Nonlinear flutter of curved plates.
Nonlinear Galerkin analysis of curved plate flutter, using shallow shell/von Karman equations and quasi-steady aerodynamic theory
Dowell, E. H.↗
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Results for “EQUATIONS - STRESSES PLATES”
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Calculation of oblique-shock-wave laminar-boundary-layer interaction on a flat plate
A finite difference solution to the problem of the interaction between an impinging oblique shock wave and the laminar boundary layer on a flat plate is presented. The boundary layer equations coupled with the Prandtl-Meyer relation for the external flow are used to calculate the flow field. A method for the calculation of the separated flow region is presented and discussed. Comparisons between this theory and the experimental results of other investigators show fairly good agreement. Results are presented for the case of a cooled wall with an oncoming flow at Mach number 2.0 without and with suction. The results show that a small amount of suction greatly reduces the extent of the separated region in the vicinity of the shock impingement location.
Goldberg, U.↗
A general explicit solution of the central overlap problem
The matrix of the normal equations of a central overlapping-plate solution with general models for frame parameters and the star parameters is inverted explicitly in terms of the inverses of the matrices in the isolated systems for the frame and star parameters. This makes it possible to calculate from explicit formulas the numerical estimates of the star and frame parameters which would follow from a rigorous overlapping-plate solution. Also, the covariance matrix of the adjustment parameters are calculated.
Eichhorn, Heinrich↗
A numerical method for unsteady aerodynamics via acoustics
Formal solutions to the wave equation may be conveniently described within the framework of generalized function theory. A generalized function theory is used to yield a formulation and formal solution of a wave equation describing oscillation of a flat plate from which a numerical method may be derived.
Hodge, Steve↗
Models of space averaged energetics of plates
The analysis of high frequency vibrations in plates is of particular interest in the study of structure borne noise in aircrafts. The current methods of analysis are either too expensive (finite element method) or may have a confidence band wider than desirable (Statistical Energy Analysis). An alternative technique to model the space and time averaged response of structural acoustics problems with enough detail to include all significant mechanisms of energy generation, transmission, and absorption is highly desirable. The focus of this paper is the development of a set of equations which govern the space and time averaged energy density in plates. To solve this equation, a new type of boundary value problem must be treated in terms of energy density variables using energy and intensity boundary conditions. A computer simulation verification study of the energy governing equation is performed. A finite element formulation of the new equations is also implemented and several test cases are analyzed and compared to analytical solutions.
Bouthier, O. M.↗
A Theoretical and Experimental Study of Planing Surfaces Including Effects of Cross Section and Plan Form
A summary is given of the background and present status of the pure-planing theory for rectangular flat plates and v-bottom surfaces. The equations reviewed are compared with experiment. In order to extend the range of available planing data, the principal planing characteristics for models having sharp bottom surfaces having constant angles of dead rise of 20 degrees and 40 degrees. Planing data were also obtained for flat-plate surfaces with very slightly rounded chines for which decreased lift and drag coefficients are obtained.
Shuford, Charles L , Jr↗
Electromagnetic Scattering From a Polygonal Thin Metallic Plate Using Quadrilateral Meshing
The problem of electromagnetic (EM) scattering from irregularly shaped, thin, metallic flat plates in free space is solved using the electric field integral equation (EFIE) approach in conjunction with the method of moments (MoM) with quadrilateral meshing. An irregularly shaped thin plate is discretized into quadrilateral patches and the unknown electric surface current over the plate is expressed in terms of proper basis functions over these patches. The basis functions for the electric surface current density that satisfy the proper boundary conditions on these quadrilateral patches are derived. The unknown surface current density on these quadrilateral patches is determined by setting up and solving the electric field integral equation by the application of the MoM. From the knowledge of the surface current density, the EM scattering from various irregularly shaped plates is determined and compared with the earlier published results. The novelty in the present approach is the use of quadrilateral patches instead of well known and often used triangular patches. The numerical results obtained using the quadrilateral patches compare favorably with measured results.
Deshpande, Manohar D.↗
Incipient transition phenomena in compressible flows over a flat plate
The full three-dimensional time-dependent compressible Navier-Stokes equations are solved by a Fourier-Chebyshev method to study the stability of compressible flows over a flat plate. After the code is validated in the linear regime, it is applied to study the existence of the secondary instability mechanism in the supersonic regime.
Erlebacher, G.↗
Layering, interface and edge effects in multi-layered composite medium
Guided waves in a cross-ply laminated plate are studied. Because of the complexity of the exact dispersion equation that governs the wave propagation in a multi-layered fiber-reinforced plate, a stiffness method that can be applied to any number of layers is presented. It is shown that, for a sufficiently large number of layers, the plate can be modeled as a homogeneous anisotropic plate. Also studied is the reflection of guided waves from the edge of a multilayered plate. These results are quite different than in the case of a single homogeneous plate.
Datta, S. K.↗
Reversed flow above a plate with suction
A minor extension is developed for Kovasznay's (1948) solution, and an exact solution is presented for Navier-Stokes equations that may represent the reversed flow about a flat plate with suction. This exact solution is the result of a search for a solution that may serve as an exact basic flow for a model stability analysis of nonparallel flows involving flow reversal.
Lin, S. P.↗
Modeling of the heat transfer in bypass transitional boundary-layer flows
A low Reynolds number k-epsilon turbulence model and conditioned momentum, energy and turbulence equations were used to predict bypass transition heat transfer on a flat plate in a high-disturbance environment with zero pressure gradient. The use of conditioned equations was demonstrated to be an improvement over the use of the global-time-averaged equations for the calculation of velocity profiles and turbulence intensity profiles in the transition region of a boundary layer. The approach of conditioned equations is extended to include heat transfer and a modeling of transition events is used to predict transition onset and the extent of transition on a flat plate. The events, which describe the boundary layer at the leading edge, result in boundary-layer regions consisting of: (1) the laminar, (2) pseudolaminar, (3) transitional, and (4) turbulent boundary layers. The modeled transition events were incorporated into the TEXSTAN 2-D boundary-layer code which is used to numerically predict the heat transfer. The numerical predictions in general compared well with the experimental data and revealed areas where additional experimental information is needed.
Simon, Frederick F.↗
Static-temperature distribution in a flat plate compressible turbulent boundary layer with heat transfer
Differential equations based on heat transfer and shear for temperature and velocity in turbulent boundary layers
Pinckney, S. Z.↗
Finite stretching of an annular plate.
The problem of the finite stretching of an annular plate which is bonded to a rigid inclusion at its inner edge is considered. The material is assumed to be isotropic and incompressible with a Mooney-type constitutive law. It is shown that the inclusion of the effect of the transverse normal strain leads to a rapid variation in thickness which is confined to a narrow edge zone. The explicit solutions to the boundary layer equations, which govern the behavior of the plate near the edges, are presented.
Biricikoglu, V.↗
Finite difference solutions of the Euler equations in the vicinity of sharp edges
Attempts have been made to explain why finite difference solutions of the Euler equations can describe flows with large vortical structures around sharp-edged bodies. The present paper is concerned with the influence of a singular sharp edge on the truncation error for a set of discretized Euler equations. An analysis is conducted of the distribution of the truncation error of one finite difference approximation of the Euler equations near a sharp edge of a thin plate. The analysis leads to a determination of the size of the region of the neighborhood of such a singularity. Attention is given to the consistency of a discretization of the Euler equations, and numerical experiments.
Hartwich, P.-M.↗
Reflection of weak shock wave from a boundary layer along a flat plate II : interaction of oblique shock wave with a laminar boundary layer analyzed by differential-equation method
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Kuo, Yung-Huai↗
Wake interference behind two flat plates normal to the flow - A finite-element study
A finite-element model of the Navier-Stokes equations is used for numerical simulation of flow past two normal flat plates arranged side by side at Reynolds number 80 and 160. The results from this simulation indicate that when the gap between the plates is twice the width of a single plate, the individual wakes of the plates behave independently, with the antiphase vortex shedding being dominant. At smaller gap sizes, the in-phase vortex shedding, with strong wake interaction, is favored. The gap flow in those cases becomes biased, with one of the wakes engulfing the other. The direction of the biased flow was found to be switching at irregular intervals, with the time histories of the indicative flow parameters and their power spectra resembling those of a chaotic system.
Behr, M.↗
Rarefied gas channel flows for three molecular models.
Boltzmann equation for rarefied gas flows between two parallel infinite plates for Maxwellian, hard sphere and BGK models
BOLTZMANN EQUATION↗
A study of the effect of a boundary layer profile on the dynamic response and acoustic radiation of flat panels
The response of a thin, elastic plate to a harmonic force which drives the plate from below and a compressible air stream with a viscous boundary layer flowing parallel to the upper surface along the length was investigated. Equations governing the forced response of the coupled plate-aerodynamic system are derived along with appropriate boundary conditions. Calculations of basic solution parameters for a linear velocity profile and for a Blasius profile showed that the same system response could be obtained from each profile if appropriate values of boundary layer thickness were chosen for each profile.
Mixson, J. S.↗