bluuebunny/crossref_metadata_2025 huggingface dataset:
Theoretical Analysis of the Effect of Compressibility and Free-Stream Turbulence on Free-Mixing Turbulent Gas Flows
Authors: Shivamoggi B. K.
Published: November 2010

A theoretical investigation is made of the effect of compressibility and free-stream turbulence on the mixing-layer flow between high-speed parallel turbulent gas streams. Compressibility effects on turbulence are formulated through suitable phenomenological models. The flow similarity principle is then invoked to analyze the flow equations; the results of which directly reveal the manner in which the compressibility effects and the free-stream turbulence affect the development of the mixing flow.
On Some Unbonded Contact Problems in Plane Elasticity Theory
Authors: Gladwell G. M. L.
Published: November 2010

Paper considers plane, frictionless, unbonded contact problems. It is shown that the integral equation relating the unknown contact pressure to the specified displacement in the contact region may be solved approximately by using an expansion in terms of Chebyshev polynomials. Three examples are chosen, a beam resting on a half plane, a rigid cylinder pressed into an elastic strip, and an elastic cylinder pressed between rigid planes. Graphs of results are presented.
In-Plane and Shear-Bending Impact of Laminated Composite Plates
Authors: Mortimer R. W. , Chou P. C. , Rodini B. T.
Published: November 2010

The accuracy of the lamination theory in transient wave propagation problems was studied. In-plane and shear-bending impact experiments were conducted with graphite epoxy angle-ply and cross-ply plates. The measured strain histories of these plates were compared with the theoretical predictions of the lamination theory. The results show that, under the given loading conditions, the lamination theory adequately predicts wave velocities and strains in symmetric angle-ply and cross-ply graphite epoxy plates.
Kinetic and Dynamic Effects on the Upper-Bound Loads in Metal-Forming Processes
Authors: Tirosh Jehuda , Kobayashi Shiro
Published: November 2010

The regular upper-bound approach in metal-forming processes is extended to time-dependent processes. The ultimate goal is to estimate, in an approximate manner, time rate effects such as machine speed and material inertia, on the forming load of time independent materials. The admissible velocity field with associated jumps is used to generate an acceleration flow field and associated flow resistance. Two fundamental nondimensional numbers emerge from the analysis for all processes considered. One is related to the speed at which the deforming load is applied, ρu02/σ0 (called the “kinetic head”) and the second is related to the acceleration of the deforming tool and its contact area with the flowing metal ρu˙0R/σ0 (called the “dynamic head”). The uniqueness of each specific process is characterized by appropriate functions representing the unsteady (or steady) pertinent geometry of the product and multiplying the foregoing numbers. The resulting expressions appear to be dominant only at relatively high speed and/or impact operations, and thus amplify the role of the time rate on the limit load. Three typical processes (forging, extrusion, and piercing) exemplify the approach with some experimental evidence.
The Frequency of Inertial Waves in a Rotating, Sectored Cylinder
Authors: Scott W. E.
Published: November 2010

An analysis of the inertial wave eigenfrequencies of a rapidly rotating liquid in a cylinder whose cross section is divided into four 90 deg sectors reveals that only if the cylinder height is less than the cylinder diameter can the fundamental frequencies be of the order of magnitude of the frequencies of spin-stablilized projectiles. Hence, sectoring the usual long cavities in liquid-filled, spin-stabilized projectiles will preclude the occurrence of a “Stewartson” resonance.
Nonlinear Propagation of Wave-Packets on Fluid Interfaces
Authors: Nayfeh A. H.
Published: November 2010

The method of multiple scales is used to derive two partial differential equations which describe the evolution of two-dimensional wave-packets on the interface of two semi-infinite, incompressible, inviscid fluids of arbitrary densities, taking into account the effect of the surface tension. These differential equations can be combined to yield two alternate nonlinear Schro¨dinger equations; one of them contains only first derivatives in time while the second contains first and second derivatives in time. The first equation is used to show that the stability of uniform wavetrains depends on the wave length, the surface tension, and the density ratio. The results show that gravity waves are unstable for all density ratios except unity, while capillary waves are stable unless the density ratio is below approximately 0.1716. Moreover, the presence of surface tension results in the stabilization of some waves which are otherwise unstable. Although the first equation is valid for a wide range of wave numbers, it is invalid near the cutoff wave number separating stable from unstable motions. It is shown that the second Schro¨dinger equation is valid near the cutoff wave number and thus it can be used to determine the dependence of the cutoff wave number on the amplitude, thereby avoiding the usual process of determining a new expansion that is only valid near the cutoff conditions.
Transient Response of an Elastic Half Space Subjected to a Reciprocating Antiplane Shear Load
Authors: Watanabe K.
Published: November 2010

In this paper we consider a problem of the response of an elastic half space subjected to an antiplane shear load. The load is suddenly applied and thereafter moves in an interval reciprocally as a trigonometric function of time. An analytical solution for the displacement is obtained in terms of single integration. It is shown that the discontinuity in the displacement occurs only for the case that the initial (maximum) speed of the load is greater than the speed of SH-wave. In this case the displacement has a finite jump on the leading wave front and a logarithmic discontinuity immediately behind the wave front which emanates from a point where the load speed comes up with SH-wave speed. Numerical calculations are carried out for several cases of the initial (maximum) speed of the load and are shown graphically.
Plastic Internal Variables Formalism of Cyclic Plasticity
Authors: Dafalias Y. F. , Popov E. P.
Published: November 2010

The notion of Plastic Internal Variables (PIV) is used in reformulating, in a general form, the equations of rate-independent plasticity. The stress, temperature, and the PIV are the state variables for the present development. Loading-unloading is defined in terms of the usual loading function of classical plasticity. The concept of discrete memory parameters entering the constitutive equations for the PIV is introduced, in order to describe realistically the material behavior under cyclic loading. Within the framework of the general development, a simple model is constructed. By generalizing uniaxial experimental observations the concept of the “bounding surface” in stress space is introduced, defined in terms of appropriate PIV. This surface always encloses the yield surface, and their proximity in the course of their coupled translation and deformation in stress space during plastic loading determines an appropriate quantity function of the state variables and a corresponding discrete memory parameter on which the value of the plastic modulus depends. The model is compared with experimental results in a uniaxial case.
Admissible Singular Solutions and the Hypercircle Method in Shallow Shell Theory
Authors: Antes H.
Published: November 2010

The object of this study is the construction of geometrically and statically admissible solutions of the basic shallow shell equations in the case of singular loads, especially for the use in the hypersphere theorems. An iterative procedure extends known solutions of plate theory to the classical and an improved shallow shell theory. The results contain all important terms of the exact solution near the singular point.
Response of Three Oscillators Coupled by a Weak Nonlinearity
Authors: Yen N. , Kronauer R. E.
Published: November 2010

As a simplified model of the exchange processes occurring among resonance modes in physical systems, such as a piezoelectric crystal plate or an acoustic interferometer, a study is made of the response of three oscillators that are coupled by a weak nonlinearity and whose frequencies satisfy the condition ω1 + ω2 ≅ ω3. The transient behavior is obtained by a perturbation expansion. There exist three integral constraints on the amplitude and phase variation of the oscillations for a conservative system, and the solution of the response can be reduced to quadrature. The phase diagram describing the motion indicates that the high frequency oscillation is unstable; the energy associated with it, under certain conditions, can be diverted to lower frequency oscillations. For nonconservative systems, the effects of dissipation and detuning are examined for their role in limiting the energy exchange among the oscillations and in determining the steady-state response to forcing. Predictions from this analysis are compared with results of a reported experiment in which a piezoelectric crystal plate is forced to oscillate at amplitudes sufficient to generate coupled subharmonics.
Derivation of Polycrystal Creep Properties From the Creep Data of Single Crystals
Authors: Lin T. H. , Yu C. L. , Weng G. J.
Published: November 2010

A method developed for calculating the polycrystal stress-strain-time relation from the creep data of single crystals is shown. Slip is considered to be the sole source of creep deformation. This method satisfies, throughout the aggregate, both the condition of equilibrium and that of continuity of displacement as well as the creep characteristics of single crystals. A very large three-dimensional region is assumed to be filled with innumerable identical cubic blocks, each of which consists of 64 cube-shaped crystals of different orientations. This region is assumed to be embedded in an infinite elastic isotropic medium. This infinite medium is subject to a uniform loading. The average stress and strain of a cubic block at the center of the region is taken to represent the macroscopic stress and strain of the polycrystal. This method is self-consistent and considers the heterogeneous interaction effect of the creep deformation of all slid crystals. The macroscopic stress-strain-time relations of the polycrystal were calculated for three tensile loadings, one radial loading, and two nonradial loadings of combined tension and torsion. The numerical results given by the present theory agree well with those predicted by the so-called “Mechanical Equation of State.” The creep strain components calculated by the present theory for the case of a constant tensile loading followed by an additional constant tensile loading are found to be considerably higher than those predicted by von Mises and Tresca’s theories. These results agree well qualitatively with experimental results.
Impact of a Rigid Body on an Elastic Half Space
Authors: Bycroft G. N.
Published: November 2010

A Fourier synthesis of the steady-state vibrations of a rigid plate on an elastic half space is used to determine the deceleration and penetration of a rigid body impacting an elastic half space over a flat circular area. In order to obtain a satisfactory solution, it is necessary to integrate to a large value of the frequency factor. The theoretical values are compared with some simple experiments on lead and Neoprene.
Branching Analysis at Coincident Buckling Loads of Nonconservative Elastic Systems
Authors: Plaut R. H.
Published: November 2010

Discrete nonconservative elastic systems which lose stability by buckling (divergence) are considered. Simple (distinct) critical points were treated previously, and the case of coincident buckling loads is analyzed here. An asymptotic procedure in the neighborhood of the critical point is used to determine postbuckling behavior and imperfection-sensitivity. It is shown that the system may exhibit no bifurcation at all. In other cases postbuckling paths may be tangential to the fundamental path at the critical point. The sensitivity to imperfections is shown to be more severe than for systems with distinct buckling loads (e.g., one-third, one-fourth, and one-fifth power laws are obtained for certain cases).
A Note on the Pure Bending of Unsymmetrical Prismatic Beams
Authors: Stokes V. K.
Published: November 2010

It is shown that the equations governing the pure bending of unsymmetrical prismatic beams can be written in a coordinate-free invariant form.
Experimental Investigation of the Angled Elliptic Notch Problem in Tension
Authors: Wu H. C. , Yao R. F. , Yip M. C.
Published: November 2010

Polymethylmethacrylate (PMMA) plates with angled elliptic notch are experimentally investigated under monotonic tension. The major interests of this investigation are the direction of crack initiation on the boundary of the notch and the critical stress that causes the crack initiation. It is found that the “fracture angle” in this investigation is generally smaller than that obtained from PMMA plate with slit crack which was reported in the literature. Furthermore, the paths of crack propagation are experimentally determined and “lance-like” fracture surface is observed.
Free-Stream Vorticity Disturbances Adjusting to the Presence of a Plate—A Quarter-Plane Problem
Authors: Rogler H.
Published: November 2010

Vorticity disturbances are introduced at a grid and convect with the uniform mean flow alongside a flat plate. The influence of the plate on this rotational, unsteady flow is found by solving Laplace’s equation in a quarter plane subject to Dirichlet boundary conditions. In the corner region downstream of the grid and near the plate, the streamline patterns do not convect with the mean flow and Taylor’s hypothesis is not valid as indicated by the velocity correlations. The influence of the plate is limited to a region from the plate to about one vortex diameter away from the plate. Near the plate and about one diameter downstream of the grid, a new streamline pattern evolves which convects along without further change. The alteration to the free-stream disturbances produced by the plate also represents the flow introduced by a wavy wall.
On the Stress Field Due to Initial Strains in a Cuboid Surrounded by an Infinite Elastic Space
Authors: Chiu Y. P.
Published: November 2010

This paper solves the problem of a stress field in an infinitely large matrix having a cuboidal element (of the same material) within which the initial (transformation) strains are uniform. Using a method which employs the Galerkin vector, expressions for stresses are obtained in terms of triple Fourier integrals. The resulting multiple integrals are integrated in closed form. Numerical stress evaluation has been performed for cuboids of three different shapes.
First-Passage Time for Oscillators With Nonlinear Damping
Authors: Roberts J. B.
Published: November 2010

A simple numerical scheme is proposed for computing the probability of first passage failure, P(T), in an interval O-T, for oscillators with nonlinear damping. The method depends on the fact that, when the damping is light, the amplitude envelope, A(t), can be accurately approximated as a one-dimensional Markov process. Hence, estimates of P(T) are found, for both single and double-sided barriers, by solving the Fokker-Planck equation for A(t) with an appropriate absorbing barrier. The numerical solution of the Fokker-Planck equation is greatly simplified by using a discrete time random walk analog of A(t), with appropriate statistical properties. Results obtained by this method are compared with corresponding digital simulation estimates, in typical cases.
A Methodology for Optimal Sensor Locations for Identification of Dynamic Systems
Authors: Shah P. C. , Udwadia F. E.
Published: November 2010

The problem of optimally positioning sensors in lumped and distributed parameter dynamic systems for the purpose of system identification from time-domain input-output data is formulated and a methodology for its solution is presented. A linear relation between small perturbations in a finite-dimensional representation of the system parameters and a finite sample of observations of the system time response is used to determine approximately the covariance of the parameter estimates. The locations of a given number of sensors are then determined such that a suitable norm of the covariance matrix is minimized. The methodology is applied to the problem of optimally locating a single sensor in a building structure modeled by a shear beam, such that the estimates of the stiffness distributions, obtained from the records of strong ground shaking and the building response at the sensor location, are least uncertain.
On the Dynamic Expansion of a Circular Hole in an Infinite Plate of Rate-Sensitive Plastic Material
Authors: Upadhyay P. C. , Stokes V. K.
Published: November 2010

The dynamic expansion of a circular hole in an infinite plate has been considered for rate-sensitive plastic materials by using an elastic-visco-perfertly plastic model of the exponential type. Numerical solutions have been obtained, by the method of characteristics, for the case when the hole is subjected to a constant acceleration. Solutions have been presented in the form of nondimensional plots covering a wide range of material properties and accelerations.
Sudden Appearance of a Crack in a Stretched Finite Strip
Authors: Chen E. P.
Published: November 2010

The dynamic response of a central crack in a finite elastic strip was considered in this study. The crack was assumed to appear suddenly when the strip is being stretched at its two ends. Laplace and Fourier transform techniques were used to formulate the mathematical solution. Numerical results on the dynamic stress-intensity factor were obtained. The influence of inertia, finite boundaries and their interactions on the load transmission to the crack tip were discussed.
Application of Stress Functions to Initial Stress Problems
Authors: Tabarrok B. , Dost S.
Published: November 2010

The governing equations of the linear initial stress problem are obtained from the pertinent equations of large deformation analysis. These equations are then cast in the framework of a variational statement. The functional has the incremental stresses and displacements as competing functions. However, in contrast to mixed formulations the displacement and stress fields are required to satisfy the equilibrium equations. This is done by invocation of classical stress functions and introduction of some new functions. The stationary conditions of the functional emerge as a set of compatibility equations. As such, the variational statement is referred to as the complementary energy principle, in spite of the presence of the displacements in its functional. The paper includes an example from 2D elasticity and a second example on buckling of cylindrical shells.
Further Investigation of a New Hardening Law in Crystal Plasticity
Authors: Havner K. S. , Shalaby A. H.
Published: November 2010

A simple theory of latent hardening in crystals, recently proposed by the authors [1], is applied to the determination of anisotropic hardening in slip systems of face-centered cubic crystals in the tensile test, based upon a parabolic resolved-shear-stress versus slip curve in the active system. The theory predicts the generally observed continuation of finite single slip beyond the crystallographic symmetry line. Moreover, the predicted diversity of finite distortional hardening among latent slip systems is in qualitative agreement with experiment.
Singular Reflection and Refraction of Elastic Waves Due to Separation
Authors: Comninou Maria , Dundurs J.
Published: November 2010

The effect of separation on the reflection and refraction of elastic waves by a unilateral interface was investigated before. It was found that no bounded solutions exist in a certain range of angles of incidence and combinations of materials. The present paper investigates singular solutions. It is shown that three different solutions satisfying all required inequalities can be found depending on the choice of the singularities. It is reasoned that singularities can be admitted only at the trailing edges of the separation zones. This makes the solution unique, and the singularities are weaker than inverse square root.
The Parametric Response of a Horizontal Beam Carrying a Concentrated Mass Under Gravity
Authors: Sato K. , Saito H. , Otomi K.
Published: November 2010

This investigation treats the steady-state response of parametric vibration of a simply supported horizontal beam, carrying a concentrated mass under the influence of gravity. Nonlinear terms arising from moderately large curvatures, longitudinal inertia of the beam and concentrated mass, and rotatory inertia of the concentrated mass are included in the equation of motion. By using the one mode approximation and applying Galerkin’s method, the governing equation of motion is reduced to a nonlinear ordinary differential equation with periodic coefficient. The harmonic balance method is applied to solve the equation and the dynamic response is derived. The effects of the weight, the rotatory inertia, the location, and the vibratory amplitude of the concentrated mass on the natural frequency are also discussed.
Nonlinear Kinematics of Wheel-Rail Contact
Authors: Burton T. D. , Whitman A. M.
Published: November 2010

We derive relations which describe the nonlinear geometry of contact between a railway vehicle wheelset and rail. Geometric constraint relations are derived and expanded about the central (rest) positions. These are solved for the rolling and vertical motions, instantaneous left and right wheel rolling radii, angles between the contact and horizontal planes, and lateral and longitudinal creepages. The results are given explicitly in terms of the lateral and yawing motions for mildly noncircular wheel and rail profiles. A kinematic (pure rolling) solution is obtained for the case where the wheel profile is sufficiently noncircular to invalidate the classical linear kinematic solution.
A Flow Potential Function for Hyperbolic Sine Creep
Authors: Davis E. A.
Published: November 2010

A new flow potential function or yield surface is presented. This function produces the hyperbolic sine law relating stress to minimum creep rate for creep tests in uniaxial tension.
On the Symmetry and Stability of Thermoelastic Solids
Authors: Ericksen J. L.
Published: November 2010

For the most part, nonlinear continuum theory has been based on the premise that the symmetry of a material never really changes. To analyze common phase transitions, we need to revise such theory of symmetry, but this is easier said than done. What seems to be needed is a theory of symmetry which is, in some sense, more local. Classical linear theories have a local nature, dealing only with the neighborhood of some state, so it seems worthwhile to rethink what is involved in symmetry considerations for them. Here, and not only here, symmetry is strongly linked to stability. Our purpose is to elaborate these matters.
Stress Singularity at the Corner of a Wedge-Shaped Crack or Inclusion
Authors: Parihar K. S. , Keer L. M.
Published: November 2010

The problems of shear loading of a crack having a wedge-shaped planform and of a planar, wedge-shaped inclusion are considered. A Green’s function formulation is used and the problem of finding the corner stress singularity is reduced to an eigenvalue problem of a simultaneous pair of singular integral equations. For large crack angles (i.e., a crack with angle nearly 2π) the integral equations can be solved and an approximate equation for the eigenvalue derived. The integral equations are solved numerically for the general case.
Effect of an Axisymmetric Imperfection on the Plastic Buckling of an Axially Compressed Cylindrical Shell
Authors: Gellin S.
Published: November 2010

The effect of a sinusoidal axisymmetric shape imperfection on the plastic buckling of a long cylindrical shell under axial compression is studied. The load at which nonaxisymmetric bifurcation from the axisymmetric state occurs is determined as a function of the imperfection amplitude for relatively thin shells. Imperfection-sensitivity in the plastic range is contrasted with that in the elastic range.
Buckling of a Superconducting Ring in a Toroidal Magnetic Field
Authors: Moon F. C.
Published: November 2010

Experimental evidence and a theoretical model are presented for the magnetoelastic buckling of a rigid superconducting ring in a steady circumferential (toroidal)magnetic field. The theoretical model predicts a coupled translation and pitch displacement of the coil in the buckled mode. A discussion is given of both the linear and nonlinear magnetic perturbation forces. The experiments were conducted in liquid helium (4.2°K). The lowest natural frequency of the rigid coil on elastic springs was observed to decrease near the buckling current. Agreement between theory and experiment is fair. These results may have design implications for poloidal field coils in magnetic fusion Tokamak reactors.
Buckling of Angle-Ply Laminated Circular Cylindrical Shells
Authors: Hirano Y.
Published: November 2010

This Note presents closed-farm solutions for axisymmetrical and axially unsymmetrical buckling of angle-ply laminated circular cylindrical shells under axial compression. The axisymmetrical and axially unsymmetrical buckling stress are found to be different from each other, and the best lamination angles which give the highest buckling stress are obtained.
Comparative Analysis by the Displacement-Discontinuity Method of Two Energy Criteria of Fracture
Authors: Cornet F. H.
Published: November 2010

This paper discusses the applicability of the displacement-discontinuity technique to crack propagation analysis for plane strain conditions. Results derived from the maximum strain-energy release-rate hypothesis are compared to those obtained with the critical strain-energy-density-factor theory. It is shown that for tensile stress fields both theories give similar results but that they differ for compressive stress fields. Experimental results are more in support of the maximum strain-energy release-rate model.
Base Pressure Associated With Incompressible Flow Past Wedges at High Reynolds Numbers
Authors: Warpinski N. R. , Chow W. L.
Published: November 2010

A model is suggested to study the viscid-inviscid interaction associated with steady incompressible flow past wedges of arbitrary angles. It is shown from this analysis that the determination of the nearly constant pressure (base pressure) prevailing within the near wake is really the heart of the problem and this pressure can only be determined from these interactive considerations. The basic free streamline flow field is established through two discrete parameters which should adequately describe the inviscid flow around the body and the wake. The viscous flow processes such as boundary-layer buildup along the wedge surface, jet mixing, recompression, and reattachment which occurs along the region attached to the inviscid flow in the sense of the boundary-layer concept, serve to determine the aforementioned parameters needed for the establishment of the inviscid flow. It is found that the point of reattachment behaves as a saddle point singularity for the system of equations describing the viscous recompression process. Detailed results such as the base pressure, pressure distributions on the wedge surface, and the wake geometry as well as the influence of the characteristic Reynolds number are obtained. Discussion of these results and their comparison with the experimental data are reported.
The Hydrodynamic Stability of Two Viscous Incompressible Fluids in Parallel Uniform Shearing Motion
Authors: Tsahalis D. T.
Published: November 2010

The stability problem of a thin film of a viscous incompressible fluid bounded on one side by another more viscous and less dense incompressible fluid of semi-infinite extent and on the other side by a fixed wall, where both fluids are in steady motion parallel to their interface and each fluid has a linear velocity profile, is solved for large values of the Reynolds number and small values of the viscosity ratio. Neutral stability curves of the Reynolds number versus the wave number are presented, parametrized with either the density ratio or the viscosity ratio as the family parameters.
The Propagation of a Crack by a Rigid Wedge in an Infinite Power Law Viscoelastic Body
Authors: Walton J. R. , Nachman A.
Published: November 2010

Closed-form solutions are obtained for the problem of a crack propagated by a 2-dimensional rigid wedge of finite thickness in an infinite power law viscoelastic body. The distance from the crack tip to the point of contact with the wedge is determined from the assumption that in the vicinity of the crack tip, forces of cohesion act to produce a smoothly closing crack with continuous stresses. Finally, a simple formula expressing the stress-intensity factor as a function of the speed of penetration and the length of the free crack surface is exhibited.
Thickness Oscillations in Deformed Elastic Plate
Authors: Hirao M. , Fukuoka H.
Published: November 2010

The theory of elastic waves superposed on finite deformation is applied to the study of thickness oscillations in a deformed elastic plate. Perturbation scheme, based on multiple scales, is employed to obtain a set of governing equations for the amplitudes of transverse thickness oscillations which are perpendicularly polarized with each other. It is shown that such oscillations, being strongly coupled by the initial deformation, undergo slow and sinusoidal amplitude modulation and slight shift in the resonance frequencies. The results suggest new techniques of experimental stress analysis.
Airfoil Design in Subcritical and Supercritical Flows
Authors: Chin W. C. , Rizzetta D. P.
Published: November 2010

The “inverse” or “design” problem in aerodynamics, which solves for the airfoil shape that induces a prescribed chordwise surface pressure subject to additional requirements on trailing edge closure, is considered in the transonic small-disturbance limit. A new formulation for the stream function ψ is suggested which uses well-set Neumann conditions on the chordwise slit, with the degree of closure dictated by a specified jump in ψ across the downstream slit emanating from the trailing edge. The boundary-value problem is solved by a type-dependent relaxation method that automatically generates closed airfoils on convergence. Computed airfoil shapes using subcritical and supercritical pressure distributions obtained from existing finite-difference analysis codes, in the latter case, with and without shockwaves, give results in reasonable agreement with the original specified shapes, and validate the basic ideas.
The Stefan Problem of a Polymorphous Material
Authors: Tao L. N.
Published: November 2010

The problem of freezing or melting of a polymorphous material in a semi-infinite region with arbitrarily prescribed initial and boundary conditions is studied. Exact solutions of the problem are established. The solutions of temperature of all phases are expressed in polynomials and functions in the error integral family and time t and the position of the interfacial boundaries in power series of t1/2. Existence and uniqueness of the series solutions are considered and proved. It is also shown that these series are absolutely and uniformly convergent. The paper concludes with some remarks on density changes at the interfacial boundary and various special cases, one of which is the similarity solution.
Thermoelastic Contact Between Bodies With Wavy Surfaces
Authors: Panek Carl , Dundurs J.
Published: November 2010

The problem treated involves two elastic solids with wavy surfaces that are pressed together and at the same time exchange heat by conduction because of an externally imposed temperature gradient. The conventional boundary conditions of no interface resistance to heat flow in the contact zones, and no heat transmission in the separation zones are adopted. It is found that the contact tractions are compressive if heat flows into the material with the higher distortivity (essentially the thermal coefficient of expansion divided by the thermal conductivity). For heat flow in the opposite direction, however, the conventional boundary conditions lead to some tensile tractions at the ends of the contact zones. The same observation has also been made by Barber who considered the indentation of an elastic solid by a rigid sphere that is either heated or cooled. The modification of the boundary conditions proposed by Barber, and which maintains linearity, is mentioned parenthetically.
Theory of Distributed Systems
Authors: Oldenburger Rufus
Published: November 2010

This paper concerns the wide class of physical networks made up of lumped components with transfer matrices whose elements are rational functions of the Laplace variables and hydraulic, pneumatic, electric, thermal, and elastic lines. It is advisable to lump on the basis of mathematical considerations after first obtaining the system equations with the lines unlumped. It is proved here that in a first approximation, the output vector of a system with hydraulic, pneumatic, electric, and elastic lines is related to the input vector by a transfer matrix whose elements are quotients of linear combinations of hyperbolic sines and cosines of Kis for constants {Ki} with coefficients which are polynomials in s. First approximations are often if not generally sufficient. The numerators and denominators of the elements of the transfer matrix may be expanded into infinite products with the aid of computers, and a finite number of dominant terms kept so that the numerators and denominators are now polynomials in s. If the elements of the input vector are rational functions of s, the inverse Laplace transforms of the elements of the output vector are readily obtained by known techniques. Thus lumping on the basis of mathematical considerations is accomplished. When thermal lines are included rational functions of s and hyperbolic functions of constants times s also arise.
Application of Pontryagin’s Principle to a Minimum Weight Design Problem
Authors: de Silva B. M. E.
Published: November 2010

A minimum weight design problem has been formulated as a general problem in optimal-control theory with the addition of state and control inequality constraints. Complete analytical solutions have been derived using the maximum principle of Pontryagin.
Liapunov Stability of Parabolic Distributed Systems: The Catalyst Particle Problem
Authors: Murphy E. N. , Crandall E. D.
Published: November 2010

The second method of Liapunov is applied to a distributed parameter reaction system. A Liapunov functional is assumed and theorems are developed which yield sufficient conditions for analyzing the stability of a steady state. The method is applied to the problem of the catalyst particle treated as a slab. The conditions obtained are valid for general perturbations and general system parameters.
Turbulent Jet Over an Inclined Wall
Authors: Sarpkaya T. , Richardson D. C.
Published: November 2010

The flow in a turbulent wall jet, with a control port and setback between the nozzle exit and the leading edge of the wall, was probed at various stations along the jet for Reynolds numbers (based on the nozzle width) ranging from 20,000 to 140,000. The similarity or the dissimilarity of the velocity profiles (for all Reynolds numbers) in the outer and inner regions of the jet and the pressure distribution along the wall were investigated. A new integral equation was used in the interpretation of the results and in the determination of the limitations of the range of applicability of Glauert’s wall-jet analysis. It was found that, whereas the similarity law holds true for the outer layer of the jet (beyond the entrance region), there is no similarity between the velocity profiles either in the inner layer or in the entrance region and that the pressure along the wall is slightly higher than that of the surrounding fluid which is at rest.
The Application of Thermal Transpiration to a Gaseous Pump
Authors: Orner P. A. , Lammers G. B.
Published: November 2010

A direct thermal-to-pneumatic energy converter utilizing the principle of thermal transpiration through a porous membrane is described. The applicability of this no-moving-part pump to a fluidic control system is discussed. A laboratory model has been constructed and experimentally evaluated for several gases, membrane types, and temperature ranges. A theoretical model is derived from the binary diffusion equations of kinetic theory. A linearized version of this model is verified experimentally for small temperature gradients. The kinetic theory model is evaluated numerically to predict the static performance of a pump for large temperature gradients.
Cavitation Suppression and Stress Effects in High-Speed Flows of Water With Dilute Macromolecule Additives
Authors: Ellis A. T. , Waugh J. G. , Ting R. Y.
Published: November 2010

Experiments were carried out to study the effect of dilute aqueous polymer solutions on flow-generated cavitation inception. The cavitation inception on 1/4 and 1/2-in-dia models with a hemispherical nose in a blowdown water tunnel was definitely inhibited at Reynolds numbers from 7 × 104 to 3.1 × 105. Reduction of the incipient cavitation number to 30 percent of its value for tap water was observed, depending on the kind of polymer used, its concentration, and the Reynolds number. Flow velocity field visualization was achieved by optical techniques, which measured the flow velocities and was used to correct values computed from venturi pressure drop. For guar gum (300 ppm) tests, the computed velocities were approximately 8 percent low.
An Initial Value Method for the Solution of a Class of Nonlinear Equations in Fluid Mechanics
Authors: Na T. Y.
Published: November 2010

An initial value method is introduced in this paper for the solution of a class of nonlinear two-point boundary value problems. The method can be applied to the class of equations where certain physical parameters appear either in the differential equation or in the boundary conditions or both. Application of this method to two problems in Fluid Mechanics, namely, Blasius’ boundary layer equation with suction (or blowing) and/or slip and the unsteady flow of a gas through a porous medium, are presented as illustrations of this method. The trial-and-error process usually required for the solution of such equations is eliminated.
Parameter Representation of Dynamic Equilibrium in Creep and Fatigue
Authors: Gain B. R. , Sinclair G. M.
Published: November 2010

In this study, a set of two parameters was used to describe the state of dynamic equilibrium for hardening and softening behavior in a variety of metallic materials, subjected to cyclic and static loading conditions, temperatures, and strain rates in the range of practical interest. The parameters consisted of a time-temperature parameter and a cyclic stress-strain parameter. Stable or near-stable values of cyclic stress and strain and of creep rate were extracted from numerous sources in the literature. Values for each parameter were calculated from that data and their functional relationship was studied. Results suggest a single relationship between the two parameters for pure FCC metals for both creep and fatigue.
Effects of Heterogeneous Nucleation of Water Vapor in Nozzles
Authors: Pouring A. A.
Published: November 2010

Condensation initiated by heterogeneous nucleation, which is surface dependent, is examined experimentally for the case of rapid nozzle expansions of water vapor. In contrast to previous de Laval nozzle steam experiments for vapor condensation initiated by homogeneous nucleation, the present results are for flows seeded with inorganic smoke and metallic ions. The influence of heterogeneous seeding materials on the condensation process is readily observable by comparison of seeded and unseeded experiments which are otherwise identical. Quantitative results for temperature and other properties, as well as condensation rates, follow based on pressure distribution. The results indicate that the prolonged isentropic expansion of a seeded flow gives a substantial decrease in entropy production for 1/10 micron and below particle sizes determined by electron microscopy. An attempt is made at determining the relative influence of ions and smokes. The competitive nature between heterogeneous and homogeneous processes is clearly evident.
The Effects of an Annular Fluid on the Vibrations of a Long Rotor, Part 2—Test
Authors: Fritz R. J.
Published: November 2010

Analyses and tests were made to investigate the hydrodynamic mass and damping of a fluid in a thin annulus surrounding a rotor which is vibrating due to unbalance forces. The analysis is described in Part 1. This report describes the tests. Vibrational amplitudes were measured of a constant-speed rotor with various fluids and radius-to-clearance ratios. Axial flow was restricted by limited-leakage end seals. The fluid flow was considered to be either vortex or turbulent, based on the Taylor or Reynolds number. The presence of the fluid was found to lower the critical speed. This effect was ascribed to a hydrodynamic mass which was evaluated from the tests. Hydrodynamic masses were also determined for the rotor vibrating without rotation and were found to be in agreement with the results of Stokes [1]. All results were in reasonable agreement with the predictions of Part 1.
Generalized Contraction Coefficient of an Orifice for Subsonic and Supercritical Flows
Authors: Benedict R. P.
Published: November 2010

After a brief historical review of the pertinent literature, expressions are developed which approximate the compressible contraction coefficient of any orifice in any installation for both subsonic and supercritical flows. These coefficients are based on a presumed knowledge of the incompressible contraction coefficient for the same orifice. Included in the formulations are compressibility effects upstream and downstream of the orifice as well as velocity-of-approach effects. Comparisons between the suggested approximations and recent experimental data are made.
Confined Jet Mixing for Nonseparating Conditions
Authors: Razinsky E. , Brighton J. A.
Published: November 2010

The mixing of an air jet with a lower-velocity air stream is described. The mixing takes place in a constant diameter pipe, and the flow is investigated from the inlet where the jet and secondary velocities are uniform (but different) to a location downstream where the flow is fully developed. Measurements are made of (1) the wall static pressure, (2) the mean velocity, (3) the turbulence velocities and Reynolds stress throughout the flow field for different velocity ratios and diameter ratios. This work differs from previous investigations in that a wider range of flow conditions is considered, i.e., different diameter and velocity ratios in addition to the flow in the latter stages of mixing. Also, the turbulence velocities and Reynolds stress as determined throughout the flow are described.
Integral Method for Flow Between Corotating Disks
Authors: Boyack B. E. , Rice W.
Published: November 2010

An integral method is developed for the three-dimensional, nonboundary-layer flow which occurs for laminar, radially inward through-flow of an incompressible Newtonian fluid between parallel corotating disks. The method is a forward-stepping procedure which forces satisfaction of integrals of the governing differential equations, plus boundary conditions, plus the governing differential equations at every radius. The velocity components are represented by polynomials of order N; the method is extendable with extraordinary ease to any value of N. It is reported that, with N = 8, the results agree very closely with results earlier obtained by a conventional finite-difference method and which agree with experiment. It is pointed out that the method presented is extremely conservative of computational time and might be adapted to many other problems.
Ultrasonic Velocity of Sound and Void Fraction in a Bubbly Mixture
Authors: Card D. C. , Sims G. E. , Chant R. E.
Published: November 2010

The velocity of sound at a frequency much greater than resonance in a bubbly air-water mixture has been measured for varying void fractions in a “pool” system. Only measurements of acoustic velocity well below resonance for varying void fraction, or near resonance for a few low void fractions, were previously available. The results presented in this paper show marked differences in the velocity of sound at high frequency (500 kHz) compared with existing low-frequency data. Existing theory, for low void fractions, is discussed in relation to phase, group, and signal velocity, with the limitations at high void fractions being given. The application of the technique for determining void fractions in two-phase flow systems is discussed.
Fatigue Crack Growth in Notched Parts With Compressive Mean Load
Authors: Saal H.
Published: November 2010

A fracture mechanics model is proposed to describe fatigue crack propagation in notched specimens. This model accounts for residual stresses which are present at the notch root after unloading from maximum compressive load. This is of particular interest for specimens subjected to compressive mean load. According to the model, cracks will stop growing at the boundary of the plastically deformed zone if the specimen is subjected to compressive load only. Validity of the model was verified with notched specimens of mild steel.
Flow Angle and Shear Stress Measurements Using Heated Films and Wires
Authors: McCroskey W. J. , Durbin E. J.
Published: November 2010

The heat transfer characteristics of yawed slender filaments have been generalized to include pairs of heated-film skin friction gages, as well as conventional hot wire probes, New sensor designs have been combined with a novel double-bridge electronic feedback system with accurate differential power capabilities for improved measurements in complex environments. Results of detailed calibration experiments illustrate the accuracy, simplicity, and utility of the probe designs and circuit techniques.
Boundary Conditions for Symmetry in Bourdon Tubes
Authors: Dressler R. F.
Published: November 2010

The four natural boundary conditions are derived for a newly observed symmetry in Bourdon tube action. The problem is described by an eighth-order system of pde’s for a Donnell-type shell theory. These, together with boundary conditions for the geometric symmetry and for the free end with rigid plug, comprise a well-posed mathematical problem. It requires only one-fourth the integration domain of the problem posed without symmetry, hence reduces storage requirements in computer calculations to one-sixteenth the number for the original problem.