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At least 235 records · Page 13

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NASA NTRS1983

Nonlinear structural dynamics analysis using a modified modal method

The procedure for predicting the nonlinear dynamic response of structural components subjected to a step loading is presented. The procedure is a modified modal method that involves a change of dependent variables from the unknown nodal degrees of freedom of the finite element model of the structure to a smaller set of generalized coordinates. This change of dependent variables uses a combination of the nonlinear static solution and some selected vibration mode shapes. The vibration mode shapes correspond to the eigenvectors obtained by solving a standard free vibration eigenvalue problem wherein the stiffness matrix is expanded about the nonlinear static solution. A strategy is also presented for determining which and how many vibration mode shapes to include in the transformation. The effect of inaccurate representation of the spatial distribution of the applied load on the nonlinear dynamic response is discussed for two classes of structural behavior. Application of the procedure to structures which exhibit a stiffening behavior and to those with a softening behavior is presented.

Knight, N. F., Jr.↗

NASA NTRS1983

Linear and Nonlinear Aspects of Rotordynamics

Excessive vibrations of the liquid oxygen pump in the Space Shuttle's Main Engine have been recorded during hot firing ground testing. In order to determine mathematical explanations of this possibility, destructive phenomenon differential equations have been examined which describe the rotordynamics of the pump. Modeling the rotor as a random eigenvalue problem was considered. Analytical expressions were derived for the solution in the case of symmetric damping and stiffness. This enables one to determine accuracy estimates when testing numerical techniques to solve both asymmetric and nonlinear problems. Finally, the rotor model has had nonlinear elements incorporated to improve its simulation of the pump and to expand the corresponding mathematical theory.

Day, W. B.↗

NASA NTRS1984

Vibration and buckling of general periodic lattice structures

A method is presented for vibration and buckling analysis of arbitrary lattice structures having repetitive geometry in any combination of coordinate directions. The approach is based on exact member theory for representing the stiffness of an individual member subject to axial load, and in the case of vibration, undergoing harmonic oscillation. The method is an extension of previous work that was limited to specific geometries. The resulting eigenvalue problem is of the size associated with the repeating element of the structure. A computer program has been developed incorporating the theory and results are given for vibration of rectangular platforms and a large antenna structure having rotational symmetry. Buckling and vibration results for cable-stiffened rings are also given.

Anderson, M. S.↗

NASA NTRS1983

Mechanics of composite materials: Recent advances; Proceedings of the Symposium, Virginia Polytechnic Institute and State University, Blacksburg, VA, August 16-19, 1982

The present conference on the mechanics of composites discusses microstructure's influence on particulate and short fiber composites' thermoelastic and transport properties, the elastoplastic deformation of composites, constitutive equations for viscoplastic composites, the plasticity and fatigue of metal matrix composites, laminate damping mechanisms, the micromechanical modeling of Kevlar/epoxy composites' time-dependent failure, the variational characterization of waves in composites, and computational methods for eigenvalue problems in composite design. Also discussed are the elastic response of laminates, elastic coupling nonlinear effects in unsymmetrical laminates, elasticity solutions for laminate problems having stress singularities, the mechanics of bimodular composite structures, the optimization of laminated plates and shells, NDE for laminates, the role of matrix cracking in the continuum constitutive behavior of a damaged composite ply, and the energy release rates of various microcracks in short fiber composites.

Hashin, Z.↗

NASA NTRS1984

A survey of payload integration methods

Several full-scale and short-cut methods for analyzing a booster/payload system are presented. Two full-scale techniques are considered: (1) a technique that uses a restrained payload together with a free-booster model, the latter being augmented with residual mass and stiffness correction and (2) a technique that uses a restrained payload and booster model. Both techniques determine the 'modal modes', which require the solution of a system eigenvalue problem; the loads usually are then determined via an acceleration approach. A brief description is given of a number of short-cut methods which are of special interest to Shuttle payload design: structural modification, base drive, and interface impedance methods. Directions for further research and development are suggested.

Engels, R. C.↗

NASA NTRS1983

Planar dynamics of a uniform beam with rigid bodies affixed to the ends

The planar dynamics of a uniform elastic beam subject to a variety of geometric and natural boundary conditions and external excitations were analyzed. The beams are inextensible and capable of small transverse bending deformations only. Classical beam vibration eigenvalue problems for a cantilever with tip mass, a cantilever with tip body and an unconstrained beam with rigid bodies at each are examined. The characteristic equations, eigenfunctions and orthogonality relations for each are derived. The forced vibration of a cantilever with tip body subject to base acceleration is analyzed. The exact solution of the governing nonhomogeneous partial differential equation with time dependent boundary conditions is presented and compared with a Rayleigh-Ritz approximate solution. The arbitrary planar motion of an elastic beam with rigid bodies at the ends is addressed. Equations of motion are derived for two modal expansions of the beam deflection. The motion equations are cast in a first order form suitable for numerical integration. Selected FORTRAN programs are provided.

Storch, J.↗

NASA NTRS1985

Differentiating matrices for arbitrarily spaced grid points

Differentiating matrices allow the numerical differentiation of functions defined at points of a discrete grid. A type of differentiating matrix based on local approximation on a sequence of sliding subgrids is considered. Previous derivations of this type of matrix have been restricted to grids with uniformly spaced points, and the resulting derivative approximations have lacked precision, especially at endpoints. The new formulation allows grids which have arbitrarily space points. It is shown that high accuracy can be achieved through use of differentiating matrices on non-uniform grids which include near-boundary points. Use of the differentiating matrix as an operator to solve eigenvalue problems involving ordinary differential equations is also considered.

Lakin, W. D.↗

NASA NTRS1985

Long-time asymptotics of a system for plasma diffusion

A system of parabolic nonlinear equations that describe the diffusion of a fully collisional plasma across a strong magnetic field is discussed. It is demonstrated that the solution to this system tends to a time asymptotic state which is of space-time separable form, theta(t)f(x). Furthermore, f(x) is independent of the initial conditions and theta(t) depends slightly on the initial conditions. The rate of decay of the temporal part is governed by a nonlinear eigenvalue problem. Since the equations are considered in a bounded domain we are able to analyze the effect of boundary conditions on the evolution of the system. Additional effects on radiation, heating, and particle injection can also be accounted for. Essential differences between the behavior of a fully-coupled system and a scalar equation are observed.

Rosenau, P.↗

NASA NTRS1985

Vibrations of circular orthotropic plates in affine space

The vibration of an initially compressed plate having a circular geometry and orthotropy is examined in an affine space. The classical linear plate theory and Hamilton's principle are employed. The equations of motion of the plate are particularly simple in the chosen affine space, permitting a free-vibration study of the entire spectrum of composite materials with polar orthotropy. Approximate but very accurate standing-wave-type mode shapes are used in solving the essentially double eigenvalue problem to determine the effects of midplane forces on the vibration frequencies of the plate. The results indicate that the affine-space frequency increases with increasing stiffness ratio but decreases with increasing midplane compression. It is also discovered that, contrary to the trends observed for rectangular geometry and orthotropy by Oyibo (1981), Brunelle (1982), and Brunelle and Oyibo (1983), the affine-space frequency increases with increasing generalized Poisson's ratio.

Oyibo, G. A.↗

NASA NTRS1986

Acoustic-Liner Admittance in a Duct

Method calculates admittance from easily obtainable values. New method for calculating acoustic-liner admittance in rectangular duct with grazing flow based on finite-element discretization of acoustic field and reposing of unknown admittance value as linear eigenvalue problem on admittance value. Problem solved by Gaussian elimination. Unlike existing methods, present method extendable to mean flows with two-dimensional boundary layers as well. In presence of shear, results of method compared well with results of Runge-Kutta integration technique.

Watson, W. R.↗

NASA NTRS1985

Application of the finite element method in the calculation of transmission loss of flat and curved panels

This investigation represents an extension of a study of Roussos (1985) who considered the noise transmission loss of a rectangular plate in an infinite baffle. Roussos, who employed an analytical formulation, considered an unstiffened plate. While it is difficult to consider stiffeners by means of analytical methods, the difficulties can be avoided by employing a finite element procedure. For this reason, the present study is concerned with the implementation of a finite element method. The representation of the panel transmission loss is discussed, and the determination of the panel motion by means of the finite element technique is described, taking into account an isotropic flat panel, the exciting force, an eigenvalue problem, the radiation pressure, a plate element, and a cylindrical shell element. Numerical results are considered for a flat panel, a curved panel, and a stiffened flat panel.

Koval, L. R.↗

NASA NTRS1986

Linear and weakly nonlinear aspects of free shear layer instability, roll-up, subharmonic interaction and wall influence

The growth of the momentum thickness and the modal disturbance energies are examined to study the nature and onset of nonlinearity in a temporally growing free shear layer. A shooting technique is used to find solutions to the linearized eigenvalue problem, and pseudospectral weakly nonlinear simulations of this flow are obtained for comparison. The roll-up of a fundamental disturbance follows linear theory predictions even with a 20 percent disturbance amplitude. A weak nonlinear interaction of the disturbance creates a finite-amplitude mean shear stress which dominates the growth of the layer momentum thickness, and the disturbance growth rate changes until the fundamental disturbance dominates. The fundamental then becomes an energy source for the harmonic, resulting in an increase in the growth rate of the subharmonic over the linear prediction even when the fundamental has no energy to give. Also considered are phase relations and the wall influence.

Cain, A. B.↗

NASA NTRS1986

On the screech tones of supersonic rectangular jets

The shock cell structure and screech tone frequencies of nonaxisymmetric supersonic jets are examined. A linear shock cell model that utilizes a vortex sheet as the mixing layer of the jet is developed in order to estimate the characteristics of the shock structures and tone frequencies. Eigenvalue problems for rectangular and elliptical jets are solved, and shock cell structure solutions for the jets are derived. The shock cell spacings calculated with the model are compared to the data of Powell (1953) and Hammitt (1961); good correlation is obtained over a wide range of Mach numbers. The shock cell spacing formula is applied to the computation of screech tone frequencies of rectangular jets. It is observed that the calculated frequencies agree with the measurements of Powell and Krothapalli et. al. (1986) for the Mach number range 1.15-1.80.

Tam, C. K. W.↗

NASA NTRS1987

Control of SCOLE

A relatively low order model is used to control SCOLE. Drastic truncation of the discretized model is proposed by means of a modal expansion. An open loop eigenvalue problem is illustrated as is truncated modal equations, modal state equations, actual output vector and modal Kalman filter. Also illustrated is independent modal-space control.

Meirovitch, L.↗

NASA NTRS1987

Vortex breakdown simulation based on a nonlinear inviscid model

It is shown that the inviscid equations governing steady axisymmetric flow with swirl, admit solutions with closed streamlines. Results are obtained using two different numerical algorithms. The first is based on a multigrid method for nonlinear eigenvalue problems, while the second is based on a least squares formulation.

Hafez, M. M.↗

NASA NTRS1985

Implementation of design sensitivity analysis with existing finite element codes

A numerical method is presented to implement structural design sensitivity analysis theory, using the versatility and convenience of existing finite element structural analysis programs. Design variables such as thickness and cross-sectional areas of components of individual members and built-up structures are considered. Structural performance functionals considered include displacement and stress. The method is also applicable for eigenvalue problem design sensitivity analysis. It is shown that calculations can be carried out outside existing finite element codes, using postprocessing data only. Thus, design sensitivity analysis software does not have to be embedded in an existing finite element code. Feasability of the method is shown through analysis of several problems, including a built-up structure. Accurate design sensitivity results are obtained without the uncertainty of numerical accuracy associated with selection of finite difference perturbations.

Choi, Kyung K.↗

NASA NTRS1987

Stability of viscous flow past a circular cylinder

A spectral method which employs trigonometric functions and Chebyshev polynomials is used to compute the steady, incompressible laminar flow past a circular cylinder. Linear stability methods are used to formulate a pair of decoupled generalized eigenvalue problems for the growth of symmetric and asymmetric (about the dividing streamline) perturbations. It is shown that, while the symmetric disturbances are stable, the asymmetric perturbations become unstable at a Reynolds number about 40 with a Strouhal number about 0.12. The critical conditions are found to depend on the size of the computational domain in a manner similar to that observed in the laboratory.

Zebib, A.↗

NASA NTRS1987

On the acceleration of charged particles at relativistic shock fronts

The diffusive acceleration of highly relativistic particles at a shock is reconsidered. Using the same physical assumptions as Blandford and Ostriker (1978), but dropping the restriction to nonrelativistic shock velocities, the authors find approximate solutions of the particle kinetic equation by generalizing the diffusion approximation to higher order terms in the anisotropy of the particle distribution. The general solution of the transport equation on either side of the shock is constructed, which involves the solution of an eigenvalue problem. By matching the two solutions at the shock, the spectral index of the resulting power law is found by taking into account a sufficiently large number of eigenfunctions. Low-order truncation corresponds to the standard diffusion approximation and to a somewhat more general method described by Peacock (1981). In addition to the energy spectrum, the method yields the angular distribution of the particles and its spatial dependence.

Kirk, J. G.↗