynamic transformation is obtained from the partitioned equations of motion that relates modes not explicitly in the condensed solution to the retained modes at a selected system frequency. The generalized mass and stiffness matrices, obtained with existing modal synthesis methods, are reduced using this transformation and solved. Revised solutions are then obtained using new transformations at the calculated eigenvalues and are also used to assess the accuracy of the results. Computations are made tractable by simplified forms of the transformation that result with various modal synthesis methods. Three examples using the dynamic transformation in conjunction with a General Electric stiffness coupling method and the method of Craig and Bampton indicate large reductions in truncation errors and demonstrate the method for sequential groups of modes.

Kuhar, E. J.↗
NASA NTRS1981

Automated dynamic analytical model improvement

A method is developed and illustrated which finds minimum changes in analytical mass and stiffness matrices to make them consistent with a set of measured normal modes and natural frequencies. The corrected model is an improved base for studies of physical changes, changes in boundary conditions, and for prediction of forced responses. Features of the method are: efficient procedures not requiring solutions of the eigenproblem; the model may have more degrees of freedom than the test data; modal displacements at all the analytical degrees of freedom are obtained; the frequency dependence of the coordinate transformations are properly treated.

Berman, A.↗
NASA NTRS1963

Investigation of Propeller-power-plant Autoprecession Boundaries for a Dynamic-aeroelastic Model of a Four-engine Turboprop Transport Airplane

A flexibly mounted aircraft engine may under certain conditions experience a self-excited whirling instability involving a coupling between the gyroscopic and aerodynamic forces acting on the propeller, and the inertial, elastic, and damping forces contributed by the power plant, nacelle, and wing. This phenomenon has been called autoprecession, or whirl instability. An experimental investigation was made in the Langley transonic dynamics tunnel at Mach numbers below 0.3 to study some of the pertinent parameters influencing the phenomenon. These parameters included propeller rotational speed, stiffness of the power-plant assembly in the pitch and yaw planes and the ratio of pitch stiffness to yaw stiffness, structural damping of the power-plant assembly in the pitch and yaw planes, simulated fuel load in the wings, and the location and number of autoprecessing powerplant assemblies. A large dynamic-aeroelastic model of a four-engine turboprop transport airplane mounted on a vertical rod in a manner which provided several limited body degrees of freedom was used in the investigation. It was found that the boundary for autoprecession decreased markedly with Increasing proreduction of power-plant stiffness and/or damping, and to a lesser degree decreased with reduction of simulated fuel load in the wings. peller rotational speed generally lowered the autoprecession boundary. This effect was more pronounced as the stiffness was increased. An inboard power plant was found to be more susceptible to autoprecession than an outboard one. Combinations in which two or more power plants had the same level of reduced stiffness resulted in autoprecession boundaries considerably lower than that of a single power plant with the same level of reduced stiffness.

POWER PLANT↗
NASA NTRS1974

User's Manual for Computer Program ROTOR

A detailed description of a computer program to calculate tilt-rotor aircraft dynamic characteristics is presented. This program consists of two parts: (1) the natural frequencies and corresponding mode shapes of the rotor blade and wing are developed from structural data (mass distribution and stiffness distribution); and (2) the frequency response (to gust and blade pitch control inputs) and eigenvalues of the tilt-rotor dynamic system, based on the natural frequencies and mode shapes, are derived. Sample problems are included to assist the user.

Yasue, M.↗
NASA NTRS1986

Symbolic generation of elastic rotor blade equations using a FORTRAN processor and numerical study on dynamic inflow effects on the stability of helicopter rotors

The process of performing an automated stability analysis for an elastic-bladed helicopter rotor is discussed. A symbolic manipulation program, written in FORTRAN, is used to aid in the derivation of the governing equations of motion for the rotor. The blades undergo coupled bending and torsional deformations. Two-dimensional quasi-steady aerodynamics below stall are used. Although reversed flow effects are neglected, unsteady effects, modeled as dynamic inflow are included. Using a Lagrangian approach, the governing equations are derived in generalized coordinates using the symbolic program. The program generates the steady and perturbed equations and writes into subroutines to be called by numerical routines. The symbolic program can operate on both expressions and matrices. For the case of hovering flight, the blade and dynamic inflow equations are converted to equations in a multiblade coordinate system by rearranging the coefficients of the equations. For the case of forward flight, the multiblade equations are obtained through the symbolic program. The final multiblade equations are capable of accommodating any number of elastic blade modes. The computer implementation of this procedure consists of three stages: (1) the symbolic derivation of equations; (2) the coding of the equations into subroutines; and (3) the numerical study after identifying mass, damping, and stiffness coefficients. Damping results are presented in hover and in forward flight with and without dynamic inflow effects for various rotor blade models, including rigid blade lag-flap, elastic flap-lag, flap-lag-torsion, and quasi-static torsion. Results from dynamic inflow effects which are obtained from a lift deficiency function for a quasi-static inflow model in hover are also presented.

Reddy, T. S. R.↗
NASA NTRS1991

Active damping application to the shuttle RMS

Control Structure Interaction (CSI) is a relatively new technology developed over the last 10 to 15 years for application to large flexible space vehicles. The central issue is recognition that high performance control systems necessary for good spacecraft performance may adversely interact with the dynamics of the spacecraft structures, a problem increasingly aggravated by the large size and reduced stiffness of modern spacecraft structural designs. The CSI analysis and design methods were developed to avoid interactions while maintaining spacecraft performance without exceeding structural capabilities, but they remain largely unvalidated by hardware experiments or demonstrations, particularly in-space flight demonstrations. One recent proposal for a low cost flight validation of CSI technology is to demonstrate active damping augmentation of the Space Shuttle Remote Manipulator System (RMS). An analytical effort to define the potential for such an active damping augmentation demonstration to improve the structural dynamic response of the RMS following payload maneuvers is described. It is hoped that this study will lead to an actual inflight CSI test with the RMS using existing shuttle hardware to the maximum extent possible. By using the existing hardware, the flight demonstration results may eventually be of direct benefit to actual Space Shuttle RMS operations, especially during the construction of the Space Station Freedom.

Gilbert, Michael G.↗
NASA NTRS1990

Dynamic analysis of space-related linear and non-linear structures

In order to be cost effective, space structures must be extremely light weight, and subsequently, very flexible structures. The power system for Space Station Freedom is such a structure. Each array consists of a deployable truss mast and a split blanket of photovoltaic solar collectors. The solar arrays are deployed in orbit, and the blanket is stretched into position as the mast is extended. Geometric stiffness due to the preload make this an interesting non-linear problem. The space station will be subjected to various dynamic loads, during shuttle docking, solar tracking, attitude adjustment, etc. Accurate prediction of the natural frequencies and mode shapes of the space station components, including the solar arrays, is critical for determining the structural adequacy of the components, and for designing a dynamic controls system. The process used in developing and verifying the finite element dynamic model of the photo-voltaic arrays is documented. Various problems were identified, such as grounding effects due to geometric stiffness, large displacement effects, and pseudo-stiffness (grounding) due to lack of required rigid body modes. Analysis techniques, such as development of rigorous solutions using continuum mechanics, finite element solution sequence altering, equivalent systems using a curvature basis, Craig-Bampton superelement approach, and modal ordering schemes were utilized. The grounding problems associated with the geometric stiffness are emphasized.

Bosela, Paul A.↗
NASA NTRS1990

Dynamic analysis of space-related linear and non-linear structures

In order to be cost effective, space structures must be extremely light weight, and subsequently, very flexible structures. The power system for Space Station Freedom is such a structure. Each array consists of a deployable truss mast and a split blanket of photo-voltaic solar collectors. The solar arrays are deployed in orbit, and the blanket is stretched into position as the mast is extended. Geometric stiffness due to the preload make this an interesting non-linear problem. The space station will be subjected to various dynamic loads, during shuttle docking, solar tracking, attitude adjustment, etc. Accurate prediction of the natural frequencies and mode shapes of the space station components, including the solar arrays, is critical for determining the structural adequacy of the components, and for designing a dynamic control system. The process used in developing and verifying the finite element dynamic model of the photo-voltaic arrays is documented. Various problems were identified, such as grounding effects due to geometric stiffness, large displacement effects, and pseudo-stiffness (grounding) due to lack of required rigid body modes. Analysis techniques, such as development of rigorous solutions using continuum mechanics, finite element solution sequence altering, equivalent systems using a curvature basis, Craig-Bampton superelement approach, and modal ordering schemes were utilized. The grounding problems associated with the geometric stiffness are emphasized.

Bosela, Paul A.↗
NASA NTRS1992

Lumped mass modelling for the dynamic analysis of aircraft structures

Aircraft structures may be modelled by lumping the masses at particular strategic points and the flexibility or stiffness of the structure is obtained with reference to these points. Equivalent moments of inertia for the section at these positions are determined. The lumped masses are calculated based on the assumption that each point will represent the mass spread on one half of the space on each side. Then these parameters are used in the differential equation of motion and the eigen characteristics are determined. A comparison is made with results obtained by other established methods. The lumped mass approach in the dynamic analysis of complicated structures provides an easier means of predicting the dynamic characteristics of these structures. It involves less computer time and avoids computational errors that are inherent in the numerical solution of complicated systems.

Abu-Saba, Elias G.↗
NASA NTRS1977

Fluid-film bearing damper

Device for rotating machinery has noncircular support that allows changes in dynamic properties. Device can be controlled for either manually or automatically altering its stiffness and damping properties without interruption of operation.

Cunningham, R. E.↗
NASA NTRS1982

Comparative evaluation of three shaft seals proposed for high performance turbomachinery

Experimental pressure profiles and leak rate characteristics for three shaft seal prototype model configurations proposed for the space shuttle turbopump were assessed in the concentric and fully eccentric, to point of rub, positions without the effects of rotation. The parallel-cylindrical configuration has moderate to good stiffness with a higher leak rate. It represents a simple concept, but for practical reasons and possible increases in stability, all such seals should be conical-convergent. The three-stepdown-sequential, parallel-cylindrical seal is converging and represents good to possible high stiffness when fluid separation occurs, with a significant decrease in leak rate. Such seals can be very effective. The three-stepdown-sequential labyrinth seal of 33-teeth (i.e., 12-11-10 teeth from inlet to exit) provides excellent leak control but usually has very poor stiffness, depending on cavity design. The seal is complex and not recommended for dynamic control.

Hendricks, R. C.↗