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At least 253 records · Page 14

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NASA NTRS1972

The response of a plate bonded to a randomly vibrating viscoelastic half-space.

The response of an infinite Bernoulli-Euler plate placed on the surface of a randomly vibrating viscoelastic half-space is calculated, allowing for the presence of shear stresses between the plate and the half-space. The shear stresses arise from the condition that the relative motion between the plate and the half-space vanishes at the interface. The three components of displacement of the free surface of the half-space before the plate is added are assumed to be stationary homogeneous random functions of position and time. From the wavenumber-frequency spectra of these displacements the frequency spectra of the three components of displacement of the plate half-space interface are calculated. As an example, the frequency spectrum of the vertical interface displacement is calculated for two assumed forms of the wavenumber spectra of the free-surface displacements.

Remington, P. J.↗

NASA NTRS1972

A sandwich plate with a part-through and a debonding crack.

The stress analysis of a metal base plate stiffened by a fiber-reinforced composite layer is considered. It is assumed that the two materials are bonded through an adhesive of constant thickness which is treated as a two-dimensional shear spring in the analysis. The metal plate is assumed to contain a through crack of finite length. The composite plate has no flaws. However, due to the high stress concentration around the crack and on the interface, a debonding crack is assumed to exist, encircling the crack in the base plate. The problem is reduced to a pair of integral equations of the second kind with Fredholm-type kernels. By solving these equations the stress intensity factor in the base plate, the boundary of the debonding crack, and the interface shear stresses acting on the adhesive are calculated.

Erdogan, F.↗

NASA NTRS1973

Free vibrations of thermally stressed orthotropic plates with various boundary conditions

An analytical investigation of the vibrations of thermally stressed orthotropic plates in the prebuckled region is presented. The investigation covers the broad class of trapezoidal plates with two opposite sides parallel. Each edge of the plate may be subjected to different uniform boundary conditions. variable thickness and arbitrary temperature distributions (analytical or experimental) for any desired combination of boundary conditions may be prescribed. Results obtained using this analysis are compared to experimental results obtained for isotropic plates with thermal stress, and to results contained in the literature for orthotropic plates without thermal stress. Good agreement exists for both sets of comparisons.

Bailey, C. D.↗

NASA NTRS1973

Down-bucklng of a corner of a descending plate

A model of the earth's crust is presented as a set of rigid crustal blocks in which the crust is consumed, compressed, or created only at the boundaries of the blocks. As such the trench boundary moves with respect to the colliding plates because of down-buckling at the corner of the descending plate. It is further shown that this mechanism requires plate consumption of the descending plate at a rate faster than the relative plate motion, which in turn causes infilling of the basin behind the arc to compensate for the increased destruction. It is demonstrated that earthquake, heat flow, paleomagnetic, gravity anomaly, and geologic data derived from Japan and the Sea of Japan support the model.

Lowrey, B. E.↗

NASA NTRS1973

Plate motion and the secular shift of the mean pole

The global plate motion indicates that changes in the products of inertia of the earth due to tectonic plate movement may provide a secular shift of the mean pole. A mathematical procedure for calculating this shift based on the plate theory is presented. Explicit expressions were obtained for the dependence of the secular polar shift on the dimensions and locations of the plate boundaries. Numerical results show that the secular motion of the mean pole is 0.0002 sec/year in the direction of 67 W. Hence, it is deduced that the influence of the plate motion on the secular polar shift may account for 10% of the observed value.

Liu, H.↗

NASA NTRS1973

Free vibrations of multilayered composite plates.

Summary of some of the results of a recent study of the reliability and range of validity of two-dimensional plate theories in application to low-frequency free vibration analysis of simply supported, bidirectional, multilayered plates consisting of a large number of layers. These results show that for composite plates the error in the predictions of the classical plate theory is strongly dependent on the number and stacking of the layers, in addition to the degree of orthotropy of the individual layers and the thickness ratio of the plate.

Noor, A. K.↗

NASA NTRS1973

Analysis of transient heat flow to thick-walled plates and cylinders

A methodology is described for the analysis of a transient temperature measurement made in a flat or curved plate subjected to convective heat transfer, such that the surface heat flux, the hot-gas temperture, and the gas heat transfer coefficient can be determined. It is shown that if the transient temperature measurement is made at a particular point located nearly midway in the thickness of the plate there is an important simplification in the data analysis process, in that the factor relating the surface heat flux to the measured rate of rise of temperature becomes invariant for a Fourier Number above 0.60 and for all values of the Biot Number. Parameters are derived, tabulated, and plotted which enable straightforward determination of the surface heat flux, the hot-gas temperature, of the plate, the rate of rise of temperature, the plate thickness and curvature, and the mean thermal properties of the plate material at the test temperature.

Powell, W. B.↗

NASA NTRS1974

Elastic stability of laminated, flat and curved, long rectangular plates subjected to combined inplane loads

A method is presented to predict theoretical buckling loads of long, rectangular flat and curved laminated plates with arbitrary orientation of orthotropic axes each lamina. The plate is subjected to combined inplane normal and shear loads. Arbitrary boundary conditions may be stipulated along the longitudinal sides of the plate. In the absence of inplane shear loads and extensional-shear coupling, the analysis is also applicable to finite length plates. Numerical results are presented for curved laminated composite plates with boundary conditions and subjected to various loadings. These results indicate some of the complexities involved in the numerical solution of the analysis for general laminates. The results also show that the reduced bending stiffness approximation when applied to buckling problems could lead to considerable error in some cases and therefore must be used with caution.

Viswanathan, A. V.↗

NASA NTRS1974

An experimental-theoretical study of free vibrations of plates on elastic point supports

A theoretical and experimental study is made to investigate the effect on plate vibrations of varying the stiffness of corner elastic point supports. An experiment is conducted in which the bending stiffness of horizontal beams is used to support a square plate at its four corners. The stiffness of these supports can be varied over such a range that the plate fundamental frequency is lowered to 40% of the rigid support frequency. The variation with support stiffness of the frequencies of the first eight plate modes is measured and is compared with results from a theoretical model in which a Rayleigh-Ritz analysis is used which approximates the plate mode shapes as products of free-free beam modes. The elastic point supports are modeled both as massless translational springs and springs with tip masses, which are included to better represent the experimental supports.

Leuner, T. R.↗

NASA NTRS1973

On the dynamic stability of multilayer sandwich plates

Study of the dynamic stability of plates which are constructed of several alternating soft and hard layers and are subjected to time-dependent periodic in-plane loads. A theory that accounts for all of these effects is presented for multilayer sandwich plates. The plate thickness consists of (k - 1) orthotropic soft core layers sandwiched between k hard isotropic membrane layers, each of which may have a different thickness and elastic properties. It is assumed that the core layers carry only the transverse shear stresses, while the hard membrane layers carry the in-plane normal and shear stresses. The complementary variational principle for dynamics is used to derive the governing differential equations and the necessary boundary conditions for the dynamic stability of the sandwich plate. The equations governing the vibration of the plate and those governing its static stability are deduced from the more general equations for dynamic stability.

Salama, A. M.↗

NASA NTRS1976

Symmetries in laminated composite plates

The different types of symmetry exhibited by laminated anisotropic fibrous composite plates are identified and contrasted with the symmetries of isotropic and homogeneous orthotropic plates. The effects of variations in the fiber orientation and the stacking sequence of the layers on the symmetries exhibited by composite plates are discussed. Both the linear and geometrically nonlinear responses of the plates are considered. A simple procedure is presented for exploiting the symmetries in the finite element analysis. Examples are given of square, skew and polygonal plates where use of symmetry concepts can significantly reduce the scope and cost of analysis.

Noor, A. K.↗

NASA NTRS1976

A high order theory for uniform and laminated plates

A theory of plate deformation is derived which accounts for the effects of transverse shear deformation, transverse normal strain, and a nonlinear distribution of the in-plane displacements with respect to the thickness coordinate. The theory is compared with lower order plate theories through application to a particular problem involving a plate acted upon by a sinusoidal surface pressure. Comparison is also made with exact elasticity solution of this problem. It is found that when the ratio of the characteristic length of the load pattern to the plate thickness is of the order of unity, lower order theories are inadequate and the present high order theory is required to give meaningful results. Results are given for the bending of symmetric cross-ply and angle-ply laminates. Comparison with exact elasticity solutions indicates that the present plate theory is sufficiently accurate for predicting the behavior of thick laminates.

Lo, K. H.↗

NASA NTRS1976

Gaussian ideal impulsive loading of rigid viscoplastic plates

The response of a thin, rigid, viscoplastic plate subjected to a spatially axisymmetric Gaussian ideal impulse loading was studied analytically. The Gaussian ideal impulse distribution instantaneously imparts a Gaussian initial velocity distribution to the plate, except at the fixed boundary. The plate deforms with monotonically increasing deflections until the initial dynamic energy is completely dissipated in plastic work. The simply supported plate of uniform thickness obeys the von Mises yield criterion and a generalized constitutive equation for rigid, viscoplastic materials. For the small deflection bending response of the plate, neglecting the transverse shear stress in the yield condition and rotary inertia in the equations of dynamic equilibrium, the governing system of equations is essentially nonlinear. A proportional loading technique, known to give excellent approximations of the exact solution for the uniform load case, was used to linearize the problem and obtain analytical solution in the form of eigenvalue expansions. The linearized governing equations required the knowledge of the collapse load of the corresponding static problem.

Hayduk, R. J.↗

NASA NTRS1977

Pressure distributions induced by elevon deflections on swept wings and adjacent end-plate surfaces at Mach 6

Surface pressure distributions are presented for regions where three-dimensional separated flow effects are prominent on swept-wing-elevon-end-plate models of 0 degree, 50 degree, and 70 degree sweepback, and with 0 degree, 10 degree, 20 degree, and 30 degree elevon deflections. Surface-oil-flow photographs and pressure distributions on the flat-plate wing, elevon, and end-plate surfaces are presented for numerous geometric variations, including various spacings between the elevon and the end plate, with and without a tip fin. The data, for a free-stream Mach number of 6 and a wing-root-chord Reynolds number of 20 x 10 to the sixth power, reveal considerably larger regions of elevon induced loads on the adjacent end-plate surface than would be anticipated by using inviscid flow analyses.

Kaufman, L. G., II↗

NASA NTRS1977

Transient wave propagation in composite plates due to impact

Stress-wave propagation in a composite plate due to an impact has been examined using anisotropic elasticity theory. The plate is modelled as a number of identical anisotropic layers whose elastic moduli are given. Mindlin's (1959) approximate theory of plates is then applied to each layer to obtain a set of difference-differential equations of motion by using the interlaminar stresses and displacements as explicit variables. Dispersion relationships for harmonic waves are found when traction-free boundary conditions are applied to both surfaces of the plate. The difference-differential equations are reduced to difference equations via integral transforms. With given impact boundary conditions these equations are solved for an arbitrary number of layers in the plate, and the transient propagation of a stress wave is calculated by means of a fast Fourier transform algorithm.

Sung Kim, B.↗

NASA NTRS1977

Application of the TRPLT1 element to large amplitude free vibrations of plates

A finite element formulation is developed for analyzing large amplitude free flexural vibrations of thin plates in NASTRAN. Stress distributions in the plate, in addition to deflection shapes and nonlinear frequencies are determined. Linearized equations of motion governing large amplitude oscillations of plates and a linearized geometrical stiffness matrix are presented. The solution procedure and convergence characteristics are discussed. The quasi-linear geometrical stiffness matrix for an eighteen degree-of-freedom higher order triangular plate element is evaluated by using a seven-point numerical integration. Nonlinear frequencies for square, rectangular, rhombic, and isosceles triangular plates, with edges simply supported or clamped, are compared with earlier solutions. The present formulation is found to give results entirely adequate for engineering purposes.

Mei, C.↗

NASA NTRS1977

Present-day plate motions

A data set comprising 110 spreading rates, 78 transform fault azimuths and 142 earthquake slip vectors was inverted to yield a new instantaneous plate motion model, designated RM2. The mean averaging interval for the relative motion data was reduced to less than 3 My. A detailed comparison of RM2 with angular velocity vectors which best fit the data along individual plate boundaries indicates that RM2 performs close to optimally in most regions, with several notable exceptions. On the other hand, a previous estimate (RM1) failed to satisfy an extensive set of new data collected in the South Atlantic Ocean. It is shown that RM1 incorrectly predicts the plate kinematics in the South Atlantic because the presently available data are inconsistent with the plate geometry assumed in deriving RM1. It is demonstrated that this inconsistency can be remedied by postulating the existence of internal deformation with the Indian plate, although alternate explanations are possible.

Minster, J. B.↗

NASA NTRS1978

Pressure pulsations on a flat plate normal to an underexpanded supersonic jet

An experiment was devised to study the interaction between an underexpanded supersonic gas jet and a flat plate, with the plate located in a region in which the interaction produces shock wave and flow fluctuations. Nitrogen gas at ambient stagnation temperature flowed through a convergent nozzle with exit diameter of 2.03 cm and impinged on a square metal plate normal to the jet. Results revealed local peak pressure fluctuations on the plate at nozzle pressure ratios of about 2 and 4.5, with the latter case producing fluctuations of the same order as the mean pressure on the plate; the frequency of the oscillations was as large as 20 kHz. For choked jet flow at ambient pressure higher than atmospheric, the pressure fluctuations would increase accordingly, and adjacent solid structures would therefore be subjected to proportionately higher normal stresses.

Back, L. H.↗