bluuebunny/crossref_metadata_2025 huggingface dataset:
Wave Propagation in a Viscoelastic Fiber Subjected to Transverse Impact
Authors: Roylance David
Published: November 2010

A dynamical finite-element analysis is used to demonstrate the effect of viscoelastic relaxation on a 3-element rate-dependent model fiber subjected to transverse impact. The transverse shock waves produced by the impact are seen to propagate more slowly and at a larger fiber inclination than the rate-independent theory predicts, and these perturbations are shown to have an appreciable effect on dynamic stress-strain curves which are inferred from measurements of the fiber configuration during impact.
Propagation of Harmonic Waves in Orthotropic Circular Cylindrical Shells
Authors: Armena`kas A. E. , Reitz E. S.
Published: November 2010

In this investigation, the general frequency equation for trains of harmonic waves having an arbitrary number of circumferential nodes, traveling in orthotropic, circular, cylindrical shells is established on the basis of the three-dimensional linear theory of elasticity, by expanding the displacement components in power series of the radial coordinate. Simpler forms of the frequency equation for axisymmetric nontorsional and torsional motion and for longitudinal-shear and plane-strain motion are established and discussed. The frequency equation has been evaluated numerically on an IBM 360/50 digital computer system and the numerical results are compared with those obtained on the basis of an approximate shell theory.
Practical Techniques for Estimating the Accuracy of Finite-Difference Solutions to Parabolic Equations
Authors: Clausing A. M.
Published: November 2010

A criterion is proposed which provides a priori means of choosing increments in the independent variables for effecting accurate finite-difference solutions to parabolic partial-differential equations. This is accomplished by relating the increments to the thickness of the diffusion layer. In this manner, the size of the increments is related to the magnitude of the derivatives which are known to influence strongly the accuracy. The fac- that the thickness of the diffusion layer is unknown is surmounted by relating the parameters of the discrete, physical plane to the diffusion variable and to the diffusion thickness. The diffusion variable is a dimensionless coordinate which governs the diffusion process. In similar problems, the diffusion variable is identical to the independent similarity variable. The thickness of the diffusion layer in terms of the diffusion coordinate is shown to be of the same order of magnitude for a wide variety of problems. The utility of the proposed criterion is demonstrated with numerous finite-difference solutions to problems in the areas of heat conduction and boundary-layer theory.
The Use and Evaluation of Shock Spectra in the Dynamic Analysis of Structures
Authors: Butzel L. M. , Merchant H. C.
Published: November 2010

An important use of shock spectra is to make estimates of the maximum responses of linearly modeled multidegree-of-freedom structures to shock excitations. In this paper a lower-bound estimate to complement a well known upper bound on such a maximum response is proposed and examined. The conditions under which the estimate is a lower bound are delineated. The set of bounds is applied to an examination of the performance of two maximum response estimators in current use, the root-mean-square, and one which is a function of the root-mean-square and dominant mode. The results of an empirical study show that the estimators do not perform well except when the bounds are close together.
Acoustically Induced Vibrations of Slender Rods in a Cylindrical Duct
Authors: Hine M. J.
Published: November 2010

The slender fuel rods of a gas-cooled nuclear reactor are contained in a cylindrical duct and are subjected to parallel gas flow together with an acoustic field produced by the gas blowers. The fundamental aspects of the acoustically induced rod vibrations have been studied for bundles of rods and single rods. In both cases the rod vibrations are critically dependent upon a close structural-acoustic wavelength match.
One-Dimensional Transient Waves in Anisotropic Plates
Authors: Moon F. C.
Published: November 2010

The stresses and displacements induced in anisotropic plates by short-duration impact line forces are calculated in this paper. The anisotropy is related to the lay-up angles of the fibers of a laminated fiber composite plate. A modification of Mindlin’s theory of crystal plates is used. The plate responses are calculated for various fiber lay-up angles and inclination of the line load to the axes of symmetry. Use is made of the computational method of the fast Fourier transform.
The Dynamic Response of Columns Under Short Duration Axial Loads
Authors: McIvor I. K. , Bernard J. E.
Published: November 2010

Coupled nonlinear equations of motion in the axial and transverse directions are derived for a column under dynamic end load. Material dissipation is included by employing a Kelvin model for the material behavior. The dynamic response of the column in the presence of small transverse perturbations is investigated for short duration of axial loads. For certain geometric configurations, the inclusion of axial inertia permits parametric resonance of transverse modes due to the transient axial motion after the load is removed. The parametric effects are studied in detail. It is found that the usual simplified theory which neglects axial inertia adequately describes the column response provided the material dissipation is sufficiently large and/or the duration of loading is sufficiently long. For given dissipation parametric excitation becomes important as the load duration decreases. It becomes the dominant effect for very short duration loads.
Lateral Bending-Torsion Vibrations of a Thin Beam Under Parametric Excitation
Authors: Dugundji J. , Mukhopadhyay V.
Published: November 2010

A thin platelike cantilever beam, well below static lateral buckling under gravity, is subjected to vertical harmonic excitation of its base. The governing equations indicate combination resonance possible, where the primary instability regions occur near forcing frequencies ωF = Ωi + Ωj, and each mode oscillates at its own natural frequency, Ωi. Experimental results are given for an actual beam showing this behavior. Since the beam had nonlinear damping, the instability regions settled down to steady nonlinear limit cycles whose frequencies and also amplitudes were well predicted by theory. This example of simultaneous excitation of two modes, each oscillating steadily at its own natural frequency, may be of considerable interest in vibration testing of actual structures.
Waves in a Periodic Composite
Authors: Balanis G. N.
Published: November 2010

The problem of transient wave propagation normal to the layers of a periodic composite is given an analytical solution.
Boundary and Interior Approximation Errors in the Finite-Element Method
Authors: Fried I.
Published: November 2010

Application of the finite-element method brings with it some perturbations in the original problem; either voluntary in order to simplify the analysis or inevitable due to the approximate nature of the method. Typically perturbed are the elastic, thermal, or inertia coefficients, the load function, the essential boundary conditions, and the domain. It is the purpose of this paper to estimate these errors.
Wave Motions in a Fluid Saturated Porous Medium
Authors: Hsieh L. , Yew C. H.
Published: November 2010

Wave motion in a fluid saturated porous medium is studied analytically in this paper. By assuming that the porous medium is homogeneous, isotropic, elastic, and permeable and by treating the interporous fluid as an incompressible fluid, linearized governing equations for wave motion in a fluid saturated porous medium were derived using the concept of superimposed continua, and the modified Lubinski’s stress-strain relationship. Frequency equations for dilatational and rotational waves were obtained. Numerical solutions of the frequency equation are presented and discussed.
Crack Propagation Analysis by Finite Differences
Authors: Shmuely M. , Alterman Z. S.
Published: November 2010

A finite-difference scheme for treating the dynamic stress field around a crack tip under plane-strain conditions, is proposed. The scheme is initially applied to the case of a crack of constant length which is suddenly opened in an infinite elastic medium loaded by a remotely uniform stress. By this, a numerical solution corresponding to the static state of stress is obtained which is compared with analytic solutions. It is shown that the numerically evaluated strain-energy-release rates are close to values calculated analytically. A modified scheme which presupposes a cuspated crack tip results in nearly the same strain-energy-release rates. Hence the validity of both numerical schemes is confirmed. For the numerical schemes adjusted to handle the propagating crack problem, the results represent a situation which is very close to reality; namely, the crack velocity accelerates up to a stage where propagation continues with a practically constant velocity. This terminal velocity moves from about 0.77 C2 to about 0.57C2 (C2 being the shear wave velocity). The last-mentioned velocity value corresponds to the cuspated crack model.
The Prediction of Creep-Rupture Times of Rotating Disks Using Biaxial Damage Relationships
Authors: Hayhurst D. R.
Published: November 2010

Lower-bound expressions for the rupture times corresponding to a maximum tension stress damage law are developed for the creep of disks rotating under conditions of plane stress and plane strain. Computed values of the lower-bound rupture times are shown to be in close agreement with the results of numerical solutions for maximum tension and biaxial tension stress damage laws. The lower-bound rupture time is shown to correspond with the result of a constant stress rupture test carried out under the conditions of the steady-state stress at a reference point in the structure. The steady-state reference stress, for two kinematically determinate structures and different rupture laws, is shown to closely predict values of the rupture time obtained from independent solutions.
On the Behavior of a Numerical Approximation to the Rotatory Inertia and Transverse Shear Plate
Authors: Krieg R. D.
Published: November 2010

A set of finite-difference equations which approximate the plane-strain motion of a rotatory inertia and transverse shear plate are examined in detail. The equations are stated in such a form that the usual norm is an energy expression. Proper posedness, consistency, stability, and convergence are all examined. The von Neumann stability analysis is supplemented by a numerical verification. The critical time step size is shown to fall into three different regimes depending on the ratio of mesh size to plate thickness. The largest allowable time step size is found to be dictated not by mesh spacing, but rather by physical dimensions of the plate.
Feasibility of Two-Dimensional Numerical Analysis of the Split-Hopkinson Pressure Bar System
Authors: Bertholf L. D.
Published: November 2010

The feasibility of two-dimensional numerical analysis of the split-Hopkinson pressure bar experiment is proven. A general elastic-plastic artificial viscosity computer program is shown to give an adequate solution for two-dimensional elastic response of a pressure bar subjected to a Heaviside step loading in time which is applied uniformly over the end. This elastic solution agrees with other numerical solutions and with asymptotic series solutions. An elastic specimen is used to verify the split-Hopkinson pressure bar numerical analysis and a numerical solution is also obtained for an elastic-plastic specimen. Special emphasis is placed on the two-dimensional response of the specimen including the sliding between the bars and the specimen with two extremes of interface friction. For large interface friction it is found that induced multidimensional stresses give the appearance of increased material strength which may be misconstrued as a strain-rate effect.
Magnetoelastic Buckling of Thin Magnetically Soft Plates in Cylindrical Mode
Authors: Dalrymple J. M. , Peach M. O. , Viegelahn G. L.
Published: November 2010

When a plate of magnetically soft material is supported with its wide face normal to a uniform magnetic field, it will buckle when the field reaches a critical value. It is shown theoretically that the critical buckling field for a “half-restrained” rectangular plate should be 0.833 of that for a half-restrained elliptical plate of identical dimensions and material. Limited experimental data support this conclusion. The effect of plate width upon critical buckling field is investigated experimentally and an empirical formula is presented which fits the data reasonably well.
Multiple Circular Inclusion Problems in Plane Elastostatics
Authors: Yu I.-W. , Sendeckyj G. P.
Published: November 2010

The problem of an unbounded elastic matrix containing any number of elastic inclusions is considered. The inclusions can have any radii and elastic moduli. Furthermore, the spacing of the inclusions can be arbitrary. The solution for the cases of uniaxial tension and in-plane bending is found by the Schwarz alternating method. Graphical results are presented for a number of examples.
Generalized Initial Yield Surfaces for Unidirectional Composites
Authors: Dvorak G. J. , Rao M. S. M. , Tarn J. Q.
Published: November 2010

A numerical method is described for determination of generalized initial yield surfaces of unidirectional metal matrix composites under arbitrary external loads and uniform temperature changes. The method leads to the representation of the surface in a three-dimensional system of generalized stress coordinates which, respectively, coincide with the direction of the normal composite stress in the fiber direction, and with the two principal directions of the composite stresses acting in the transverse plane. The initial yield surface of the composite is an irregular ellipsoid with its longest axis inclined toward the hydrostatic stress axis. A thermomechanical analogy is used to show that as a result of a uniform temperature change, the yield surface experiences a rigid-body translation in the direction of the hydrostatic axis in the stress space. The initial yield behavior of a B-Al composite is described in detail. It is shown that microplastic yielding can take place in the composite under relatively small magnitudes of external loads, and hydrostatic stress, or as a result of moderate temperature changes.
Identification of Damping Coefficients in Multidimensional Linear Systems
Authors: Caravani P. , Thomson W. T.
Published: November 2010

The inverse problem of determining damping from frequency response is formulated as an optimization problem. Response data are sequentially processed by an algorithm which refines the estimate of damping at each frequency point. The method is illustrated by numerical examples involving viscous damping. Other forms of damping can be considered without altering the procedure discussed here.
Critical Velocity for Collapse of a Shell of Circular Cross Section Without Buckling
Authors: Abrahamson G. R.
Published: November 2010

Many practical devices involve high-speed collapse of shells of circular cross section, In all of the devices the stability of the collapse motion is of interest and in some it is essential for successful operation. In this paper, the buckling motion of shells of circular cross section during high-speed collapse is analyzed and critical collapse velocities are determined for which the growth of initial nonuniformities by buckling during collapse is 10 and 100.
An Experimentally Validated Dynamic Model of the Spine
Authors: Prasad P. , King A. I.
Published: November 2010

Although there has been a large number of mathematical models proposed for the simulation of spinal response to acceleration, few have been validated against experimental data and none appears to reflect the actual conditions of load transmission from one vertebra to the next. This paper provides a brief survey of existing spinal models and presents a discrete parameter model with experimental validation. The transmission of load via the articular facets is a major new feature of the model, based on previously obtained experimental data. Good correlation was obtained between the model results and experimentally measured spinal loads for different impact acceleration levels and spinal configurations.
Flow About a Stationary Sphere in a Slowly Rotating, Viscous Fluid
Authors: Singh S. N.
Published: November 2010

Analytical solutions are presented for the flow about a nonrotating sphere immersed in a slowly rotating fluid by the singular perturbation technique valid for small Reynolds numbers. Streamlines are plotted and the torque necessary to hold the sphere stationary is calculated. It is found that the transition from inflow near the equator to outflow near the poles takes place at an angle of 54.50 deg measured from the poles. Flow velocities and the stream function are also calculated for the problem when the sphere rotates with an angular velocity different from that of the fluid.
A Model for Vortex Induced Oscillation of Structures
Authors: Iwan W. D. , Blevins R. D.
Published: November 2010

A model is presented for the analysis of the response of structural systems excited by vortex shedding. The model is based on the introduction of a hidden variable to describe the fluid dynamic effects. Model parameters may be determined from experimental data for fixed and forced elements and the model used to predict the response of elastically mounted elements. Analytical model predictions are compared with experimental results for a circular cylinder.
Thermoelastic Constitutive Equations for Chemically Hardening Materials
Authors: Shaffer Bernard W. , Levitsky Myron
Published: November 2010

Thermoelastic constitutive equations are derived for a material undergoing solidification or hardening as the result of a chemical reaction. The derivation is based upon a two component model whose composition is determined by the degree of hardening, and makes use of strain-energy considerations. Constitutive equations take the form of stress rate-strain rate relations, in which the coefficients are time-dependent functions of the composition. Specific results are developed for the case of a material of constant bulk modulus which undergoes a transition from an initial liquidlike state into an isotropic elastic solid. Potential applications are discussed.
On the Large Axisymmetrical Deflection of Thin Plates Made of the Mooney-Rivlin Material
Authors: Abe´ H. , Utsui M.
Published: November 2010

A large deflection theory of axially symmetric and thin plates made of the Mooney-Rivlin material is developed by making a systematic and consistent approximation from the exact three-dimensional theory. The problem of a circular plate made of the neo-Hookean material subjected to uniform lateral pressure is investigated with the use of the basic equations just derived, and the results are compared with the solutions based on the von Karman plate equations.
On Wave Reflection in an Elastic Plate
Authors: Doby R.
Published: November 2010

A precursor boundary concept is introduced which decouples the stress-free boundary conditions at the parallel surfaces of the plate. The resulting orthogonal eigenfunctions are longitudinal and transverse waves. This property is exploited so as to satisfy stress-free conditions at the edge. The theoretical analysis reveals that the reflected waves are reordered so that the longitudinal and transverse modes represent the gradients of the incident transverse and longitudinal waves.
On Vibration Problems With Discretely Distributed Loads—A Rigorous Formalism
Authors: Ramkrishna D. , Amundson N. R.
Published: November 2010

Three problems in simple vibration theory are treated, the longitudinal vibration of a prismatic bar, the lateral vibration of a beam, and the vibration of a circular plate, each with arbitrarily placed discrete loads. It is shown that with the appropriate definition of an inner product on a Hilbert space the spatial differential operator may be made self-adjoint with all of the formal advantages of that reduction. The key to the solution of the problem is in the redefinition of the inner product from the normal one to one which is slightly more complicated but obvious once it is seen.
The Galloping Response of a Two-Degree-of-Freedom System
Authors: Blevins R. D. , Iwan W. D.
Published: November 2010

The galloping response of a two-degree-of-freedom system is investigated using asymptotic techniques to generate approximate steady-state solutions. Simple closed-form analytic solutions and stability criteria are presented for the case where the two structural natural frequencies are harmonically separated. Examples of the nature of the galloping response of a particular section are presented for the case where the frequencies are harmonically separated as well as for the case where the two natural frequencies are near an integer multiple of each other. The results of the approximate analysis are compared with experimental and numerical results.
Hydrodynamic Development in a Duct With Suction and Blowing
Authors: Raithby G. D. , Knudsen D. C.
Published: November 2010

The development of flow in a parallel-plate channel is determined by solving the two-dimensional, elliptic equations of motion for laminar flow. Cases involving blowing, suction, and no mass transfer through the walls are considered, but attention is focused on the wall suction case. It is shown that for strong suction, the hydrodynamically developed solutions for the velocity profile published previously are normally not attained or approached by the developing flow. The results of an experimental investigation are also reported for the wall suction problem, and it is confirmed that hydrodynamically developed velocity profiles are not attained for the range of wall-suction Reynolds numbers tested.
Flow Transient Near the Leading Edge of a Flat Plate Moving Through a Viscous Fluid
Authors: Kinney R. B. , Paolino M. A.
Published: November 2010

An investigation is made of the unsteady flow in the leading-edge region of a semi-infinite plate impulsively started from rest. Based entirely on the vorticity concepts outlined by Lighthill, numerical results are obtained for the complete two-dimensional flow field by solving the single vorticity transport equation. An essential input to the calculations is the distribution of vorticity production at the plate surface. This is determined at each instant of time from the no-slip condition at the plate and represents a departure from conventional numerical analyses of viscous flows. Departing further from conventional approaches, the velocity field is computed from the law of induced velocities (Biot-Savart law) rather than the stream function. Because of vorticity diffusion well ahead of the plate, a significant disturbance propagates upstream, thereby destroying the uniformity of the approaching flow. Calculations are carried sufficiently forward in time for an approximately steady state to be reached at a distance downstream of the leading edge equal to the thickness of the viscous layer. As viewed by an observer moving with the plate, the flow transient exhibits a velocity overshoot relative to the apparent free-stream velocity. This effect was unexpected for a semi-infinite plate and represents a novel aspect of the flow not found in transient analyses based on the boundary-layer approximations.
A Method for Direct Determination of Small Curvatures
Authors: Chiang F. P. , Bailangadi M.
Published: November 2010

A method is proposed whereby the diffraction pattern produced by the distorted grating obtained from the Ligtenberg method can be suitably filtered to give lines of constant curvatures in problems of flexure.
The Problem of a Finite Strip Compressed Between Two Rough Rigid Stamps
Authors: Gupta G. D.
Published: November 2010

A finite strip compressed between two rough rigid stamps is considered. The elastostatic problem is formulated in terms of a singular integral equation from which the proper stress singularities at the corners are determined. The singular integral equation is solved numerically to determine the stresses along the fixed ends of the strip. The effect of material properties and strip geometry on the stress-intensity factor is presented graphically.
On the Ballistic Impact of Textile Body Armor
Authors: Vinson J. R. , Zukas J. A.
Published: November 2010

A mathematical model is developed and methods of analysis are formulated for determining the structural response of textile fabric flat panels subjected to ballistic impact by a dense projectile. A stepwise procedure in time is formulated which is suitable for either desk calculator use or for a digital computer in calculating strains, projectile position, forces, and decelerations as functions of time. Analytical results are compared with experimental data for impact of a .22 caliber fragment simulator impacting 1 ply and 12 ply nylon cloth as well as Kevlar (PRD)-49-IV cloth from 1–24 plies.
Elliptical Cutouts in Cylindrical Shells
Authors: Tsai C.-J. , Sanders J. L.
Published: November 2010

The stress concentrations due to an elliptical cutout in a shallow cylindrical shell are determined by means of a system of singular integral equations, solved numerically. Three loading conditions are considered: tension, torsion, and internal pressure. Results confirm those obtained by previous authors by other methods and extend the range of parameters over which results are available.
Thermal Effect on the Transverse Vibration of Spinning Disk of Variable Thickness
Authors: Ghosh N. C.
Published: November 2010

An attempt has here been made to consider the thermal effect on the transverse vibration of a spinning disk of variable thickness. For a comprehensive study of the problem, it has been assumed that the rate of generation of heat is fixed per unit volume. Consequently, it is observed that such a heat-generation influences the natural frequency of vibration considerably and thereby the traveling waves which happen to be moving around the disk-circumference during vibration. Toward the end of the paper it has also been shown that there may exist an additional condition for the formation of a standing wave other than the condition of coincidence of backward speed of the traveling waves with the forward speed of disk-rotation in the absence of chosen thermal distribution.
On Wave Propagation in Composite Materials Reinforced by Fibers With Continuously Varying Directions
Authors: Weitsman Y. , Benveniste Y.
Published: November 2010

This paper concerns certain aspects of wave propagation in composite materials reinforced by fibers whose directions vary continuously in space. Special attention is focused on the case of slight variations in fiber directions and on plane waves that propagate parallel to the unperturbed direction, a case that can be detailed entirely in analytic expressions. The paper concludes with a solution to a specific example in which we assume that the fiber directions vary linearly from an initial to a final position. A discussion of the specific solution follows.
Holographic Interferometry Applied to Rotating Disks
Authors: Chen Yu
Published: November 2010

To measure vibration of a rotating disk by holographic interferometry, the double exposure of holograms must be taken at precisely coincidental positions of the disk. A technique of accomplishing the precise repositioning of the disk after the first hologram is taken is described in this Note.
On the Creep Rupture of a Tube and a Sphere
Authors: Goel R. P.
Published: November 2010

Lower bounds on rupture times of a thick-walled tube in pure torsion and a hollow sphere under constant internal pressure are obtained. Numerical values of rupture times for the tube case with different forms of damage rate laws are presented. The type of damage law assumed makes a significant effect on predicting the time to rupture but failure in all cases occurs almost instantaneously after the appearance of first crack.
Axisymmetric Potential Flow Over Two Spheres in Contact
Authors: Small R. D. , Weihs D.
Published: November 2010

An exact solution for the axisymmetric incompressible potential flow over two touching spheres is presented. A tangent-sphere coordinate system is used to simplify the boundary conditions. The Laplace equation is solved by means of separation of variables and the expression for the added mass obtained.
Two-Ellipsoidal Inhomogeneities by the Equivalent Inclusion Method
Authors: Moschovidis Z. A. , Mura T.
Published: November 2010

The problem of two ellipsoidal inhomogeneities in an infinitely extended isotropic matrix is treated by the equivalent inclusion method. The matrix is subjected to an applied strain field in the form of a polynomial of degree M in the position coordinates xi. The final stress and strain states are calculated for two isotropic ellipsoidal inhomogeneities both in the interior and the exterior (in the matrix) by using a computer program developed. The method can be extended to more than two inhomogeneities.
Pressure Development in the Entrance Region and Fully Developed Region of Generalized Channel Turbulent Flows
Authors: Hai S. M.
Published: November 2010

In this paper, the pressure drops in the developing length of generalized turbulent channel flows are investigated, and the effects of Reynolds number and distance from the channel entrance are examined. The numerical method is also used to predict the pressure drops in simple channel flows for very high Reynolds numbers (of the order of 100,000). Excellent agreement is obtained between experimental data and numerical predictions.
On Separation of a Divergent Flow at Moderate Reynolds Numbers
Authors: Matsuzaki Yuji , Fung Yuan-Cheng
Published: November 2010

Flow separation in a divergent channel was investigated in connection with problems of instability and oscillations in physiology at a Reynolds number range much smaller than that usually considered in engineering diffuser design. Experimental data on a divergent flow through a two-dimensional water tunnel in the Reynolds number range Re = 1000 to 6000 are presented. The quantities measured are flow rate, divergence angle, and mean pressure differential between two fixed points at the throat and downstream. In a lower range of divergence angle flow separation is characterized by a sharp decrease in the mean pressure differential when the flow rate is increased continuously and gradually; whereas recovery from separation is signaled by a discontinuous increase in pressure when the flow rate is decreased again. The critical Reynolds numbers for separation and reattachment are detectably different. Some discussion is given about flow separation in external and internal flows.
Dunkerley-Mikhlin Estimates of Gravest Frequency of a Vibrating System
Authors: Brock J. E.
Published: November 2010

Estimates are made of the smallest nonzero frequency of vibration of undamped linear mechanical systems having lumped and/or distributed mass and permitting rigid body motions. The approximations are smaller than the correct values but remarkable accuracy may be achieved. The procedures are based upon methods of S. Dunkerley and S. G. Mikhlin.
Generalized Plane Problems of Elastic Inclusions in Anisotropic Solids
Authors: Yang H. C. , Chou Y. T.
Published: November 2010

A general method, based on the line force concept, is presented for solving the generalized plane problems of elastic inclusions in anisotropic solids. Detailed analyses of the displacement and stress fields and the strain energies are developed for elliptic inclusions. A simple example in which both the inclusion and the matrix exhibit orthotropic symmetry is illustrated.
An Experimental Study of Package Cushioning for the Human Head
Authors: Liu Y. King , Chandran K. B.
Published: November 2010

An experiment was performed to determine the container acceleration and pressure distribution in a Plexiglass cylinder, filled either with water or 3 percent set-gelatin, and impacted against a wall. This experiment serves to quantitatively validate a theoretical model simulating an one-dimensional closed-head impact given earlier. The experiments showed important differences between the theoretical and experimental pressure measurements. When the medium contained within the cylinder was water the coup pressure as found by experiment, was higher than the mathematical model prediction while the contrecoup pressure was in good agreement. When the container was filled with a set gel, the coup pressure was in agreement with the mathematical model but the contrecoup pressure is considerably lower than the calculated result. Since the brain is neither water nor gel, in vivo animal experiments are needed to obtain meaningful tolerance limits for injury due to cavitation at the contrecoup region in closed-head impacts.
An Approximate Analysis of Laminar Dispersion in Circular Tubes
Authors: Yu J. S.
Published: November 2010

The combined effects of convection and diffusion for dispersion on mass transport in fully developed laminar flow through circular tubes are investigated. The present method, which in general may be used to yield solutions at any arbitrary dimensionless time, in its zeroth-order approximation is identical to Taylor’s analysis for the average concentration. Solutions to the basic differential equation for an initial input of solute either concentrated at a section of the tube or uniformly distributed in the form of a slug of finite axial extension are developed. Numerical results for the former input are presented over a large range of dimensionless time and Peclet numbers. The time limitations of Taylor’s solution and Lighthill’s small time approximation [15] are placed on more reliable quantitative bases by comparison with the present calculations.
Production and Dissipation of Energy in the Turbulent Flow of a Particle-Fluid Mixture, With Some Results on Drag Reduction
Authors: Drew D. A.
Published: November 2010

The production and dissipation of energy in a two-phase model for particle-fluid turbulent flow is considered. For plane parallel mean flow use of several scaling arguments yields a balance between production and drag dissipation for the particles, and between production and viscous dissipation for the fluid. A simple particle motion model is used to obtain estimates of the drag dissipation. Energy balance considerations are made for situations where drag reduction by the addition of particles is observed. Significant drag reduction is found to occur for sufficiently large Reynolds number. Discussion of the extra effectiveness of polymers for drag reduction is given within the framework of energy balance.
Surface Integral Method Applied to the Problems of an Elastic Strip With Periodically Spaced Holes
Authors: Melnikov Yu. A.
Published: November 2010

One version of the surface integral method has been used to obtain the solutions of two-dimensional elasticity problems of the infinite strip with periodically spaced holes. Numerical results are presented and generalization to the case of a layered strip is obtained.
The Plane Solution for the Elastic Contact Problem of a Semi-Infinite Strip and Half Plane
Authors: Adams G. G. , Bogy D. B.
Published: November 2010

The solution is obtained for both smooth and bonded contact between the strip and half plane of different elastic materials. First, the problems are reduced to singular integral equations of the second kind. Then the order of the stress singularity at the corners is extracted from the integral equations and numerical solutions are obtained. Interface normal and shearing stress are exhibited graphically for several material combinations.
Transverse Vibration of a Uniform, Simply Supported Timoshenko Beam Without Transverse Deflection
Authors: Downs B.
Published: November 2010

An additional solution is obtained for the vibrational behaviour of a uniform, simply supported Timoshenko beam. The characteristics of the mode are explained in physical terms.
The Transverse Vibration of a Doubly Tapered Beam
Authors: Banks D. O. , Kurowski G. J.
Published: November 2010

We analyze the transverse vibrations of a thin homogeneous beam which is symmetric with respect to the x-y and x-z planes. The cross section of the beam at x is assumed to have the form D(x)={(x,y,z)|x∈[0,1],y=xαy1,z=xβz1,(y1,z1)∈D1} where D1 is the cross section at x = 1. Expressions are obtained from which the eigenvalues and eigenfunctions can be easily found for 0 ≤ α < 2 and all combinations of clamped, hinged, guided, and free boundary conditions at both ends of the beam.
Pulse Propagation in Fluid-Filled Tubes
Authors: Walker J. S. , Phillips J. W.
Published: November 2010

A new theory for the propagation of pressure pulses in an inviscid compressible fluid contained in a thin-walled elastic tube is presented. This theory represents an improvement over the classical waterhammer theory because the restriction that the speed of sound in the tube material must be much greater than that in the fluid has been removed and because the restriction that the pulse length must be much greater than the tube diameter has been somewhat relaxed. The new theory is applied to a water-filled copper tube with an axial impulsive force of very short duration applied either to a piston inserted in the anchored end of the tube or to a cap on the free end of the tube. Numerical solutions using the method of characteristics are presented, and comparison is made with the predictions of classical waterhammer theory. A check on the numerical solution is provided by the analytical solution for the capped tube and for the special case when the speeds of sound in the tube material and in the fluid are equal.
The Linear Magnetoelastic Problem for a Soft Ferromagnetic Elastic Solid With a Finite Crack
Authors: Shindo Y.
Published: November 2010

Following a linear theory for the soft ferromagnetic elastic materials of multidomain structure, the distribution of magnetoelastic stresses and Maxwell stresses in an infinite body with a finite crack permeated by an uniform magnetostatic field normal to the crack surfaces is investigated. The soft ferromagnetic elastic solids with a finite crack are considered to be composed of materials with isotropic, cubic, or uniaxial symmetry. A solution for the infinite solid is obtained by the use of integral transform technique. The magnetoelastic stresses and the Maxwell stresses are expressed in closed forms.
Fully Plastic Asymmetric Edge Crack Under Longitudinal Shear
Authors: Amazigo J. C.
Published: November 2010

The problem of a semi-infinite work-hardening material with a finite length asymmetric edge crack subjected to uniform remote longitudinal shear is solved exactly by the use of hodograph transformation and the Wiener-Hopf technique. The material behavior is governed by a pure power-hardening stress-strain relation and for monotone loading the results are valid for both deformation and flow theories of plasticity. Numerical values are obtained for the path independent J integral for several values of both the angle of asymmetry and the power-hardening exponent.
Multiple Fracture of Beams Under Localized Impulsive Loading
Authors: Colton J. D.
Published: November 2010

The fracture patterns produced by localized impulsive loading on brittle beams and their dependence on the intensity and length of the load have been determined. Experiments were performed on effectively infinite beams loaded over a finite length with sheet explosive. The mechanisms, location, and time sequence of deformation and fracture were determined by posttest observation and by high-speed framing camera photographs. It was found experimentally that all fractures were initiated by bending stress and that the localized impulsive loading produced three different fracture patterns. The beam response was also predicted analytically by numerically integrating the characteristic equations of Timoshenko beam theory. It was found analytically that, depending on load length and intensity, a total of four fracture patterns, including the three observed experimentally, can be produced by localized impulsive loads.
Properties of Wall Shear Stress Fluctuations in a Turbulent Duct Flow
Authors: Sreenivasan K. R. , Antonia R. A.
Published: November 2010

Measurements of wall shear stress fluctuations have been made in a fully developed turbulent duct flow, using a surface heat transfer gauge. Measurements, made over a moderate Reynolds number range, include RMS values, probability density functions, spectra, and zero-crossing frequencies of the wall shear stress fluctuation. The ratio of RMS of the fluctuation to the mean value of the wall shear stress is found to be about 0.25. The zero-crossing frequency computed from the measured spectra using the relation derived by Rice for a Gaussian process is found to be a good approximation to the measured value, although the measured probability density function is not Gaussian. The zero crossing frequency and spectra of wall shear stress fluctuations appear to scale with outer variables for asymptotically large Reynolds numbers.
Stability of a Cluster of Flexible Cylinders in Bounded Axial Flow
Authors: Paidoussis M. P. , Suss S.
Published: November 2010

This paper deals with the dynamics of a cluster of parallel flexible cylinders in a cylindrical channel in the presence of an axially flowing fluid. The equations of motion are derived, taking into account inviscid and viscous hydrodynamic coupling of small arbitrary motions of the cylinders. Solutions of the equations of motion yield the eigenfrequencies and modal shapes of the system. For sufficiently high flow velocities the system loses stability by divergence and flutter, similarly to a solitary cylinder in unbounded flow; however, the critical flow velocities are much lower, as proximity to other cylinders and to the channel wall severely destabilize the system.
The Elastic Field Outside an Ellipsoidal Inclusion
Authors: Mura T. , Cheng P. C.
Published: November 2010

The elastic field outside an ellipsoidal inclusion is investigated. No particular restrictions are imposed to eigenstrain distributions throughout the inclusion and to the anisotropy of elastic media for matrices. The solution is expressed in the form of integrals defined on a subspace of a unit sphere. Since the integrands of these integrals have no singularities, the numerical calculation on a computer can easily be performed.
Transverse Vibrations of Cantilever Beams Having Unequal Breadth and Depth Tapers
Authors: Downs B.
Published: November 2010

Natural frequencies of doubly symmetric cross section, isotropic cantilever beams, based on both Euler and Timoshenko theories, are presented for 36 combinations of linear depth and breadth taper. Results obtained by a new dynamic discretization technique include the first eight frequencies for all geometries and the stress distribution patterns for the first four (six) modes in the case of the wedge. Comparisons are drawn wherever possible with exact solutions and with other numerical results appearing in the literature. The results display outstanding accuracy and demonstrate that it is possible to model with high precision the dynamic behaviour of continuous systems by discretization on to a strictly limited number of degrees of freedom.
A New Cumulative Damage Model: Part 1
Authors: Bogdanoff J. L.
Published: November 2010

A new history-dependent phenomenological model of cumulative damage is presented. It is a stochastic model. The model includes as an inherent part of its structure the major sources of variability encountered in fatigue and wear. The generality possessed by the model is much more in accord with the complexity of fatigue and wear processes than possessed by models in current use. It also implies that the frequent inaccuracies encountered in life prediction when using current models are not surprising and cannot be substantially reduced using such models.
A New Cumulative Damage Model: Part 2
Authors: Bogdanoff J. L. , Krieger W.
Published: November 2010

A series of illustrative examples are presented to aid in understanding the generality of the model as it applies to cumulative damage. Results from the model are used to describe and analyze some fatigue and wear life test data. Comments are made on the uses of the model. A discussion is presented on the shortcomings of current methods of life testing when prediction is involved.
The Interface Crack in a Shear Field
Authors: Comninou Maria
Published: November 2010

The interface crack in a tension field was reconsidered in a recent paper, and the unrealistic oscillatory singularities were eliminated by assuming small frictionless contact zones near the crack tips. In the present paper, the interface crack in a shear field is studied. Some unexpected results emerge: one of the contact zones is large, affecting thus the global nature of the solution; the gap closes extremely abruptly at one of its ends, but the normal stresses remain zero at this point; and the shear stress-intensity factors have opposite signs at the crack tips.
Elastic Interface Waves and Sliding Between Two Solids
Authors: Comninou Maria , Dundurs J.
Published: November 2010

The paper investigates possible interface waves between two solids in presence of separation and frictional slip and examines the effect of the waves on the sliding motion of the bodies. It is shown that interface waves are mathematically feasible between solids with identical mechanical properties, and that they can propagate with any phase velocity that falls between the Rayleigh and shear wave speeds. In the presence of such interface waves, global sliding may take place at much lower applied shearing tractions than would be required to slide the solids as rigid bodies. The waves also involve singular interface tractions that lead to energy emission and absorption at the singular points, and some aspects of them appear controversial.
Implicit-Explicit Finite Elements in Transient Analysis: Stability Theory
Authors: Hughes T. J. R. , Liu W. K.
Published: November 2010

A stability analysis is carried out for a new family of implicit-explicit finite-element algorithms. The analysis shows that unconditional stability may be achieved for the implicit finite elements and that the critical time step of the explicit elements governs for the system.
Dynamically Induced Interfacial Stresses in Fibrous Composites
Authors: Nayfeh Adnan H.
Published: November 2010

The recently developed continuum mixture theories of fibrous composites are further extended to determine the interfacial shear stresses that develop in such composites upon their dynamic loadings. Exact results are not possible. Two special cases are however discussed in details. In the first, one of the composite constituents is assumed rigid and in the second both constituents are assumed elastic and results are obtained at the wave fronts.
Fracture Under Combined Loads by Maximum-Energy-Release-Rate Criterion
Authors: Wu C.-H.
Published: November 2010

The title problem is studied for the cases: (1) crack-perpendicular tension and crack-parallel shear, (2) plane biaxial load, (3) crack-parallel shear and antiplane shear, and (4) unidirectional load and antiplane shear. All the results are based on a fundamental investigation reported in references [1, 2], the results of which are partly exact, and partly asymptotic and numerical. Neither the maximum-stress nor the minimum-strain-energy-density criterion indicates a coupling between plane and antiplane loads.
Pipes Supported at Both Ends Cannot Flutter
Authors: Holmes P. J.
Published: November 2010

We use a development of Liapunov’s second method to study the local and global stability of the equilibrium positions adopted by a pipe conveying fluid. The pipe is simply supported at both ends and the analysis includes first-order (structural) nonlinearities. The major conclusion is that, contrary to the suggestions of linear analyses and of recent nonlinear numerical studies, sustained flutter motions are impossible in the case of the equation studied here.