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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

An approximate solution for the free vibrations of rotating uniform cantilever beams

Approximate solutions are obtained for the uncoupled frequencies and modes of rotating uniform cantilever beams. The frequency approximations for flab bending, lead-lag bending, and torsion are simple expressions having errors of less than a few percent over the entire frequency range. These expressions provide a simple way of determining the relations between mass and stiffness parameters and the resultant frequencies and mode shapes of rotating uniform beams.

Peters, D. A.↗
NASA NTRS1945

Bending and Shear Stresses Developed by the Instantaneous Arrest of the Root of a Moving Cantilever Beam

A theoretical and experimental investigation has been made of the behavior of a cantilever beam in transverse motion when its root is suddenly brought to rest. Equations are given for determining the stresses, the deflections, and the accelerations that arise in the beam as a result of the impact. The theoretical equations, which have been confirmed experimentally, reveal that, at a given percentage of the distance from root to tip, the bending stresses for a particular mode are independent of the length of the beam, whereas the shear stresses vary inversely with the length.

Stowell, Elbridge, Z↗
NASA NTRS1991

Effects of T-tabs and large deflections in double cantilever beam specimen tests

A simple strength of materials analysis was developed for a double-cantilever beam (DCB) specimen to account for geometric nonlinearity effects due to large deflections and T-tabs. A new DCB data analysis procedure was developed to include the effects of these nonlinearities. The results of the analysis were evaluated by DCB tests performed for materials having a wide range of toughnesses. The materials used in the present study were T300/5208, IM7/8551-7, and AS4/PEEK. Based on the present analysis, for a typical deflection/crack length ratio of 0.3 (for AS4/PEEK), T-tabs and large deflections cause a 15 and 3 percent error, respectively, in the computer Mode I strain energy release rate. Design guidelines for DCB specimen thickness and T-tab height were also developed in order to keep errors due to these nonlinearities within 2 percent. Based on the test results, for both hinged and tabbed specimens, the effects of large deflection on the Mode I fracture toughness (G sub Ic) were almost negligible (less than 1 percent) in the case of T300/5208 and IM7/8551-7; however, AS4/PEEK showed a 2 to 3 percent effect. The effects of T-tabs G sub Ic were more significant for all the materials with T300/5208 showing a 5 percent error, IM7/8551-7 a 15 percent error, and, AS4/PEEK a 20 percent error.

Naik, Rajiv A.↗
NASA NTRS1976

Response of long, flexible cantilever beams applied root motions

Results are presented for an analysis of the response of long, flexible cantilever beams to applied root rotational accelerations. Maximum values of deformation, slope, bending moment, and shear are found as a function of magnitude and duration of acceleration input. Effects of tip mass and its eccentricity and rotatory inertia on the response are also investigated. It is shown that flexible beams can withstand large root accelerations provided the period of applied acceleration can be kept small relative to the beam fundamental period.

Fralich, R. W.↗
NASA NTRS1983

An improved finite-difference analysis of uncoupled vibrations of tapered cantilever beams

An improved finite difference procedure for determining the natural frequencies and mode shapes of tapered cantilever beams undergoing uncoupled vibrations is presented. Boundary conditions are derived in the form of simple recursive relations involving the second order central differences. Results obtained by using the conventional first order central differences and the present second order central differences are compared, and it is observed that the present second order scheme is more efficient than the conventional approach. An important advantage offered by the present approach is that the results converge to exact values rapidly, and thus the extrapolation of the results is not necessary. Consequently, the basic handicap with the classical finite difference method of solution that requires the Richardson's extrapolation procedure is eliminated. Furthermore, for the cases considered herein, the present approach produces consistent lower bound solutions.

Subrahmanyam, K. B.↗
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 NTRS2014

A Novel Method for Characterizing Fatigue Delamination Growth Under Mode I Using the Double Cantilever Beam Specimen

A novel method is proposed to obtain Mode I delamination growth rate from a Double Cantilever Beam (DCB) specimen. In the proposed method, Unidirectional (UD) DCB specimens are tested in fatigue at different initial maximum energy release rates levels. The growth rate data obtained in the first increments of crack growth at each maximum energy release rate level are used to generate a Paris Law equation, which characterizes delamination growth rate without fiber-bridging, and can also be used to determine a delamination onset curve. The remaining delamination growth rate data from each test are used to determine a modified Paris law, which characterizes the delamination growth rate in a DCB specimen, explicitly accounting for fiber-bridging. The proposed expression captures well the scatter in experimental data obtained using the DCB specimens, suggesting its adequacy. The Paris Law characterizing delamination growth rate without fiber-bridging predicts higher delamination growth rates for the same maximum energy release rate applied, leading to a conservative estimate for delamination growth. This is particularly relevant, since in generic ply interfaces, fiber-bridging is less predominant than in UD DCB specimens. Failing to account for fiber-bridging in UD DCB specimens may underestimate the delamination growth rate, yielding non-conservative predictions.

Carvalho, Nelson↗
NASA NTRS1959

Experimental Investigation of Effects of Random Loading on the Fatigue Life of Notched Cantilever-Beam Specimens of 7075-T6 Aluminum Alloy

Results of random-loading fatigue tests on 125 notched cantilever-beam specimens and constant-amplitude fatigue tests on 46 similar specimens are presented in terms of the root-mean-square value of peak stresses. The results from the two sets of tests are compared on the basis of time to failure, where the results from the constant-amplitude tests are expressed in terms of an equivalent time to failure based on the natural period of vibration. Compared on this basis, failure at the lower stress levels occurred in a shorter time for the random loading than for the constant-amplitude loading, whereas at the higher stress levels failure occurred in the reverse order. A theoretical result for random loading is also presented and compared with the experimental results. The theoretical result shows good agreement with experiment for low values of stress but underestimates the time to failure at the higher stresses.

Fralich, Robert W.↗
NASA NTRS1996

Vibration Characteristics of Partially Covered Double-Sandwich Cantilever Beam

The differential equations of motion together with the boundary conditions for a partially covered, double-sandwich cantilever beam are derived. Bending and extension, rotational and longitudinal inertia of damping layers, and shear deformation and rotational and longitudinal inertia of the constraining layers and the primary beam are included in the equations. The theory is applicable for long as well as short, soft, or stiff damping layer, double-sandwich beams. Also, the effects of different parameters on the system loss factor and resonance frequency are discussed. Differences are found to exist with the previous beam model (called the Euler beam model) when the damping layers are stiff, when the thickness of the damping layer is large compared to the primary-beam thickness, and in the case of higher modes of vibration.

Chen, Qinghua↗
NASA NTRS1985

Finite difference analysis of torsional vibrations of pretwisted, rotating, cantilever beams with effects of warping

Theoretical natural frequencies of the first three modes of torsional vibration of pretwisted, rotating cantilever beams are determined for various thickness and aspect ratios. Conclusions concerning individual and collective effects of warping, pretwist, tension-torsion coupling and tennis racket effect (twist-rotational coupling) terms on the natural frequencies are drawn from numerical results obtained by using a finite difference procedure with first order central differences. The relative importance of structural warping, inertial warping, pretwist, tension-torsion and twist-rotational coupling terms is discussed for various rotational speeds. The accuracy of results obtained by using the finite difference approach is verified by a comparison with the exact solution for specialized simple cases of the equation of motion used in this paper.

Subrahmanyam, K. B.↗
NASA NTRS2006

Nonlinear Elastic J-Integral Measurements in Mode I Using a Tapered Double Cantilever Beam Geometry

An expression for the J-integral of a nonlinear elastic material is derived for an advancing crack in a tapered double cantilever beam fracture specimen. The elastic and plastic fracture energies related to the test geometry and how these energies correlates to the crack position are discussed. The dimensionless shape factors eta(sub el and eta(sub p) are shown to be equivalent and the deformation J-integral is analyzed in terms of the eta(sub el) function. The fracture results from a structural epoxy are interpreted using the discussed approach. The magnitude of the plastic dissipation is found to strongly depend upon the initial crack shape.

Macon, David J.↗
NASA NTRS1951

Analytical determination of coupled bending-torsion vibrations of cantilever beams by means of station functions

A method based on the concept of station functions is presented for calculating the modes and the frequencies of nonuniform cantilever beams vibrating in torsion, bending, and coupled bending-torsion motion. The method combines some of the advantages of the Rayleigh-Ritz and Stodola methods, in that a continuous loading function for the beam is used, with the advantages of the influence-coefficient method, in that the continuous loading function is obtained in terms of the displacements of a finite number of stations along the beam.

Mendelson, Alexander↗
NASA NTRS1988

Effects of initial delamination on CIc and GIth values from glass/epoxy double cantilever beam tests

The effect of insert thickness and method of precracking on mode I interlaminar fracture toughness, GIc, and delamination fatigue threshold, GIth, values were determined for a glass/epoxy double cantilever beam specimen. The results of the static tests showed that precracking in tension would cause fiber bridging and thus may yield unconservative values of GIc and GIth. Precracking in shear yields suitable values of GIc but overly conservative values of GIth. For the glass/epoxy composite used, an insert thickness of 0.5 mil was most suitable for determining GIc and GIth values, although an insert thickness up to 3 mil was acceptable. Inserts thicker than 3 mil were not acceptable for determining GIc and GIth values.

Martin, Roderick H.↗
NASA NTRS1988

Three-dimensional elastic analysis of a composite double cantilever beam specimen

Attention is given to the stresses and the strain energy release rate along the delamination front in the present three-dimensional elastic analysis of a 24-ply, cocured double-cantilever beam specimen by means of 20-noded parabolic-isoparametric finite elements. At the free surface, the strain energy release rate was found to be substantially smaller than the plane strain value; this is suggested to be due to the free-surface effect that exists where the delamination meets the surface edge.

Raju, I. S.↗