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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Vibrations of circular elastic plates due to sonic boom.

The problem of transient axisymmetric vibrations of thin circular elastic plates due to sonic boom excitation is investigated. The equation of motion for a solid circular plate is solved by applying the modified finite Hankel transform and the Laplace transform, and the numerical results are obtained with the help of the digital computer. From the analysis of the data, obtained for the dynamic deflections of the plates for the boom duration, it is concluded that for a normal flight the boom duration has a significant effect on the vibrations of plates as compared to the overpressure of the boom.

Pavagadhi, L. J.↗
NASA NTRS1985

Nonlinear theory for laminated and thick plates and shells including the effects of transverse shearing

Nonlinear strain displacement relations for three-dimensional elasticity are determined in orthogonal curvilinear coordinates. To develop a two-dimensional theory, the displacements are expressed by trigonometric series representation through-the-thickness. The nonlinear strain-displacement relations are expanded into series which contain all first and second degree terms. In the series for the displacements only the first few terms are retained. Insertion of the expansions into the three-dimensional virtual work expression leads to nonlinear equations of equilibrium for laminated and thick plates and shells that include the effects of transverse shearing. Equations of equilibrium and buckling equations are derived for flat plates and cylindrical shells. The shell equations reduce to conventional transverse shearing shell equations when the effects of the trigonometric terms are omitted and to classical shell equations when the trigonometric terms are omitted and the shell is assumed to be thin.

Stein, M.↗
NASA NTRS1991

Variational finite element-tensor formulation for the large deflection random vibration of composite plates

A numerical integration routine is derived from a set of unified single step integration algorithms using a weighted satisfaction of the equilibrium equation governing the large deflection random response of laminated composite plates. The equilibrium equation is derived using a constant matrix large deflection finite-element formulation. In-plane inertia terms are considered in the formulation, however, rotary inertia terms are assumed negligible. Probability density, spectral density and autocorrelation functions of the maximum displacement and strain responses are presented for three acoustic excitation levels. Classical thin plate boundary conditions and pseudo white noise excitation are used in this investigation.

Robinson, Jay H.↗
DOE OSTI2025

Elastic Bayesian Model Calibration

Functional data are ubiquitous in scientific modeling. For instance, quantities of interest are modeled as functions of time, space, energy, density, etc. Uncertainty quantification methods for computer models with functional response have resulted in tools for emulation, sensitivity analysis, and calibration that are widely used. However, many of these tools do not perform well when the computer model’s parameters control both the amplitude variation of the functional output and its alignment (or phase variation). This paper introduces a framework for Bayesian model calibration when the model responses are misaligned functional data. The approach generates two types of data out of the misaligned functional responses: (1) aligned functions so that the amplitude variation is isolated and (2) warping functions that isolate the phase variation. These two types of data are created for the computer simulation data (both of which may be emulated) and the experimental data. The calibration approach uses both types so that it seeks to match both the amplitude and phase of the experimental data. The framework is careful to respect constraints that arise, especially when modeling phase variation, and is framed in a way that it can be done with readily available calibration software. In conclusion, we demonstrate the techniques on two simulated data examples and on two dynamic material science problems: a strength model calibration using flyer plate experiments and an equation of state model calibration using experiments performed on the Sandia National Laboratories’ Z-machine.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1972

Numerical solutions of the Navier-Stokes equations for the supersonic laminar flow over a two-dimensional compression corner

Numerical solutions have been obtained for the supersonic, laminar flow over a two-dimensional compression corner. These solutions were obtained as steady-state solutions to the unsteady Navier-Stokes equations using the finite difference method of Brailovskaya, which has second-order accuracy in the spatial coordinates. Good agreement was obtained between the computed results and wall pressure distributions measured experimentally for Mach numbers of 4 and 6.06, and respective Reynolds numbers, based on free-stream conditions and the distance from the leading edge to the corner. In those calculations, as well as in others, sufficient resolution was obtained to show the streamline pattern in the separation bubble. Upstream boundary conditions to the compression corner flow were provided by numerically solving the unsteady Navier-Stokes equations for the flat plate flow field, beginning at the leading edge. The compression corner flow field was enclosed by a computational boundary with the unknown boundary conditions supplied by extrapolation from internally computed points.

Carter, J. E.↗
NASA NTRS1976

The nonlinear transient response of thin, rectangular elastic plates

The results of experiments and theoretical analysis of the nonlinear, transient response of thin, rectangular, elastic, simply supported plates are presented. In the experiments, a plane wave tube with a special pulse generator at one end and a thin glass plate mounted at the other end was used to subject the glass plate to pressure pulses of different magnitudes. Whole-field measurements of the response of the plate were obtained by the reflected moire grid technique. The largest ratio of center deflection to thickness of the plate during the experiments was 5.6. The theoretical response of the glass plate to the pressure pulses was computed by solving the von Karman equations governing large deflections in elastic plates by two methods - (1) the finite-difference method, and (2) Galerkin's method. Good agreement was found between theoretically predicted and experimentally measured response.

Rajagopal, G.↗
NASA NTRS1984

Reduction of astrometric plates

A rapid and accurate method for the reduction of comet or asteroid plates is described. Projection equations, scale length correction, rotation of coordinates, linearization, the search for additional reference stars, and the final solution are examined.

Stock, J.↗
NASA NTRS1987

A Von Karman integral approach to a two phase boundary layer problem

A Von Karman integral approximation of a two phase boundary layer is developed for bodies of arbitrary shape. The flow field considered is that of the injection of water through a porous airfoil. A solution for the special case of a flat plate is presented. The equations for the airfoil solution are developed and possible effects on airflow separation are discussed.

Henry, R.↗
NASA NTRS1986

Boundary layer transition

The boundary layer stability, its active control by sound and surface heating and the effect of curvature are studied numerically and experimentally for subsonic flow. In addition, the experimental and flight test data are correlated using the stability theory for supersonic Mach numbers. Active transition fixing and feedback control of boundary layer by sound interactions are experimentally investigated at low speed over an airfoil. Numerical simulation of active control by surface heating and cooling in air shows that by appropriate phase adjustment a reduction in the level of perturbation can be obtained. This simulation is based on the solution of two-dimensional compressible Navier-Stokes equations for a flat plate. Goertler vortices are studied experimentally on an airfoil in the Low Turbulence Pressure Tunnel (LTPT). The flow pattern was visualized using the sublimating chemical technique and data were obtained using a three component laser velocimeter. The effect of curvature on swept leading-edge stability on a cylinder was numerically studied. The results suggest that transition is dominated by traveling disturbance waves and that the waves with the greatest total amplification has an amplitude ratio of e sup 11. Experimental data from the quiet supersonic tunnel and flight tests are analyzed using linear compressible stability theory.

Maestrello, L.↗
NASA NTRS1997

Application of Normal Mode Expansion to AE Waves in Finite Plates

Breckenridge et al. (1975), Hsu (1985) and Pao (1978) adapted approaches from seismology to calculate the response at the surface of an infinite half-space and an infinite plate. These approaches have found use in calibrating acoustic emission (AE) transducers. However, it is difficult to extend this theoretical approach to AE testing of practical structures. Weaver and Pao (1982) considered a normal mode solution to the Lamb equations. Hutchinson (1983) pointed out the potential relevance of Mindlin's plate theory (1951) to AE. Pao (1982) reviewed Medick s (1961) classical plate theory for a point source, but rejected it as useful for AE and no one seems to have investigated its relevance to AE any further. Herein, a normal mode solution to the classical plate bending equation was investigated for its applicability to AE. The same source-time function chosen by Weaver and Pao is considered. However, arbitrary source and receiver positions are chosen relative to the boundaries of the plate. This is another advantage of the plate theory treatment in addition to its simplicity. The source does not have to be at the center of the plate as in the axisymmetric treatment. The plate is allowed to remain finite and reflections are predicted. The importance of this theory to AE is that it can handle finite plates, realistic boundary conditions, and can be extended to composite materials.

Gorman, M. R.↗
NASA NTRS1990

A study of delamination buckling of laminates

The subject of this paper is the buckling of laminated plates, with a preexisting delamination, subjected to in-plane loading. Each laminate is modelled as an orthotropic Mindlin plate. The analysis is carried out by a combination of the finite element and asymptotic expansion methods. By applying the finite element method, plates with general delamination regions can be studied. The asymptotic expansion method reduces the number of unknown variables of the eigenvalue equation to that of the equation for a single Kirchhoff plate. Numerical results are presented for several examples. The effects of the shape, size, and position of the delamination on the buckling load are studied through these examples.

Mukherjee, Yu-Xie↗
NASA NTRS1977

Computations of supersonic viscous flow over a finite-width plate

Finite difference methods were applied to solve the parabolic Navier-Stokes equations for the flow over a finite width plate at 0 deg and 10 deg angles of attack. The methods were developed on the basis of the operator factorization concept resulting in the split of a three dimensional equation into successive two dimensional equations. Backward and centered implicit factorization schemes, were used and their results were compared. Available numerical solutions and experimental data obtained at low Reynolds number conditions were also used for comparison. The backward implicit method provides a more successful solution, which ranges from the merged layer to the strong interaction regimes. Detailed structures were revealed of the shear layer around and behind the side edge.

Li, C. P.↗
NASA NTRSDate not supplied

Accuracy of Center of Pressure Determination via Motion Capture

BACKGROUND: This study was conducted to support the stability assessment for tasks in lunar gravity and exercises on a Vibration Isolation and Stabilization (VIS) system in microgravity based on the dynamic feasibility criterion of whether the calculated position of the center of pressure (COP) falls within the base of support (BOS) which outlines the subject’s feet. Motion capture data combined with biomechanical modeling and simulation allows the forces and moments between the human and the VIS platform to be computed and the position of the COP as well as the location and shape of the BOS to be determined. The goal of this study was to assess the accuracy of the COP trajectory calculated using motion capture-based data. METHODS AND RESULTS: To obtain the dynamic quantities from which COP is calculated, motion capture data is first collected in the 1g lab environment by recording the trajectories of passive retroreflective markers placed on a subject during exercise or performance of a given task. The OpenSim [1] inverse kinematics (IK) tool is used to fit a scaled subject model to recorded marker trajectories while minimizing marker error to obtain joint angles. Then, a custom OpenSim plugin [2] is used to determine the subject’s time-varying moment of inertia and its time derivative, center of mass (CM) position, velocity, and acceleration, as well as the angular momentum and its time derivative relative to the subject’s CM. Some of these quantities are not needed for modeling tasks performed on a stationary lunar surface but, due to the moving exercise platform, are needed to model VIS response to the subject’s motion. Hand positions, used in calculating a cable force if present, are recorded as well. These quantities are used to calculate the total force (F ⃗^((plate) )) and moment (M ⃗^((plate) )) exerted by the lunar surface or the VIS plate on the subject’s shoe soles. COP is then calculated from the following equations: r_x^((cop) )= M_z^((plate) )/F_y^((plate) ) and r_z^((cop) )= 〖-M〗_x^((plate) )/F_y^((plate) ), where the y axis is normal to the surface. COP accuracy for feasibility assessments is then determined by whether it falls within the BOS, which is also computed by the plugin. To study the accuracy of COP calculated from motion capture, we first investigated whether COP remained within the BOS, as it must, for exercises performed in the 1g lab environment. Standard exercises such as back squat and deadlift were analyzed, as well as more explosive exercises including hang clean and press. Cases in which the COP exited the BOS indicated that COP accuracy required further investigation. In this study, an exercise device with cables was used, so cable force modeling accuracy should also be considered. In a separate study, we collected motion capture and force plate data for twenty-seven motions not involving an exercise device. About a third were genuine countermeasures exercises (e.g., hang clean and press), some were relevant for lunar tasks (e.g., object pick up), and the rest were of a “unit test” nature (e.g., swaying back and forth or side to side). Motion capture-based COP positions were compared with force plate measured COP. We found that while force plate measured COP remained within the BOS, motion capture-based COP was observed to briefly exit the BOS on occasion. Techniques to mitigate IK artifacts and filtering of calculated data could be used to improve the agreement of calculated and measured results, resolving excursions from the BOS within this dataset. The mean error between calculated and measured COP was found to be less than 6 mm. Additionally, we derived and investigated equations for the COP in terms of the cable force, cable location, as well as the human CM position, acceleration, and angular momentum with respect to the CM, and analyzed them for sensitivity to errors in individual quantities. Several were found, but the most significant one was that when the vertical force on the feet approaches zero, indicating a near-detachment or ‘jump off’ condition, errors are amplified. This is consistent with the observation that in the absence of pressure, the concept of the center of pressure would become meaningless.

C A Bell↗
NASA NTRS1982

Stability of mean flows over an infinite flat plate

The present investigation is mainly concerned with a stability analysis for the linearized Navier-Stokes equations for parallel and nonparallel mean flows over an infinite flat plate. The system of equations for parallel flows is presented. The system is viewed as a generalized Orr-Sommerfeld equation. Attention is given to an explicit criterion characterizing the case when the stability of all physically reasonable solutions is determined by the eigenvalues. The proof given in the investigation is applicable to both the generalized Orr-Somerfeld equations and the modified equations for nonparallel flow. The fact that the criterion is independent of the completeness or incompleteness of eigenfunctions is contrary to some expectations.

Miklavcic, M.↗
NASA NTRS1985

Noise Transmission Loss of a Rectangular Plate in an Infinite Baffle

An improved analytical procedure was developed that allows for the efficient calculation of the noise transmission characteristics of a finite rectangular plate. Both isotropic and symmetrically laminated composite plates are considered. The plate is modeled with classic thin-plate theory and is assumed to be simply supported on all four sides. The incident acoustic pressure is assumed to be a plane wave impinging on the plate at an arbitrary angle. The reradiated pressure is assumed to be negligible compared with the blocked pressure, and the plate vibrations are calculated by a normal-mode approach. A Green's function integral equation is used to link the plate vibrations to be transmitted far-field sound waves, and transmission loss is calculated from the ratio of incident to transmitted acoustic powers. The result is a versatile research and engineering analysis tool that predicts noise transmission loss and enables the determination of the modal behavior of the plate.

Roussos, Louis A.↗