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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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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Applications of the theory of optimal control of distributed-parameter systems to structural optimization

An extension of classical methods of optimal control theory for systems described by ordinary differential equations to distributed-parameter systems described by partial differential equations is presented. An application is given involving the minimum-mass design of a simply-supported shear plate with a fixed fundamental frequency of vibration. An optimal plate thickness distribution in analytical form is found. The case of a minimum-mass design of an elastic sandwich plate whose fundamental frequency of free vibration is fixed. Under the most general conditions, the optimization problem reduces to the solution of two simultaneous partial differential equations involving the optimal thickness distribution and the modal displacement. One equation is the uniform energy distribution expression which was found by Ashley and McIntosh for the optimal design of one-dimensional structures with frequency constraints, and by Prager and Taylor for various design criteria in one and two dimensions. The second equation requires dynamic equilibrium at the preassigned vibration frequency.

Armand, J. P.↗
NASA NTRS1994

Experimental and analytical study on fluid whirl and fluid whip modes

Fluid whirl and fluid whip are rotor self-excited, lateral vibrations which occur due to rotor interactions with the surrounding fluid. There exist various modes of fluid whirl and fluid whip. These modes are close to rotor modes corresponding to free vibrations (based on the linear model). Small differences are due to nonlinearities in the system. This paper presents experimental and analytical results on the lowest modes of fluid whirls and fluid whip. Examples of rotors supported in fluid lubricated bearings show the variations of rotor deflection amplitudes and phases in the whirl and whip modes with changes of rotative speeds and/or changes in lumped mass locations along the shaft.

Muszynska, Agnes↗
NASA NTRS1988

Reanalysis procedure for large structural systems

Global-basis-vector approximate reanalysis techniques for use in automated structural optimization schemes are developed and demonstrated. The vibrational response of a modified structure (MS) is estimated by lumping the design variables into a single tracing parameter, applying an operator splitting procedure to express the FEM equations of the MS in terms of the original-structure equations plus correction terms, and reducing the MS equations via a classical Bubnov-Galerkin scheme. The sensitivity of the vibrational response to structural modifications is evaluated, and the relationship between this method and the preconditioned conjugate-gradient method (Noor and Peters, 1988) is explored. Numerical results for linear static and free vibration problems involving beamlike lattices, double-layered hexahedral grids, and structural gridworks are presented in tables and graphs and briefly characterized.

Noor, Ahmed K.↗
NASA NTRS1974

Evaluation of experimental methods for determining dynamic stiffness and damping of composite materials

Various methods potentially usable for determining dynamic stiffness and damping of composite materials are reviewed. Of these, the following most widely used techniques are singled out for more detailed discussion: free vibration, pulse propagation, and forced vibration response. To illustrate the usefulness and validity of dynamic property data, their application in dynamic analyses and comparison with measured structural response are described for the following composite-material structures: free-free sandwich beam with glass-epoxy facings, clamped-edge sandwich plate with similar facings, free-end sandwich conical shell with similar facings, and boron-epoxy free plate with layers arranged at various orientations.

Bert, C. W.↗
NASA NTRS1959

Application of the Method of Stein and Sanders to the Calculation of Vibration Characteristics of a 45 deg Delta-Wing Specimen

Generalized influence coefficients are calculated by the method of NACA TN 3640 for a large-scale, built-up, 450 delta-wing specimen. These are used together with appropriate generalized masses to obtain the natural modes and frequencies in symmetric and antisymmetric free-free vibration. The resulting frequencies are compared with those obtained experimentally and are found to be consistently high. Possible sources of the disparities are discussed.

Hedgepeth, John M.↗
NASA NTRS1983

Vibration response of geometrically nonlinear elastic beams to pulse and impact loading

The governing equations for the geometrically nonlinear deformation of elastic beams subjected to dynamic bending loads are developed and solved for various initial conditions. Of primary interest is the response to pulse loading and simulated impact. Both transient and several cycle solutions are generated for the free vibration response to pulse loading. The results obtained are compared to a first mode analysis approximation. A model is developed to simulate impact loading by the distribution of additional mass to the elastic system and subjecting it to a velocity pulse. The governing equations are solved using second order finite differences in space and time. The solutions obtained are in reasonable agreement with experimental results.

Liebowitz, H.↗
NASA NTRS1983

Identification of large flexible structures mass/stiffness and damping from on-orbit experiments

Two methods for identifying the mass, damping and stiffness matrices of a linear vibrating system are presented. Both methods require the measurement of acceleration, velocity and displacement at various locations of the system. In the first method, the response of the system subjected to known forces is used while the second method employs the free vibration data. The unknown parameters are recovered through the standard least squares procedure. Numerical results are presented for several examples.

Hendricks, S. L.↗
NASA NTRS1980

Acoustic plane waves incident on an oblique clamped panel in a rectangular duct

The theory of acoustic plane waves incident on an oblique clamped panel in a rectangular duct was developed from basic theoretical concepts. The coupling theory between the elastic vibrations of the panel (plate) and the oblique incident acoustic plane wave in infinite space was considered in detail, and was used for the oblique clamped panel in the rectangular duct. The partial differential equation which governs the vibrations of the clamped panel (plate) was modified by adding to it stiffness (spring) forces and damping forces. The Transmission Loss coefficient and the Noise Reduction coefficient for oblique incidence were defined and derived in detail. The resonance frequencies excited by the free vibrations of the oblique finite clamped panel (plate) were derived and calculated in detail for the present case.

Unz, H.↗
NASA NTRS1976

Hamilton, Ritz, and elastodynamics

The theory of Ritz is applied to the equation that Hamilton called the 'Law of Varying Action.' Direct analytical solutions are obtained for the transient motion of beams, both conservative and nonconservative. The results achieved are compared to exact solutions obtained by the use of rigorously exact free-vibration modes in the differential equations of Lagrange and to an approximate solution obtained through the application of Gurtin's principles for linear elastodynamics. A brief discussion of Hamilton's law and Hamilton's principle is followed by examples of results for both free-free and cantilever beams with various loadings.

Bailey, C. D.↗
NASA NTRS1976

Hamilton, Ritz, and elastodynamics

The theory of Ritz is applied to the equation that Hamilton called the 'Law of Varying Action'. Direct analytical solutions are obtained for the transient motion of beams, both conservative and nonconservative. The results obtained are compared to exact solutions obtained by the use of rigorously exact free-vibration modes in the differential equations of Lagrange and to an approximate solution obtained through the application of Gurtin's principles for linear elastodynamics. A brief discussion of Hamilton's law and Hamilton's principle is followed by examples of results for both free-free and cantilever beams with various loadings.

Bailey, C. D.↗
NASA NTRS1990

Analytical and experimental study of the vibration of bonded beams with a lap joint

A theoretical model to study the flexural vibration of a bonded lap joint system is described in this paper. First, equations of motion at the joint region are derived using a differential element approach. The transverse displacements of the upper and lower beam are considered to be different. The adhesive is assumed to be linearly viscoelastic and the widely used Kelvin-Voight model is used to represent the viscoelastic behavior of the adhesive. The shear force at the interface between the adhesive and the beam is obtained from the simple bending motion equations of the two beams. The resulting equations of motion are combined with the equations of transverse vibration of the beams in the unjointed regions. These are later solved as a boundary value problem to obtain the eigenvalues and eigenvectors of the system. The model can be used to predict the natural frequencies, modal damping ratios, and mode shapes of the system for free vibration. Good agreement between numerical and experimental results was obtained for a system of graphite epoxy beams lap-jointed by an epoxy adhesive.

Rao, M. D.↗
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 NTRS1973

Mixed finite-difference scheme for analysis of simply supported thick plates.

A mixed finite-difference scheme is presented for the stress and free vibration analysis of simply supported nonhomogeneous and layered orthotropic thick plates. The analytical formulation is based on the linear, three-dimensional theory of orthotropic elasticity and a Fourier approach is used to reduce the governing equations to six first-order ordinary differential equations in the thickness coordinate. The governing equations possess a symmetric coefficient matrix and are free of derivatives of the elastic characteristics of the plate. In the finite difference discretization two interlacing grids are used for the different fundamental unknowns in such a way as to reduce both the local discretization error and the bandwidth of the resulting finite-difference field equations. Numerical studies are presented for the effects of reducing the interior and boundary discretization errors and of mesh refinement on the accuracy and convergence of solutions. It is shown that the proposed scheme, in addition to a number of other advantages, leads to highly accurate results, even when a small number of finite difference intervals is used.

Noor, A. K.↗
NASA NTRS1983

Transverse vibration and buckling of a cantilevered beam with tip body under constant axial base acceleration

The planar transverse bending behavior of a uniform cantilevered beam with rigid tip body subject to constant axial base acceleration was analyzed. The beam is inextensible and capable of small elastic transverse bending deformations only. Two classes of tip bodies are recognized: (1) mass centers located along the beam tip tangent line; and (2) mass centers with arbitrary offset towards the beam attachment point. The steady state response is studied for the beam end condition cases: free, tip mass, tip body with restricted mass center offset, and tip body with arbitrary mass center offset. The first three cases constitute classical Euler buckling problems, and the characteristic equation for the critical loads/accelerations are determined. For the last case a unique steady state solution exists. The free vibration response is examined for the two classes of tip body. The characteristic equation, eigenfunctions and their orthogonality properties are obtained for the case of restricted mass center offset. The vibration problem is nonhomogeneous for the case of arbitrary mass center offset. The exact solution is obtained as a sum of the steady state solution and a superposition of simple harmonic motions.

Storch, J.↗
NASA NTRS1987

Component mode synthesis and large deflection vibration of complex structures. Volume 2: Single-mode large deflection vibrations of beams and plates using finite element method

A finite element method is presented for the large amplitude vibrations of complex structures that can be modelled with beam and rectangular plate elements subjected to harmonic excitation. Both inplane deformation and inertia are considered in the formulation. Derivation of the harmonic force and nonlinear stiffness matrices for a beam and a rectangular plate element are presented. Solution procedures and convergence characteristics of the finite element method are described. Nonlinear response to uniform and concentrated harmonic loadings and improved nonlinear free vibration results are presented for beams and rectangular plates of various boundary conditions.

Mei, Chuh↗
NASA NTRS1975

NASTRAN modeling and analysis of rigid and flexible walled acoustic cavities

The acoustic slot elements, CSLOTi, are applied to analyze two-dimensional enclosures with fixed or moving boundaries. The capability utilized to compute (a) the acoustic natural modes and frequencies of a rigid walled enclosure and (b) the sound pressure at any point inside an enclosure when the surrounding walls are forced to vibrate. Applications to an automobile passenger compartment illustrate the technique. The axisymmetric fluid elements, CFLUIDi, are used in conjunction with a suitable choice of symmetry planes and a model of the surrounding structure to approximate a two-dimensional enclosure with flexible walls. The enclosure walls are modeled using finite elements or structural modes. Illustrative examples include a comparison of rectangular cavity modes with those calculated using the acoustic slot element and the free vibration modes of two enclosures coupled through a flexible rectangular panel.

Wolf, J. A., Jr.↗