bluuebunny/crossref_metadata_2025 huggingface dataset:
Impulsively Loaded Strain-Rate-Sensitive Plates
Authors: Perrone Nicholas
Published: October 2011

The response of an impulsively loaded, isotropically rate-sensitive annular plate is calculated via “exact” and approximate viewpoints. For a typical example, numerical results differed by about 3 percent. The essence of the approximate approach, which represents a natural extension of a previous one-dimensional analysis [1], is that the initial stress profile remains substantially constant during the dominant portion of plastic flow.
Diffraction of a Plane Pulse by a Semi-Infinite Barrier at a Fluid-Solid Interface
Authors: Freund L. B. , Achenbach J. D.
Published: October 2011

Transient diffraction of a plane, dilatational pulse of arbitrary shape is considered. The diffracting surface is a smooth, rigid barrier separating a semi-infinite elastic solid and a semi-infinite ideal fluid over half of the common boundary. The problem is solved by the Wiener-Hopf technique, in conjunction with a superposition principle and a version of Cagniard’s method. Real integral expressions are obtained for the displacement potentials in the solid and in the fluid. For an incident displacement impulse, closed-form expressions are derived for the displacement field. For this case, the displacements at the solid-fluid interface are shown in graphs and are compared with the corresponding surface displacements when the fluid is absent.
Incompressible Elastic Viscous Lubricants in Continuous-Sleeve Journal Bearings
Authors: Fix G. J. , Paslay P. R.
Published: October 2011

A perturbation procedure is used to find the first effects of elasticity in a lubricating fluid on the performance of the bearing. This is achieved by considering an incompressible Maxwell-type material with a small elastic effect in a continuous sleeve journal. The relationship between the external lateral load on the journal and the eccentricity is given. The parameter which measures the extent of the elastic influence on the solution is pro-proportional to (viscosity)(speed of rotation)/(elastic shear modulus)(clearance). For most liquid lubricants in standard practicing situations, the effects of elasticity other than compressibility are negligible. The solution shows that the classical normality between the eccentric displacement and lateral loading expected for incompressible fluids is not preserved when the fluid has elastic effects.
Gravitational Stresses Determined Using Immersion Techniques
Authors: Parks V. J. , Durelli A. J. , Ferrer L.
Published: October 2011

This paper deals with a generalization of an immersion analogy suggested by Biot. A simple general proof of the analogy is given. Applications are described to two-dimensional problems (using urethane rubber specimens immersed in thallium formate) and to three-dimensional problems (using epoxy models immersed in mercury). Two and three-dimensional photoelasticity is used to determine stresses. The increase in response obtained by using the immersion technique permits the solution of a number of new problems where gravitational stresses play an important role; for example, in dams and in solid propellant rocket grains.
Limit Analysis of Rotationally Symmetric Shells Under Central Boss Loadings by a Numerical Method
Authors: Biron A. , Hodge P. G.
Published: October 2011

A new method of limit analysis of rotationally symmetric shells is introduced whereby lower and upper bounds are obtained through a nonlinear programming code. Bounds for an ideal sandwich shell with the Mises yield condition are found which are sufficiently close together for almost the entire range of the problem parameters for a particular shell configuration, thus yielding results which, in many cases, could not be obtained by standard techniques because of mathematical complexities. The method is applied to conical and parabolic shells loaded by a central boss.
Axially Symmetric Cross-Sectional Strain and Stress Distributions in Suddenly Loaded Cylindrical Elastic Bars
Authors: Jones O. E. , Norwood F. R.
Published: October 2011

Axially symmetric cross-sectional strain and stress distributions in semi-infinite cylindrical elastic bars subjected to pressure-step and velocity-impact loading are considered on the basis of the exact equations of motion. Asymptotic solutions are obtained as functions of time, radius, and distance from the end of the bar for the strains, ezz, err, eθθ, and erz, and for the stresses, τzz, τrr, τrz, and τθθ. These solutions, which are valid asymptotically at large distances from the end of the bar, describe the head of the pulse when only the first mode is operative. Previous Airy integral solutions based on plane sections remaining plane are contained in these solutions as first-order terms; radial dependencies resulting from the warping of plane sections appear as second-order correction terms involving derivatives of the Airy function. The magnitudes of the correction terms decrease as the distance from the end of the bar increases. The pressure-step solution accurately predicts the experimental results of Miklowitz and Nisewanger for the radial surface displacement. Quantitative nonzero values are obtained for the radial, tangential, and shear stresses associated with the dispersive lateral inertia mechanism. These values are compared with the amplitude of the applied longitudinal load; for example, the maximum radial stress is about 4 percent of the applied stress for a propagation distance of 20 dia. Finally, the solutions to the pressure-step and velocity-impact problems are compared to determine the effect of markedly different end conditions. The difference, which is found to be less than 1 percent at 20 dia from the end of the bar, is discussed in terms of a dynamic Saint-Venant’s principle.
Optimum Design of Layered Elastic Stress Wave Attenuators
Authors: Anfinsen L. E.
Published: October 2011

The problem of maximizing or minimizing the amplitude of stress waves propagating through a one-dimensional elastic layered structure is investigated. The properties of layers in series, situated between free and fixed surfaces, are used in deriving difference equations that relate the applied stress wave form at the free surface to the transmitted stress wave form at the fixed surface along characteristic paths. Optimal material requirements are determined for the first transmitted stress wave, which strongly influences the subsequent propagation. Similarity parameters are derived by transform methods which provide optimization criteria for the two-layer case. Materials are systematically selected that can provide stress amplitude reductions of more than 99 percent.
On a New Approach to Slip Flow Using Rayleigh’s Problem
Authors: Russo E. P. , Arnas O. A.
Published: October 2011

A new approach, involving a perturbation of the Navier-Stokes equations, is used to analyze the phenomenon of slip flow over a flat plate. An expression for the coefficient of drag is derived and compared to the drag coefficient obtained by the traditional approach of solving the Navier-Stokes equations with a slip-velocity boundary condition.
Analysis of a Liquid Vapor Phase Change by the Methods of Irreversible Thermodynamics
Authors: Bornhorst W. J. , Hatsopoulos G. N.
Published: October 2011

The object of this theoretical investigation is to obtain a set of equations which will predict the behavior of a fluid as it changes phase. Irreversible thermodynamics is employed to obtain general rate equations which relate the fluxes and forces across the nonequilibrium region existing at a phase interface. Both plane and spherical interfaces are considered. Experimental means for determining the three transport coefficients which appear in the resulting equations are discussed. Approximate values for the transport coefficients are obtained from kinetic theory arguments. The present analysis is limited to phase-change problems which may be described by linear phenomenological equations; this is so when the change in the driving potentials is small as compared to their value on either side of the phase interface. This restriction is necessary since presently no general theory exists for nonlinear rate processes.
Effect of Initial Imperfections on the Instability of a Ring Confined in an Imperfect Rigid Boundary
Authors: Bucciarelli L. L. , Pian T. H. H.
Published: October 2011

The stability of a radially constrained, complete, circular ring subjected to thermal stress and of a similarly restrained portion of a circular ring under circumferential end load is investigated. The effect of three types of initial geometric imperfections on the buckling behavior is determined. Results obtained, employing shallow arch approximations, show that this behavior depends on the assumed form of imperfection. In one case, no bifurcation or limit point exists at finite load level; in the second case, bifurcation and snap buckling may occur; in the third case, the system admits of a limit point. A design curve is proposed which can be used to estimate the stability limit of a circular ring exhibiting a certain “out-of-roundness.”
Effects of Longitudinal Inertia Upon the Parametric Response of Elastic Columns
Authors: Evensen H. A. , Evan-Iwanowski R. M.
Published: October 2011

Analytical and experimental investigations have been performed in a study of longitudinal inertia effects upon the parametric response of a column under an axial load P(t) = P0 + P1 cos γt. The analysis has led to stability criteria, imposed on the load and longitudinal inertia parameters, which have shown good agreement with experimental results. A certain degree of scatter between experimental runs has been observed, though agreement within (italics) each run has been very good. The scatter, attributed to small misalignments and departure from axiality of loading, stems from the realignment procedure necessary between each experimental run. To facilitate prediction of parametric response, the analytical stability criteria have been plotted in the form of two bounding surfaces of an instability region in a three-dimensional parameter space. Use of this region permits description of the conditions and responses associated with parametric instability, and allows evaluation of the effects of disturbances.
A Transformation in Coupled Thermoelasticity Problems
Authors: Mountfort M. V.
Published: October 2011

It is shown that a simple transformation can uncouple the thermoelastic field equations but at the expense of coupled boundary conditions. A large class of coupled thermoelastic problems then becomes solvable using integral equations.
The Significance of the Concentrated Load in the Limit Analysis of Conical Shells
Authors: DeRuntz John A. , Hodge P. G.
Published: October 2011

The yield point load of a simply supported conical sandwich shell loaded at its vertex through a rigid central boss is found for a material obeying the Tresca yield condition. Exact solutions are found for a wide range of shell configurations ranging from thick shallow cones to thin steep ones, including large and small boss sizes. The results are compared with those for the limiting case of zero boss radius corresponding to a complete conical shell loaded with a concentrated load at its vertex. It is found that for thick shallow shells the concentrated-load solution is a good approximation to the solution for realistically small boss sizes, but that for thin and/or steep shells the agreement is so poor as to make the concentrated-load solution meaningless. It is shown that such behavior also can be expected for shells obeying more realistic yield conditions.
An Analysis of Longitudinal Elastic-Plastic Pulse Propagation
Authors: Clifton R. J. , Bodner S. R.
Published: October 2011

The one-dimensional, rate-independent theory of elastic-plastic wave propagation for smooth stress-strain curves concave toward the strain axis is applied to the problem of a long uniform bar loaded at one end by a pressure pulse of short duration. The essential features of the solution are obtained for the case of a semi-infinite bar and for the case of a finite bar whose other end is stress-free by using the method of characteristics in the t-x plane. The general shape of boundaries in the t-x plane which separate regions governed by the dynamic elastic equations from regions governed by the dynamic plastic equations is presented. The nature of the discontinuities that occur at these boundaries is also discussed. For the finite-bar case the analysis is given for materials which exhibit isotropic work hardening and for materials for which the stress-strain behavior in tension is independent of any previous compression. The main features of the solution are in agreement with the behavior observed for annealed, commercially pure aluminum bars subjected to explosive loading at one end. These experiments will be reported subsequently.
Nonlinear Viscoelasticity for Short Time Ranges
Authors: Huang N. C. , Lee E. H.
Published: October 2011

Approximate constitutive equations for nonlinear viscoelastic incompressible materials under small finite deformation and for short time ranges are derived. The error bound of such a constitutive equation is investigated. Nonlinear creep is analyzed on the basis of the proposed equation, and also the problem of a pressurized viscoelastic hollow cylinder bonded to an elastic casing. Numerical solutions, evaluated by assuming particular forms of kernel functions in the constitutive equation, are obtained by means of an inverse interpolation technique, and the effects of nonlinearity of material properties are discussed. An experimental procedure is also proposed for measuring kernel functions from uniaxial tension tests for real materials.
Gyrodynamics, New Approach and Solutions
Authors: Chang K. T.
Published: October 2011

A generalized “first law” of motion for spinning bodies is formulated, analogous to Newton’s First Law for particle dynamics. By such a concept, the general rotational motion of a body is described as a precession of a reference principal axis about the angular momentum vector, the motion of the latter being in turn related to the applied moment by the well-known “second law” of motion. This new approach allows vectorial visualization of body attitudes in a fixed frame of reference, as opposed to Euler’s description of motion in terms of body angular rates. The two methods are complementary in the solution of space vehicle problems.
Attitude Stability of a Spinning Satellite in an Elliptic Orbit
Authors: Kane T. R. , Barba P. M.
Published: October 2011

Floque´t theory is used to develop a procedure for testing the stability of a spinning, symmetric satellite whose mass center moves on an elliptic orbit while the symmetry axis remains normal to the orbit plane.
Conditions at the Root of a Crack in a Bent Plate
Authors: Redwood R. G. , Shepherd W. M.
Published: October 2011

Transverse displacements of a circular plate containing a radial crack are considered using classical small-deflection theory. Particular sets of boundary conditions on the circumferential edge are derived which require either infinite or zero radial slopes at the root of the crack, and these results are discussed in relation to previous work in this field.
Analysis of a Semi-Infinite Strip With Constant Stress Flanges Under Concentrated Loads
Authors: Meck H. R.
Published: October 2011

An analysis is presented for a semi-infinite strip reinforced by flanges and subjected to concentrated in-plane loads at the ends of the flanges. The taper which results in constant flange stress is determined, and the stress distribution in the sheet is also found. A simple complex variable analysis is used which leads to exact solutions in closed form.
Axisymmetrical Turbulent Swirling Natural-Convection Plume: Part 2—Experimental Investigation
Authors: Lee Shao-Lin
Published: October 2011

An experimental investigation is made of the behavior of an axisymmetrical turbulent swirling natural-convection plume in an otherwise motionless ambient fluid. The swirling plume is issued from the exit of a swirling-plume generator which couples the hot gases from a Bunsen burner flame and the swirling mass of air from a ring of distributed tangential jets. Temperature and velocity fields of the swirling plume are measured by the use of a temperature-calibrated, V-shaped hot-wire probe. Measured results of the vertical and swirling velocities, the temperature, and the characteristic radius of the swirling plume are found to agree closely with the theoretical predictions of Part 1.
Nonaxisymmetric Behavior of Shallow Shells Loaded at the Apex
Authors: Penning F. A.
Published: October 2011

Nonaxisymmetric deflections were measured on clamped shallow spherical shells loaded over a small circular area concentric with the apex. The first nonaxisymmetric pattern contained three lobes. Additional load produced a maximum of five lobes and further loading showed a tendency to reverse the pattern sequence. Each configuration occurred within a relatively small range of corresponding values of normalized deflection δ and dimensionless load P*.
Quasi-Static Stresses Due to Moving Temperature Discontinuity on a Plane Boundary
Authors: Jahanshahi A.
Published: October 2011

Closed-form solution is constructed to plane state of strain generated in a semi-infinite elastic medium when a portion of its boundary is heated. The heated region is assumed to be moving with uniform velocity. It is shown that stresses are bounded everywhere and are identically zero when the velocity of the moving temperature discontinuity vanishes. The study is based on uncoupled quasi-static thermoelastic theory.
Some Experiments on the Vibration of a Hemispherical Shell
Authors: Hwang Chintsun
Published: October 2011

The paper describes the experiments on the vibration of a thin hemispherical shell having a free edge and constant thickness. The test data are compared with the analytical data obtained through various methods originated by Rayleigh, Love-Federhofer-Naghdi, and Mushtari-Vlasov. For the axisymmetrical case, the test results compare favorably with the numerical data based on the method of Love-Naghdi. For the asymmetrical cases, it is found that the latter method fails to predict the most significant modes in the low-frequency region, while Rayleigh’s inextensional theory yields favorable frequency data. The reason for the failure of the more sophisticated method to predict the shell vibration is explored. The failure may be due to a characteristic inherent in the linear shell theory, or may be due to difficulties in numerical computation which are explained in the paper. Also noted is a typical modal shape where the deformation pattern is concentrated in the free-edge region. The phenomenon, which justifies the use of the dynamic edge effect solutions, is explained analytically.
Nonequilibrium Flow of Dilute Reacting Gases
Authors: Thommen H. U.
Published: October 2011

In this paper the nonequilibrium flow of a reading gas which is highly diluted with an inert gas is studied. As a typical example for such a gas mixture, air is considered under conditions where the oxygen dissociates to an appreciable degree while the nitrogen remains essentially inert. The resulting perturbation scheme is applied to the flow behind a normal shock wave and to the flow over a slender wedge. Viscosity, heat conduction, and diffusion are neglected in this treatment.
On the Parametrization of the Elastic Moduli of Two-Phase Materials
Authors: Wu Tai Te
Published: October 2011

A single parameter is suggested to account for the complicated stress and strain distributions in two-phase materials. Its existence requires verification from extensive experimental studies.
Axisymmetrical Turbulent Swirling Jet
Authors: Lee Shao-Lin
Published: October 2011

A simple closed-form solution has been obtained for an axisymmetrical turbulent swirling jet issuing from a circular source into a semi-infinite motionless ambient fluid by introducing the assumptions of similar axial and swirling velocity profiles and lateral entrainment of ambient fluid into the integrated governing equations. Results for the decays of the axial and swirling velocities and the spray of the jet agree closely with the existing experimental findings on the velocity fields of a swirling round turbulent jet of air generated by flow issuing from a rotating pipe into a reservoir of motionless air.
A Crack Between Dissimilar Media
Authors: England A. H.
Published: October 2011

The two-dimensional problem of a crack opened under constant pressure between two dissimilar materials is examined. It is found that an apparent solution to the problem does not satisfy a necessary physical condition.
Couple-Stress Effects on Stress Concentration Around a Cylindrical Inclusion in a Field of Uniaxial Tension
Authors: Weitsman Yechiel
Published: October 2011

This investigation is concerned with the effects of couple stresses on the elastic behavior of a composite body, formed by the presence of a cylindrical inclusion within an infinite exterior region. The exterior region is assumed to be subjected to uniaxial tension at infinity. The inclusion and the exterior are assumed to have different elastic constants G1, ν1 and G2, ν2 respectively, as well as distinct characteristic lengths l1 and l2. These characteristic lengths provide a measure of the granular or crystalline substructure of the materials and introduce the effect of couple stress. Particular attention is focused on the stress-concentration factor at the interface between the inclusion and the exterior region. The results are evaluated for various ratios of G1:G2 and l1:l2. They are shown to depend on those ratios as well as on the dimensions of the inclusion.
Rigid-Plastic Beams Under Uniformly Distributed Impulses
Authors: Florence A. L. , Firth R. D.
Published: October 2011

This paper contains the description and results of experiments in which pinned and clamped beams are subjected to uniformly distributed impulses large enough to cause considerable plastic deformation. The final permanent shapes are compared with those predicted by the rigid-plastic theory. They are also compared with the shapes predicted when the theory takes some account of large deflections and strain-hardening.
Photoelastic Analysis of Plates Subjected to Restrained Shrinkage
Authors: Parks V. J. , Durelli A. J.
Published: October 2011

Techniques have been developed to cast photoelastic materials in molds or about inserts and allow them to bond at the interfaces or remain free, at will. The birefringence associated with the restrained shrinkage developed in the process of curing can be analyzed in a polariscope. This paper deals with the stress-and-strain problems that can be studied using this method and with the interpretation to be given to the results obtained. To solve two-dimensional problems, it is suggested that a method be used to minimize the “pinching” effect or restrained shrinkage transverse to the plate plane at bonded boundaries. Applications to plates of complicated shapes with several discontinuities, with and without inserts, are shown.
Classical Normal Modes in Damped Linear Dynamic Systems
Authors: Caughey T. K. , O’Kelly M. E. J.
Published: October 2011

The purpose of this paper is to determine necessary and sufficient conditions under which both discrete and continuous damped linear dynamic systems possess classical normal modes.
Experimental Methods for Dynamic Stress Analysis in Viscoelastic Materials
Authors: Daniel I. M.
Published: October 2011

This paper deals with experimental methods of dynamic stress analysis in viscoelastic materials. Plasticized polyvinyl chloride is used as the model material. Dynamic properties, both mechanical and optical, in the form of a complex modulus and a stress fringe value as functions of frequency are determined by means of sinusoidal oscillation tests. These are converted into a relaxation modulus and a stress fringe value as functions of time. Two approaches are discussed. In the first one, measured strains in the model and the material relaxation modulus are used for the computation of stresses by numerical integration of the integral constitutive relations of viscoelasticity. In the other approach, birefringent measurements in the model and the stress fringe value of the material are used for the computation of the principal stress difference by numerical integration of the integral stress-optic relation. The application of these methods is demonstrated in the cases of a strut and a plate subjected to the impact of a falling weight. Results obtained independently by the two methods are in satisfactory agreement.
Efficiency of Pumping and Power Generation in Ultrafine Electrokinetic Systems
Authors: Burgreen D. , Nakache F. R.
Published: October 2011

In this paper, some of the practical implications of the theory of electrokinetic flow in ultrafine capillaries are examined. It is found that electroosmotic pumping efficiency can exceed mechanical pumping efficiency when the width of capillary elements become small. Computations show that electric power generation with an efficiency of approximately 17 percent may be obtained by pumping water through fine capillary media.
Stress Distribution in Bonded Dissimilar Materials Containing Circular or Ring-Shaped Cavities
Authors: Erdogan F.
Published: October 2011

The general problem of two semi-infinite elastic media with different properties bonded to each other along a plane and containing a series of concentric ring-shaped flat cavities is considered. Using the Green’s functions for the semi-infinite plane, the problem is formulated as a system of simultaneous singular integral equations. Closed-form solution of the corresponding dominant system with Cauchy kernels is given. To obtain the complete solution, a technique reducing the problem to solving a system of linear algebraic equations rather than a pair of Fredholm integral equations is outlined. The examples for which the contact stresses are plotted include the bonded media with an axially symmetric external notch subject to axial load or homogeneous temperature changes and the case of penny-shaped crack.
Physical Model of a 3-Constant Isotropic Elastic Material
Authors: Hoppmann W. H. , Shahwan F. O. F.
Published: October 2011

A study is presented of the statical deformation of a model of a supposed 3-constant isotropic elastic material which exhibits the phenomenon of couple stresses. A description of the design and construction of the physical model is given. The related theory is summarized briefly and used in order to determine the three independent elastic constants which characterize the model of the material. The specific constitutive equations are presented. Experimental results are given for the model loaded in a mode which may be called pure bending.
Kinematic-Hardening in Zinc-Alloy Tubes
Authors: Jenkins D. R.
Published: October 2011

The kinematic theory of strain-hardening is used to evaluate the post-yield behavior of tubular specimens subjected to axial force combined with internal pressure or torque. Prediction of yield-surface motion during strain-hardening is simplified through the use of piecewise linear yield criteria. The predicted behavior is compared with the results of experiments on tubes of Zamak-3 zinc alloy. After an initial loading beyond initial yield, the tubes were reloaded along a second stress path to subsequent yield. The observed state of stress at subsequent yield agreed rather well with the kinematic-hardening theory predictions.
Large-Amplitude Free Vibrations of a Beam
Authors: Wagner Hans
Published: October 2011

Free vibrations of an initially straight elastic bar having free-free or clamped-free ends are analyzed by assuming that the bar is undergoing inextensional motion and that shearing effects and rotatory inertia are negligible. If Hamilton’s principle is applied, an isoperimetric variational problem is reached. Upon elimination of the subsidiary condition, the remaining Euler equation (a highly nonlinear partial differential equation) can be reduced to an ordinary nonlinear differential equation by means of an extension of Galerkin’s procedure (Bubnov method). Because of the particular type of the reduced equation, use can be made of Atkinson’s superposition method for the frequency of the periodic solutions of the equation. Finally, a plot shows the approximate non-linear period versus the initial amplitude, both rendered nondimensional by introducing proper linear expressions.
Forced Axisymmetric Motions of Circular Elastic Plates
Authors: Weiner R. S.
Published: October 2011

Axisymmetric motions of a circular elastic plate are considered here according to the Poisson-Kirchhoff plate theory. A concentric ring loading of arbitrary time dependence is examined and used to construct solutions for a concentrated central load and for a uniform pressure loading. The boundary of the plate is considered to be elastically built-in in a manner that prevents transverse edge motion and provides a restoring edge moment linearly related to edge rotation. Thus, limiting cases are a clamped plate and a simply supported plate. Finally, a discussion relating this work to the integral-transform approach of Sneddon is presented to enable physical interpretation and generalization of his approach.
Application of a New Method of Approximation in the Solution of Ordinary Differential Equations to the Blasius Equation
Authors: Kennedy Ernest D.
Published: October 2011

A new method for the approximate solution of ordinary differential equations is applied to the Blasius equation of laminar boundary-layer theory. The Blasius equation is related to a Riccati equation which is, in the first approximation, solved in terms of Airy integrals. The approximation gives a value of the wall shear which is 6 percent below the value calculated by Howarth. In addition to furnishing the wall shear, an explicit expression is derived for the velocity distribution. The new solution is expanded in a convergent series and compared with Blasius’ original series which is known to diverge. The coefficients of only the two lowest order terms agree. Although demonstrated only for the Blasius equation, the method is useful in many problems and is being used to study the Falkner-Skan equation. There is the hope that the analytical expressions for the Blasius function can be used in the many problems where it is the zeroth-order solution and appears as coefficients in the differential equations for the higher order solutions.
Dynamics of Synchronous-Precessing Turborotors With Particular Reference to Balancing. Part 1—Theoretical Foundations
Authors: Tang T. M. , Trumpler P. R.
Published: October 2011

The commonly employed “indifferent equilibrium” postulate is rejected as internally inconsistent, and the dynamics problem is solved by using a system of discrete masses with fixed unbalances arbitrary in magnitude and direction. A method is presented for the calculation of bearing reaction as a function of machine speed including the effect of turbulent-flow damping at disk masses, so-called gyroscopic moments, and bearing oil-film and support flexibility. The calculation is particularly adapted to a digital-computer program employing successive multiplication of 5 × 5 matrices with complex elements.
The Normal Modes of Vibration of Certain Nonlinear Continuous Systems
Authors: Wah Thein
Published: October 2011

Two examples from structural theory are invoked to show that “normal modes” of vibration could have a simple interpretation in nonlinear distributed parameter systems.
Theory of Buckling of a Porous Slab and Its Thermoelastic Analogy
Authors: Biot M. A.
Published: October 2011

A theory is developed for the buckling of a fluid-saturated porous slab under axial compression. The problem is discussed in the context of the thermodynamics of irreversible processes. It is shown that there is a range of compressive loads, between a lower and upper critical value, for which the slab exhibits creep buckling. The problem of folding instability of a porous layer embedded in a viscous or viscoelastic medium is also analyzed and the dominant wavelength is evaluated. Identical behavior is derived by analogy for a thermoelastic slab with a critical range between isothermal and adiabatic buckling. The theory is applicable to a large class of two-phase materials obeying the same thermodynamics. It also provides a simple analysis of thermoelastic damping of plates.
The Elastic Cylindrical Shell Under Nearly Uniform Radial Impulse
Authors: Goodier J. N. , McIvor I. K.
Published: October 2011

In the radial motion of an elastic cylindrical shell following impulsive pressure all round, imperfections in the uniformity can cause development of flexure through interaction of (fluctuating) circumferential force with flexural curvature. Flexural modes of rather high order (several nodes in the circumference) can be strongly excited, especially those having a frequency one half that of the breathing mode (nonlinear autoparametric excitation). Almost all the original energy can be transferred, over a number of cycles, from the breathing mode to one or two high flexural modes.
An Iterative Method for the Displacement Analysis of Spatial Mechanisms
Authors: Uicker J. J. , Denavit J. , Hartenberg R. S.
Published: October 2011

An algebraic method for the displacement analysis of linkages has been the subject of earlier publications [1, 2]. This method, based on the use of a symbolic notation, allows the application of matrix algebra to the study of displacements in linkages, and permits formulation of all the kinematic relations of a linkage in terms of matrix equations. Based on this earlier work, the present paper develops an iterative method for the solution of the matrix equations required in displacement analysis. A complete solution is given for simple-closed linkages consisting of revolute and prismatic pairs (and their combinations). A brief indication of how higher pairs and multiple-closed chains may be handled is also given. Particularly useful in spatial problems, since it does not depend on visualization, this approach is developed in a manner intended for digital-computer operation.
Some Notes on Singular Solutions and the Green’s Functions in the Theory of Plates and Shells
Authors: Jahanshahi A.
Published: October 2011

Singular solutions are constructed which generate the singularities for great many types of concentrated action on shallow spherical and cylindrical shells. Subsequently a technique is introduced to construct the Green’s functions for closed circular cylindrical shells. Also, the deformation of thin plates subjected to moving hot spots is discussed briefly.
Tensile Plastic Stress-Strain Relations of 2017-T4 Aluminum Alloy Under Hydrostatic Pressure
Authors: Hu L. W. , Shull H. E.
Published: October 2011

Tension tests were conducted on an aluminum alloy 2017-T4 under hydrostatic pressures up to 50,000 psi. Effects of hydrostatic compression on the plastic stress-strain relations, the radius of curvature of the profile, and the diameter at the neck are reported in this Note.
Transient Compressional Waves in an Infinite Elastic Plate With a Circular Cylindrical Cavity
Authors: Scott R. A. , Miklowitz Julius
Published: October 2011

The problem treated is that of an infinite free plate with a circular cylindrical cavity subjected to a step normal displacement. The linear equations of elasticity are employed and the formal solution is obtained using a multi-integral transform technique, necessitating the introduction of extended Hankel transforms, and residue theory. Some properties of the Rayleigh-Lamb frequency equation, pertinent to the inversion process, are derived. Numerical information for the far field, showing the effect of the hole radius on the displacements, is obtained using the stationary phase method and, in the case of the radial displacement, the solution is compared with the corresponding slab solution. The results show that at a given station the plate-cavity solution approaches that for the slab, as the hole radius decreases. The head of the pulse and stationary-phase approximations to the corresponding horizontal slab displacement are also compared, and some discrepancies between the two are found in the vicinity of the wave-front arrival time.
Full-Strength Reinforcement of a Cutout in a Cylindrical Shell
Authors: Hodge Philip G.
Published: October 2011

A long circular cylindrical shell is to be pierced with a circular cutout, and it is desired to design a plane annular reinforcing ring which will restore the shell to its initial strength. Upper and lower bounds on the design of the reinforcement are obtained. Although these bounds are far a part, it is conjectured that the upper bound, in addition to being safe, is reasonably close to the minimum weight design. Some suggestions for further work on the problem are advanced.
Plastic Stress-Strain Relationships—Some Experiments to Derive a Subsequent Yield Surface
Authors: Parker John , Bassett M. B.
Published: October 2011

Experiments have been carried out on thin tubular specimens of alpha brass subjected to various combinations of torque and transverse tension, after initial overstrain in torsion. The loading paths were based upon a yield function expressing one degree of anisotropy which had been found previously to give good correlation of initial radial loading paths. The primary definition of yield used was the “Taylor-Quinney, Lode”; however, “Limit of Proportionality” and “Initial Loading Slope Tangent” definitions have also been investigated. The derived yield surface (Taylor-Quinney) shows strong positive cross effect, rotation, and a Bauschinger effect extending over the whole reversed quadrant to initial loading. No indication of the formation of a corner on the yield surface was found.
Application of Variational Equation of Motion to the Nonlinear Vibration Analysis of Homogeneous and Layered Plates and Shells
Authors: Yu Yi-Yuan
Published: October 2011

An integrated procedure is presented for applying the variational equation of motion to the approximate analysis of nonlinear vibrations of homogeneous and layered plates and shells involving large deflections. The procedure consists of a sequence of variational approximations. The first of these involves an approximation in the thickness direction and yields a system of equations of motion and boundary conditions for the plate or shell. Subsequent variational approximations with respect to the remaining space coordinates and time, wherever needed, lead to a solution to the nonlinear vibration problem. The procedure is illustrated by a study of the nonlinear free vibrations of homogeneous and sandwich cylindrical shells, and it appears to be applicable to still many other homogeneous and composite elastic systems.
On Vibrations of Elastic Spherical Shells
Authors: Naghdi P. M. , Kalnins A.
Published: October 2011

This investigation is concerned with axisymmetric as well as asymmetric vibrations of thin elastic spherical shells. First, with the limitation to torsionless axisymmetric motion, the basic equations for spherical shells of the classical bending theory of Love’s first approximation are reduced to a system of two coupled differential equations in normal displacement of the middle surface and a stress function; this system of equations is applied to free vibrations of a hemispherical shell with a free edge and numerical results are obtained for the lowest natural frequency as a function of the thickness of the shell. The remainder of the paper is, in the main, devoted to a study of asymmetric vibrations of a hemispherical shell with a free edge according to the extensional theory. Numerical results for natural frequencies (of the four lowest circumferential wave numbers) and mode shapes are given and the results are compared with the prediction of Rayleigh’s inextensional theory.
Effect of Small Cross Flow and Surface-Temperature Variation on Laminar Free Convection Along a Vertical Plate
Authors: Young R. J. , Yang Kwang-Tzu
Published: October 2011

The effect of small cross flow and surface-temperature variation on laminar free-convection boundary-layer characteristics along a vertical plate is studied by means of a perturbation analysis. First-order deviations from the quasi-two-dimensional solution are derived. The associated universal functions are calculated for two Prandtl numbers of 0.72 and 1.0. Essential results are given in both graphical and tabulated forms.
The Unsteady Forces Due To Propeller-Appendage Interaction
Authors: Pinkus O. , Lurye J. R. , Karp S.
Published: October 2011

This paper presents a study of the nature of the unsteady forces in the field of a propeller rotating in the vicinity of an appendage. The propeller is assumed to be one of a high aspect ratio while the appendage, although of finite width, is assumed to be infinitely long, and thus the problem is reduced to a study of the unsteady flow field around two flat plates. An essential feature of the analysis is that the mutual interference effects of propeller blade and the appendage are taken into account. The method of solution employs the technique of the substitution vortex which yields explicit analytic expressions for the quasisteady, apparent-mass and wake forces for both the propeller and appendage. These equations provide the magnitude and variation of the total forces as functions of tip clearance, distance, and relative size of appendage and propeller.
On the Mechanical Behavior of Viscoelastic/Plastic Solids
Authors: Naghdi P. M. , Murch S. A.
Published: October 2011

This paper is concerned with a theory of viscoelastic/plastic solids which reduces to that of the classical (linear) viscoelasticity as one limiting case and to the (inviscid) theory of elastic/plastic solids in another. Whereas the viscoelastic strain rates are assumed to be derivable from the appropriate creep integral laws of classical viscoelasticity, the plastic strain rates in stress space are dependent not only on the path history but also the time history of stress. After postulating the existence of a regular loading surface in the viscoelastic-plastic state and deducing the appropriate criterion for loading, a major portion of the paper is devoted to establishing (a) the convexity of the loading surface, (b) the direction of the plastic strain-rate vector in stress space, and (c) the structure of the constitutive equations for the plastic strain rates. The loading surface of the present theory (in contrast to that of the inviscid theory of plasticity), being dependent on certain measures representing time history of stress, is allowed to change its shape continually; this has implications in the interpretation of experimental results dealing with the determination of the initial and subsequent yield surfaces where corners are observed.
A Study of the Vibrations of Shallow Spherical Shells
Authors: Hoppmann W. H. , Baronet C. N.
Published: October 2011

This paper presents a comparison of the theoretically and experimentally determined frequencies and zero displacement lines for the normal mode vibrations of shallow spherical shells. Results are given for the clamped-edge and the momentless-edge boundary conditions. Calculations of frequencies and loci of zero displacement components for various shell sizes were made on an IBM 650 computer for the rotationally symmetric vibrations only, as the theory is not available for the case of asymmetric vibrations. Experiments were performed to determine the vibration characteristics both for the symmetric and the asymmetric vibrations. Several model shells constructed of steel were used for the purpose.
Application of Numerical Mapping to the Muskhelishvili Method in Plane Elasticity
Authors: Pisacane V. L. , Malvern L. E.
Published: October 2011

A procedure for treating plane-elasticity problems in simply connected regions, consisting of use of numerical mapping methods in order to apply the Muskhelishvili complex variable method, is demonstrated. This approach now makes the whole complex variable method susceptible to automatic solution on a digital computer. An example is considered for which the exact solution was known; a comparison to the finite-difference solution for this example is also made.
Theory of Flexible Aerodynamic Surfaces
Authors: Nielsen J. N.
Published: October 2011

A theoretical and experimental investigation has been made of the two-dimensional, aerodynamic characteristics of flexible airfoils or sails with no thickness. Thin-airfoil theory has been used to calculate the shapes of the camber lines as a function of angle of attack and excess length of material over the chord length. It is found that for specific eigenvalues of a nondimensional chordwise tension parameter, specific shapes arise for which there is no stagnation point. Some eigenmodes also correspond to boundaries between stable and unstable airfoil shapes. Lift, center of pressure, shapes, and pressure distributions are determined for the entire practical range of angle of attack. An experimental investigation of the lift, drag, and moment of quasi-two-dimensional flexible airfoils has been made, and the measurements have been compared with theory. Certain of the aerodynamic characteristics are in good accord with theory, but certain others are not, principally because of fabric porosity and boundary-layer separation.
The Inextensional Deformation of a Curved Panel
Authors: McKenzie K. I.
Published: October 2011

A method is developed for the solution in closed form of problems involving the inextensional deformation of curved panels and cylinders. Solutions are presented for a clamped panel under point loading and a free panel under equal and opposite point loads at its edges. The known solution for the complete cylinder under equal and opposite diametral point loads is expressed in closed form.
Transient Thermal Stresses in a Circular Cylinder
Authors: Youngdahl C. K. , Sternberg Eli
Published: October 2011

This paper contains an exact solution for the transient temperature distribution, as well as for the accompanying quasi-static thermal stresses and deformations, which arise in an infinitely long elastic circular shaft if its surface temperature undergoes a sudden uniform change over a finite band between two cross sections and is steadily maintained thereafter. The solution given is in the form of definite integrals and infinite series, whose convergence is discussed. Extensive illustrative numerical results are included.
Steady-State Behavior of Nonlinear Dynamic Vibration Absorber
Authors: Carter W. J. , Liu F. C.
Published: October 2011

The Frahm-type dynamic vibration absorber is analyzed for the case where both main and absorber springs have nonlinearities of the Duffing type. A one-term-approximation solution is assumed for the motions of the two masses, and the resulting amplitude equation is solved using a graphical procedure. It is shown that the optimum dynamic-vibration-absorber system for variable frequency excitation is that which has a hardening main spring together with a softening absorber spring.
A Plane Problem of Rolling Contact in Linear Viscoelasticity Theory
Authors: Morland L. W.
Published: October 2011

The plane problem of a rigid cylinder rolling with constant velocity over a linear viscoelastic half space is treated within the limits of quasistatic theory. Tangential surface tractions are considered sufficiently small to be neglected, so that the contact deformation is due to a normal pressure distribution. The boundary-value problem is formulated for a general viscoelastic material, and is reduced to two pairs of dual integral equations. These are solved by infinite series expansions, and a numerical example is given to show that truncated series produce adequate results.