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Results for “Euler-Bernoulli beams”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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48 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Optimum vibrating beams with stress and deflection constraints

The fundamental frequency of vibration of an Euler-Bernoulli or a Timoshenko beam of a specified constant volume is maximized subject to the constraint that under a prescribed loading the maximum stress or maximum deflection at any point along the beam axis will not exceed a specified value. In contrast with the inequality constraint which controls the minimum cross-section, the present inequality constraints lead to more meaningful designs. The inequality constraint on stresses is as easily implemented as the minimum cross-section constraint but the inequality constraint on deflection uses a treatment which is an extension of the matrix partitioning technique of prescribing displacements in finite element analysis.

Kamat, M. P.↗
NASA NTRS1989

Parallel processors and nonlinear structural dynamics algorithms and software

A nonlinear structural dynamics finite element program was developed to run on a shared memory multiprocessor with pipeline processors. The program, WHAMS, was used as a framework for this work. The program employs explicit time integration and has the capability to handle both the nonlinear material behavior and large displacement response of 3-D structures. The elasto-plastic material model uses an isotropic strain hardening law which is input as a piecewise linear function. Geometric nonlinearities are handled by a corotational formulation in which a coordinate system is embedded at the integration point of each element. Currently, the program has an element library consisting of a beam element based on Euler-Bernoulli theory and trianglar and quadrilateral plate element based on Mindlin theory.

Belytschko, Ted↗
NASA NTRS1986

Computational methods for the identification of spatially varying stiffness and damping in beams

A numerical approximation scheme for the estimation of functional parameters in Euler-Bernoulli models for the transverse vibration of flexible beams with tip bodies is developed. The method permits the identification of spatially varying flexural stiffness and Voigt-Kelvin viscoelastic damping coefficients which appear in the hybrid system of ordinary and partial differential equations and boundary conditions describing the dynamics of such structures. An inverse problem is formulated as a least squares fit to data subject to constraints in the form of a vector system of abstract first order evolution equations. Spline-based finite element approximations are used to finite dimensionalize the problem. Theoretical convergence results are given and numerical studies carried out on both conventional (serial) and vector computers are discussed.

Banks, H. T.↗
NASA NTRS1994

Variations in the modal characteristics of a telescopically deploying beam

The equations of motion for a two-segment deploying telescopic beam are derived through application of Lagrange's equation. The outer tube of the beam is fixed at one end and the inner tube slides freely relative to the fixed segment. The resulting nonlinear, non-autonomous set of equations is linearized and simplified to the standard Euler-Bernoulli partial differential equations for an elastic beam by freezing the deployment process at various stages of deployment, and examining the small amplitude and natural modes of vibration of the resulting configuration. Application of the natural boundary conditions and compatibility of motion relations for the two segments in their common region of overlap leads to a transcendental characteristic equation in the frequency parameter Beta(L). Numerical solution of the equation for the characteristic roots determines the modal frequencies, and the corresponding mode shapes are obtained from the general solution of the Euler-Bernoulli equation tailored to the natural boundary conditions. Sample results of modal frequencies and shapes are presented for various stages of deployment and discussed. It is shown that for all intermediate stages of deployment (between 0 and 100 percent) the spectral distribution is drastically altered by the appearance of regions of very closely spaced modal frequencies. The sources of this modal agglomeration are explored.

Amos, Anthony K.↗
NASA NTRS1983

Algorithms for estimation in distributed models with applications to large space structures

The author discussed the theoretical and computational results for spline based approximation schemes used in parameter estimation algorithms for distributed systems. Specific applications include beam-like structures described by the Euler-Bernoulli and Timoshenko theories and antenna surfaces such as that in the deployable Maypole Hoop/Column model.

Banks, H. T.↗
NASA NTRS1993

Planar reorientation of a free-free beam in space using embedded electromechanical actuators

It is demonstrated that the planar reorientation of a free-free beam in zero gravity space can be accomplished by periodically changing the shape of the beam using embedded electromechanical actuators. The dynamics which determine the shape of the free-free beam is assumed to be characterized by the Euler-Bernoulli equation, including material damping, with appropriate boundary conditions. The coupling between the rigid body motion and the flexible motion is explained using the angular momentum expression which includes rotatory inertia and kinematically exact effects. A control scheme is proposed where the embedded actuators excite the flexible motion of the beam so that it rotates in the desired sense with respect to a fixed inertial reference. Relations are derived which relate the average rotation rate to the amplitudes and the frequencies of the periodic actuation signal and the properties of the beam. These reorientation maneuvers can be implemented by using feedback control.

Kolmanovsky, Ilya V.↗
NASA NTRS1990

A comparison of different models for beam vibrations from the standpoint of control design

Different models for beam vibrations are analyzed from the standpoint of designing finite-dimensional controllers to stabilize the beam vibrations. A distributed system described by an undamped Euler-Bernoulli equation cannot be stabilized by any finite-dimensional controller, i.e., any controller which can be described an ordinary differential equation with constant coefficients. If viscous damping is included, a similar problem occurs in that all the poles can not be moved to the left of a given vertical line. These negative results should be interpreted as a commentary on the limitations of these models, rather than on the control of real beams. If a Rayleigh damping model is used, a finite-dimensional controller may be designed to move the closed loop system poles essentially as far to the left in the complex plane as desired. This result will also hold for certain hysteresis damping models. This has implications for the settling time of the vibrations.

Morris, K. A.↗
NASA NTRS1987

Inverse problems in the modeling of vibrations of flexible beams

The formulation and solution of inverse problems for the estimation of parameters which describe damping and other dynamic properties in distributed models for the vibration of flexible structures is considered. Motivated by a slewing beam experiment, the identification of a nonlinear velocity dependent term which models air drag damping in the Euler-Bernoulli equation is investigated. Galerkin techniques are used to generate finite dimensional approximations. Convergence estimates and numerical results are given. The modeling of, and related inverse problems for the dynamics of a high pressure hose line feeding a gas thruster actuator at the tip of a cantilevered beam are then considered. Approximation and convergence are discussed and numerical results involving experimental data are presented.

Banks, H. T.↗
NASA NTRS1984

Approximation techniques for parameter estimation and feedback control for distributed models of large flexible structures

Approximation ideas are discussed that can be used in parameter estimation and feedback control for Euler-Bernoulli models of elastic systems. Focusing on parameter estimation problems, ways by which one can obtain convergence results for cubic spline based schemes for hybrid models involving an elastic cantilevered beam with tip mass and base acceleration are outlined. Sample numerical findings are also presented.

Banks, H. T.↗
NASA NTRS1985

Approximation Techniques for Parameter Estimation and Feedback Control for Distributed Models of Large Flexible Structures

Approximation ideas that can be used in parameter estimation and feedback control for Euler-Bernoulli models of elastic systems are discussed. Focusing on parameter estimation problems, the authors outline how one can obtain convergence results for cubic spline-based schemes for hybrid models involving an elastic cantilevered beam with tip mass and base acceleration. Sample numerical findings are also presented.

Banks, H. T.↗
NASA NTRS1987

Dynamic response of a viscoelastic Timoshenko beam

The analysis presented in this study deals with the vibratory response of viscoelastic Timoshenko (1955) beams under the assumption of small material loss tangents. The appropriate method of analysis employed here may be applied to more complex structures. This study compares the damping ratios obtained from the Timoshenko and Euler-Bernoulli theories for a given viscoelastic material system. From this study the effect of shear deformation and rotary inertia on damping ratios can be identified.

Kalyanasundaram, S.↗