bluuebunny/crossref_metadata_2025 huggingface dataset:
Dynamic Response of a Rigid Footing Bonded to an Elastic Half Space
Authors: Luco J. E. , Westmann R. A.
Published: November 2010

The problem of determining the response of a rigid strip footing bonded to an elastic half plane is considered. The footing is subjected to vertical, shear, and moment forces with harmonic time-dependence; the bond to the half plane is complete. Using the theory of singular integral equations the problem is reduced to the numerical solution of two Fredholm integral equations. The results presented permit the evaluation of approximate footing models where assumptions are made about the interface conditions.
A Difference Method for Plane Problems in Magnetoelastodynamics
Authors: Recker W. W.
Published: November 2010

The two-dimensional equations of magnetoelastodynamics are considered as a symmetric hyperbolic system of linear first-order partial-differential equations in three independent variables. The characteristic properties of the system are determined and a numerical method for obtaining the solution to mixed initial and boundary-value problems in plane magnetoelastodynamics is presented. Results on the von Neumann necessary condition are presented. Application of the method to a problem which has a known solution provides further numerical evidence of the convergence and stability of the method.
Elastic Waves in Inhomogeneous Elastic Media
Authors: Nayfeh Adnan H. , Nemat-Nasser Siavouche
Published: November 2010

The WKB solution is derived together with the condition for its validity for elastic waves propagating into an inhomogeneous elastic medium. Large frequency expansion solution is also derived. It is found that the WKB solution agrees with that derived for large frequencies when the frequency approaches infinity. Some exact solutions are deduced from the WKB solution. Finally, we consider motions in medium which consists of a material with harmonic periodicity. The solution is obtained by means of a perturbation method. It is shown that, only when the wavelength of the incident wave is small compared with the periodicity-length of the material, the WKB solution constitutes a good approximation. When the wavelength is comparable with this periodicity-length, then, in certain special cases, the material cannot maintain time-harmonic waves; such harmonic waves are not “stable.” These and other solutions are discussed in detail.
On the First-Excursion Probability in Stationary Narrow-Band Random Vibration, II
Authors: Yang J.-N. , Shinozuka M.
Published: November 2010

The first-excursion probability of a stationary narrow-band Gaussian process with mean zero has been studied. Within the framework of point process approach, series approximations derived from the theory of random points and approximations based on the maximum entropy principle have been developed. With the aid of numerical examples, merits of the approximations proposed previously as well as of those developed in this paper have been compared. The results indicate that the maximum entropy principle has not produced satisfactory approximations but the approximation based on nonapproaching random points is found to be the best among all the approximations proposed herein. A conclusion drawn from the present and the previous studies is that the point process approach produces a number of useful approximations for the first-excursion probability, particularly those based on the concepts of the Markov process, the clump-size, and the nonapproaching random points.
Sandwich Beam Analysis
Authors: Krajcinovic D.
Published: November 2010

A consistent theory of sandwich beams subjected to static load is presented. The theory is developed under the assumption that the Bernoulli’s hypothesis is valid for each lamina independently but not for the entire cross section as a whole. It is shown that the generalized displacement may be chosen in such a way that the set of equations governing the motions for which the beam remains straight on one, and a set of equations describing bending and shear types of motions on the other hand are independent. Furthermore, after some simple algebra, separate equations for each generalized displacement are derived. The normal stress is given in the from which is familiar from strength of materials with two additional terms embodying the influence of the cross-sectional distortion (deviation from classical beam theory).
Curvature and Out-of-Plane-Strain for Generalized Plane Strain
Authors: Parks V. J.
Published: November 2010

Out-of-plane strains and stresses are determined using reciprocity for the central region of very long bars (approaching infinite length) of uniform transverse cross section subjected to the same in-plane loads on every cross section. The loading explicitly specifies no end loads on the bars. The results are obtained without recourse to the in-plane solution. Conversely the end force and moment are determined for the case where the out-of-plane strain is zero.
Vibratory Motion of a Body on an Orthotropic Half Plane
Authors: Freedman J. M. , Keer L. M.
Published: November 2010

Three boundary-value problems for an orthotropic half plane are solved. They correspond to the cases studied in a previous investigation by Karasudhi, Keer, and Lee [9] for a body undergoing independent vertical, horizontal, and rocking motion. Dynamic stiffnesses are computed for three typical orthotropic materials: beryllium, ice, and a steel-mylar composite.
The First Passage Time Problem for Simple Structural Systems
Authors: Shipley J. W. , Bernard M. C.
Published: November 2010

This paper presents an analysis of the first passage time problem. A lumped-parameter model for a structural system is considered, and the excitation is limited to white noise. The response of this type of system is a Markov process on a multidimensional position-velocity space (for a damped harmonic oscillator the position-velocity space is two-dimensional). The Markov property is used to develop an integral equation for the first passage time-density function. Numerical results are presented for the damped harmonic oscillator. A rest start condition is considered, i.e., position and velocity are zero, and symmetric position boundaries are considered for the region of safe operation.
Large Deformation of Notched Perfectly Plastic Tensile Bars
Authors: Morrison H. L. , Richmond O.
Published: November 2010

Solutions are obtained for the large, nonsteady deformation of U-notched rigid/perfectly plastic tensile bars in the plane and axisymmetric deformation modes. The solution for the plane mode is shown to be unique. The solutions for both modes are obtained by a general finite-difference method whose accuracy is assessed by examining different mesh sizes in both iterative and noniterative schemes. The solutions may be useful for estimating local stresses and strains in ductile fracture tests even though comparison of calculated and observed deformations indicates some discrepancies due to the neglect of hardening in the theory. The theory does successfully predict yield loads as well as the sharpening of blunt notches and the blunting of acute notches which is observed in axisymmetric tests. It also shows that the largest strains in the plane mode occur on the rigid/plastic boundary reaching a maximum at the surface while those in the axisymmetric mode occur at the center of the root plane. The tensile stresses are maximum at the center of the minimum section for both modes. These results suggest an explanation for the initiation of the shear-type fractures and the cup-cone fractures which are commonly observed in the plane and axisymmetric modes, respectively.
Solution of Kinematical Differential Equations for a Rigid Body
Authors: Kane T. R.
Published: November 2010

This paper deals with the following problem: Given the orientation of a rigid body B at time t0 and the angular velocity of B for t ≥ t0, find the orientation of B for t ≥ t0. An approximate solution is found by employing an “averaging” technique and a lemma (proved in the paper) concerned with a special form of matrix exponentials. As a test, the heretofore unsolved problem of an axisymmetric rigid body subjected to the action of a body-fixed transverse torque of constant magnitude is worked out, and results are compared with those of a digital computer solution.
Stability of Transverse Waves in a Spinning Membrane Disk
Authors: Bulkeley P. Z.
Published: November 2010

The stability of three known exact solutions to the nonlinear equations governing free transverse motions of spinning membrane disks is investigated for a particular choice of perturbations. A wave which travels circumferentially in the disk in the direction opposite to its rotation is shown to be infinitesimally unstable. A wave traveling in the direction of disk rotation and a nonlinear vibration are not shown to be unstable.
An Analysis of the Split Hopkinson Bar Technique for Strain-Rate-Dependent Material Behavior
Authors: Nicholas T.
Published: November 2010

The analysis of the split Hopkinson bar experiment for determining dynamic material behavior is examined for several specific examples of specimen materials which exhibit strain-rate-dependent mechanical behavior. The torsional mode of deformation is chosen as more closely representing a one-dimensional state of stress. Details of the propagation and reflection of stress waves within the specimen are studied using a numerical procedure based on the method of characteristics. Reconstituted stress-strain curves calculated from the conventional analysis of the split Hopkinson bar experiment are compared with actual material behavior for several simulated experiments involving variations in input stress, gage length, material behavior, and static stress-strain curves including statically prestressed materials. The validity of the experimental technique is discussed and limitations on its use are delineated.
A Numerical Study of the Laminar Flow of Non-Newtonian Fluids Along a Vertical Wall
Authors: Yang T. M. T. , Yarbrough D. W.
Published: November 2010

The momentum integral technique is used to describe the steady-state, laminar, accelerating flow of a power-law liquid film along a vertical wall. Values for film thicknesses and boundary-layer thicknesses are obtained numerically and compared with existing analytical solutions for Newtonian fluids.
On the Dynamic Response of Disordered Composites
Authors: McCoy J. J.
Published: November 2010

A formulation is obtained that is to be satisfied by the mean (i.e., statistical averaged) field quantities in a statistical sample of heterogeneous, linearly elastic solids. Inertia effects are included in the analysis. A low frequency-long wavelength theory is extracted from the general formulation as an approximation to be used when spatial variations of the mean field quantities are slow relative to spatial variations of the material properties of the inhomogeneous solids. The temporal variations are restricted to slow variations on a time scale defined by the spatial variations of material properties and a characteristic wave speed. The predictions of the low frequency-long wavelength theory can be given a purely deterministic interpretation. Some aspects of the latter formulation are investigated. In particular, it is shown that the infinite wavelength limit reduces to an effective modulus theory. The effective elastic moduli tensor is identical to one that is obtained on ignoring inertia effects from the outset; the mass density to be used is the “averaged” mass density. By retaining correction terms it is then shown that elastic wave propagation will always exhibit both dispersion and decay over large enough propagation distances.
Yield Strength and Microstructural Scale: A Continuum Study of Pearlitic Versus Spheroidized Steel
Authors: Butler T. W. , Drucker D. C.
Published: November 2010

A continuum mechanics approach is applied to the microstructure of pearlitic and spheroidized steels and compared with experiment as in earlier studies of WC-Co and aluminum-silicon. Success in the prediction of the yield strengths of pearlitic steels from the yield strengths of spheroidized steels requires little more than the conventional starting points in metallurgy and mechanics. Major conclusions which emerge are the same for all these very different crystal and microstructures. The flow stress of the ductile matrix of structural metals is determined primarily by microstructural features not visible in the optical microscope. The most rigid of particles or pearlite clumps, microns in size or larger, have negligible influence on yield or flow strength in volume fractions up to 1/10 and little influence up to 1/3. Yet, solute atoms, which raise the yield strength of pure metals significantly cannot account for the far higher yield strength of structural metals. Therefore, until very high volume fractions of very strong inclusions are present, the dominant control of plastic deformation must come from submicron particles in the ductile matrix. The microstructure visible in the optical microscope seems relevant here only to the extent that it reflects the invisible.
Steady-State Cornering of Two-Wheeled Vehicles
Authors: Krauter A. I.
Published: November 2010

The classic work of Whitcomb and Milliken on the steady-state cornering of automobiles is generalized to include a simplified two-wheeled vehicle. The relationship which results, similar to that of Whitcomb and Milliken, gives the radius of the path of the vehicle in terms of vehicle parameters, vehicle speed, and steering head angle.
On the Foundations of Thermoplasticity—An Experimental Investigation
Authors: Phillips A. , Kasper R.
Published: November 2010

This paper studies the motion of the yield surface at elevated temperatures under prestressing. A new hardening law is proposed and experimentally verified.
Approximate Elasticity Solution for Moderately Thick Shells of Revolution
Authors: Hutchins G. J. , Soler A. I.
Published: November 2010

A higher-order theory of moderately thick elastic shells is developed using Reissner’s variational principle with Legendre polynomial expansions representing variation through the thickness of all dependent variables. A truncation scheme is suggested to yield a finite set of governing differential equations. For symmetrically loaded shells of revolution, the equations are cast in first-order form suitable for numerical integration. Results are presented for pressurized cylinders and compared with exact 3-D elasticity solutions and with solutions obtained using the finite-element method. The developed approximate theory contains one level of extension and bending effects beyond what is usually contained in classical shell theory with shear deformation. Estimates are made of thickness-to-mean radius ratios and elastic moduli ratios for which the new theory yields valid results.
A Continuum Approach to the Propagation of Shear Waves in Laminated Wave Guides
Authors: Nayfeh Adnan H. , Gurtman G. A.
Published: November 2010

We develop a continuum mixture theory to study harmonic and transient shear wave motions in laminated wave guides. Both transversely (SV) and horizontally (SH) polarized waves are considered. Dispersion relations are derived and compared with exact and other approximate theory predictions. Transient solutions for both types of waves are also investigated via the “head-of-the pulse” approximations.
Lower Bounds for the Buckling Loads and the Fundamental Frequencies of Elastic Bodies
Authors: Popelar C. H.
Published: November 2010

Within the classical theory of elastic stability a lower bound to the buckling load of an elastic body is presented. The Timoshenko load is shown to be a better upper bound to the buckling load than the Rayleigh load. By appropriate modifications of the potential and complementary energies, these bounds are applicable to the fundamental frequency of an elastic body. The application of the bounds is illustrated.
Applicability of Mixing Length Theory to Turbulent Boundary Layers Beneath Intense Vortices
Authors: Chi S. W. , Glowacki W. J.
Published: November 2010

The ability of mixing length theory to correlate boundary-layer data beneath intense vortices is evaluated. The boundary-layer equations with turbulent eddy viscosity in terms of a mixing length and an appropriate shear velocity have been developed by consideration of a simplified turbulent energy equation. In the absence of quantitative knowledge of the mixing length for the vortex flow, an expression for the mixing length has been first derived from the flat-plate data and then modified for adaptation to the vortex flow. The full turbulent boundary-layer equations were finally solved on a high-speed computer; and the calculated results were compared with the available experiments under the same conditions. A conclusion was reached that the mixing length theory adequately represents the experimental data.
Quasi-Static Extension of a Tensile Crack Contained in a Viscoelastic-Plastic Solid
Authors: Wnuk M. P.
Published: November 2010

Final stretch criterion of failure is applied to the problem of quasi-static extension of a crack embedded in an elastic-plastic or viscoelastic-plastic matrix. The slow growth under subcritical conditions in a rate-sensitive Tresca solid is shown to be a superposition of creep rupture and McClintock’s ductile growth. This type of growth occurs at subcritical magnitude of the imposed K-factor and can be accounted for only through a recognition of inelastic properties of solids. In the subcritical range there is no unique value for Ko independent of geometrical configuration and flaw size. Not only the produced states of stress and strain are dependent on the loading path, but also the material resistance to fracture turns out to be a function of the history of loading that precedes catastrophic failure. A nonlinear integro-differential equation of motion is derived for a crack progressing through a viscoelastic medium with some limited ability to plastic flow. Examples of numerical integration are given incorporating both monotonic and cyclic loading programs.
Lower Bounds to Eigenvalues by Planelike Surfaces
Authors: Pnueli D.
Published: November 2010

A particular solution of a variational problem is defined as corresponding to a particular set of parameters. A general solution is the one over a continuous region of the parameters. This work presents a method to obtain lower bound to the general solution, when some particular solutions are known.
Stable Harmonic and Subharmonic Oscillations of a System With Piecewise Linear Restoring Forces
Authors: Fu C. C.
Published: November 2010

In the study of steady-state solutions of a nonlinear, or piecewise linear dynamic system under periodic forcing, it is often necessary to examine the stability of the solutions. The reason is that not all the possible solutions can persist for an arbitrarily long time in the presence of small random disturbances of all kinds. In general, some of the solutions are stable, and others are unstable. Only stable solutions can be expected to occur in physical systems. This paper analyzes the response of a certain class of piece-wise linear systems. The piecewise linearities arise solely from restoring forces which are found frequently in many engineering problems. Harmonic and subharmonic solutions of the piecewise linear systems are constructed and their stability studied. System parameters which affect the various types of solutions, and interrelations between these parameters for the various types of solutions to exist, are determined. Numerical results for practical design applications are presented. In particular, jump phenomena involving a transition from an unstable harmonic oscillation to a stable subharmonic oscillation, and vice versa, are shown to exist for the present systems.
A Theoretical Analysis of One-Dimensional Nonsteady Muscular Contraction
Authors: Steen John A. , Chiu H. H. , Moreno Augusto H.
Published: November 2010

Most of the existing theories of muscle contraction rely primarily on specific information of the internal function of the system. These theories are generally based on mechanics or chemical kinetics models. We have previously proposed a general theory based on the laws of irreversible thermodynamics that requires only a general knowledge of the physical system. The theory has been derived in a form that is applicable to the three-dimensional, nonuniform, unsteady contraction of muscle. With a knowledge of the general physical parameters of the system, the solution of the equations would specify the force and shortening at each point in the muscle as a function of space and time. So far, we have solved the specific problem of the overall contraction of a uniform element of contractile material constrained to contract isometrically [1]. Presented herein is the response within a one-dimensional element of muscle rigidly attached at one end and acted upon by a sinusoidal force at the other end. The solution indicates that force and shortening within the muscle are composed mathematically of two sinusoidal waves moving in opposite directions. It is also seen that the maximum absolute value of the transfer function (from force to shortening) corresponds to an optimum physiological condition, where the passive elastic and active contractile responses combine to produce maximum work output. This suggests that a muscle at its optimum contractile state will shorten, against the same external force, a greater amount than when it was at a different contractile state. Application of the scheme of analysis to general nonsteady contractions of muscle, including the myocardium, is also indicated.
Experimental and Analytical Investigation of Dynamic Stress Concentrations at a Circular Hole
Authors: Fang S.-J. , Hemann J. H. , Achenbach J. D.
Published: November 2010

The hoop stresses which are generated at the circumference of a circular hole in a large plate when a pressure wave is diffracted, were measured by photoelastic methods. A plane pressure pulse of short duration and approximately triangular shape was generated by the detonation of a strip-explosive over one edge of the plate. Measurements were carried out for three values of the ratio, 2a/Λ, of the diameter of the hole to the length of the stress pulse. Dimensionless hoop stresses are plotted versus the time after detonation and versus the ratio 2a/Λ. The dimensionless hoop stress decreases as 2a/Λ increases. The measured values show good agreement with analytical computations.
Effect of Prior Deformation on Cyclic Response of Metals
Authors: Valanis K. C.
Published: November 2010

The paper is concerned with the theoretical prediction of cyclic hardening and cyclic softening of metals under conditions of cyclic straining. First, a constitutive equation of a hereditary type is proposed, which is based on the notion of intrinsic time, introduced recently by the author. In essence, the intrinsic time is the cumulative sum of “deformation increments” experienced by a material in the past, weighted with respect to a weighing function which is a material property. The theory predicts that an annealed metal will harden upon cyclic straining until a critical value of the intrinsic time is reached whereupon the metal will begin to soften. It is also shown that an initial strain prehistory will accelerate the onset of softening in accord with experimental observation. Finally, the “fading memory” of metals with respect to the intrinsic time scale is demonstrated and its consequences are shown to be in agreement with observation.
A Refined Theory for Laminated Anisotropic, Cylindrical Shells
Authors: Whitney J. M. , Sun C.-T.
Published: November 2010

A set of governing equations and boundary conditions are derived which describe the static deformation of a laminated anisotropic cylindrical shell. The theory includes both transverse shear deformation and transverse normal strain, as well as expansional strains. The validity of the theory is assessed by comparing solutions obtained from the shell theory to results obtained from exact theory of elasticity. Reasonably good agreement is observed and both shear deformation and transverse normal strain are shown to be of importance for shells having a relatively small radius-to-thickness ratio.
Axially Symmetric Stress Distributions in Elastic Solids Containing Ring-Shaped Cracks Under Torsion
Authors: Kanwal R. P. , Pasha M. L.
Published: November 2010

We present the axially symmetric stress distributions in elastic solids containing ring-shaped cracks when the solids are kept under torsion. Two cases are analyzed. In the first case we discuss the crack problem in an infinite elastic medium when the ratio of the inner to the outer radius is small. In the second case this ratio is almost equal to unity.
Waves Due to a Moving Oscillatory Surface Pressure in a Stratified Fluid
Authors: Pramanik A. K.
Published: November 2010

The initial value problem of waves generated by an oscillatory pressure distribution moving uniformly on the free surface of a two-layer fluid is solved. The integral representations of the waves both on the free surface and on the surface of separation are obtained. By a passage to the limit t → ∞, the steady-state solution of the problem is derived through an asymptotic evaluation of these integrals at large distances. It is noticed that stratification sharply changes the number and the character of the progressive waves and also introduces two critical speeds instead of one as found in homogeneous fluid. At these speeds the solution becomes singular.
Occurrence of the Summed and Differential Harmonic Oscillations in a Nonlinear Multidegree-of-Freedom Vibratory System
Authors: Yamamoto T. , Yasuda K.
Published: November 2010

Simultaneous occurrence of several oscillations with frequencies ωr (≒pr) is sometimes observed in a nonlinear multidegree-of-freedom damped vibratory system subjected to harmonic excitation of frequency ω, when the frequency ω and the natural frequencies pr (r = 1, 2, …, k) of a corresponding undamped linearized system satisfy the condition Nω = Σr=1k mrpr, in which N is a positive integer and mr are positive or negative integers. Theoretical investigations on the occurrence of such oscillations are carried out for vibratory systems with nonlinear spring characteristics derivable from a potential. The analysis shows that in these systems only the summed type of oscillations with all mr positive have the possibility of occurrence, while the differential type of oscillations with some mr negative do not.
Response of Cylindrical Cavity to Traveling Load in Bore
Authors: Kojima M.
Published: November 2010

Stress analysis was carried out on a cylindrical cavity in an infinite medium. The normal tractions, which act along the circumference of the bore, rotate continuously or change their rotating directions at t = 0. In this analysis, the Fourier-transform technique according to the theory of distributions was employed to investigate the relationship between the loading condition of traveling traction and the dynamic response. The theory of distributions verified the past solutions and in this analysis it also revealed the possibility of some transient solution.
Pulse Propagation in a Helix—Theory and Experiment
Authors: Phillips J. W.
Published: November 2010

Wittrick’s general one-dimensional equations governing the propagation of small elastic disturbances in a helical waveguide are solved by the method of characteristics, and numerical results for a particular interface problem are compared with strain gage records from an impacted experimental model. The agreement between theory and experiment is found to be excellent for the type of pulse considered, namely, an initially longitudinal compressive pulse approximately seventy rod-diameters in length.
Vibration of a Plate With Internal Constraints
Authors: Yang W. H.
Published: November 2010

Plate vibration is an old subject in mechanics in which the boundary value problems have almost been exhausted. But in practice, very few plates are constrained only along the boundary. Internal constraints are often imposed on the plate in addition to its boundary conditions in the form of rivet and spot welding. A new algebraic method is applied to a internally constrained plate. The fundamental frequency modified by an internal constraint is displayed. Bounds on all frequencies are given.
The Stress and Stability Analyses of Railroad Tracks
Authors: Kerr A. D.
Published: November 2010

The paper presents a survey of the state of knowledge in the fields of stress and stability determination of a railroad track. At first, the evolution of the railroad track structure is briefly summarized. This is followed by sections which discuss the development of the methods for the determination of stresses in the rails and ties, and the stability of the railroad track due to constrained thermal expansions.
Nonsteady-State Particle Flow Under Gravity—An Extension of the Stochastic Theory
Authors: Mullins W. W.
Published: November 2010

The steady-state (ss) stochastic theory of convergent, cohesionless particle flow under gravity toward an orifice in the floor of a semi-infinite bed, based on the statistics of random flight and assuming instantaneous propagation of flow disturbances throughout the bed, is extended to nonsteady-state flow and time lag effects. The new theory, of which the ss theory is a special case, assumes flow to be restricted to an expanding zone, surmounting the orifice (opened at t = 0), of particle density ρss, separated from the rest of the bed of the original particle density ρ0 = ρss + Δρ (Δρ > 0) by a boundary whose elements advance with a velocity vn = −(1/Δρ)Jn where Jn is the normal component of the particle flux on the inside of the boundary due to flow (assumed to be ss) within the zone. Detailed equations describing the flow zone boundary as a function of time and the flow within the zone are developed; the equations depend on two material parameters (Δρ/ρss, and α of ss theory) and on the quantity of material drained out. Corrections are derived for the analysis of the z2 and z3/2 plots of layer data previously made on the basis of the ss theory. A comparison of the new predictions with one piece of flow data shows the theory capable of accounting for lag effects and for details of the flow pattern in that case. Values of Δρ/ρss and α are deduced, the latter being the order of the particle size in conformity to the expectations of the statistical theory.
Elastic-Plastic Buckling of Aluminum Cylindrical Shells Subjected to Axisymmetric Impulse Loads
Authors: Wesenberg D. L.
Published: November 2010

The elastic-plastic buckling of 6061-T4 aluminum, circular cylindrical shells is examined experimentally and analytically. Groups of shells with radius-to-thickness ratios of 100, 200, and 300 were loaded with short-duration axisymmetric pressure pulses. A fast-discharge capacitor bank and current pulse shaping technique are utilized to provide a sine-squared pressure pulse with duration of about 5 μsec, a duration sufficiently short that loading can be considered impulsive. Average peak-to-peak permanent buckling deformations and wave numbers are compared with predictions from a Lagrangian, finite-difference computer code, and good agreement is obtained between measurements and predictions.
Stress Concentration in a Stretched Cylindrical Shell With Two Equal Circular Holes
Authors: Seide P. , Hafiz A. S.
Published: November 2010

In this investigation, the stress distribution due to uniaxial tension of an infinitely long, thin, circular cylindrical shell with two equal small circular holes located along a generator is obtained. The problem is solved by the superposition of solutions previously obtained for a cylinder with a single circular hole. The satisfaction of boundary conditions on the free surfaces of the holes, together with uniqueness and overall equilibrium conditions, yields an infinite set of linear algebraic equations involving Hankel and Bessel functions of complex argument. The stress distribution along the boundaries of the holes and the interior of the shell is investigated. In particular, the value of the maximum stress is calculated for a wide range of parameters, including the limiting case in which the holes almost touch and the limiting case in which the radius of the cylinder becomes very large. As is the case for a flat plate, the stress-concentration factor is reduced by the presence of another hole.
An Outer Boundary Integral Equation Applied to Transient Wave Scattering in an Inhomogeneous Medium
Authors: Shaw R. P.
Published: November 2010

The transient scattering of waves by an island surrounded by a locally variable water depth is solved by a finite-difference integration in the inhomogeneous region terminated at an outer boundary, beyond which the medium is infinite and homogeneous. At this outer boundary, an exact relationship between wave heights and velocities is used in the form of a Kirchhoff time-retarded integral equation. Examples are given for a constant depth, to check against other solutions, and for a parabolic depth with two forms of incident waves, a ramp-step, and a Gaussian.
Propagation of Low Frequency Elastic Disturbances in a Three-Dimensional Composite Material
Authors: Kohn W.
Published: November 2010

This paper is a generalization to three dimensions of an earlier study for one-dimensional composites. We show here that in the limit of low frequencies the displacement vector ui(r,t) can be written in the form ui (r,t) = (∂ij + vijl (r) ∂/∂xl + …) Uj (r,t). Here Uj (r,t) is a slowly varying vector function of r and t which describes the mean displacement of each cell of the composite. Its components satisfy a set of three coupled partial differential equations with constant coefficients. These coefficients are obtainable from the three-by-three secular equation which yields the low-lying normal mode frequencies, ω(k). Information about local strains is contained in the function vijl(r), which is characteristic of static deformations, and is discussed in detail. Among applications of this method is the structure of the head of a pulse propagating in an arbitrary direction.
Nonlinear Vibration of Beams Using a Form-Function Approximation
Authors: Lou C. L. , Sikarskie D. L.
Published: November 2010

The nonlinear response and stability of a vibrating, buckled beam is analyzed using a form-function approximation. Such an approximation differs from the usual linear series approximations in that the unknown parameter appears nonlinearly. This new approximation has two major advantages. Since all harmonics (in both space and time) are represented, the dominant harmonics are “singled out” in the solution, thus making it very efficient. The form-function representation also permits an insight into system behavior not found in other methods. Knowledge of the form parameter shows explicitly how the form of the response changes with the system parameters, e.g., forcing function magnitude and frequency, material constants, etc.
Forces on Cylinders and Spheres in a Sinusoidally Oscillating Fluid
Authors: Sarpkaya T.
Published: November 2010

The in-line and transverse forces acting on circular cylinders and the in-line force acting on spheres immersed in a harmonically oscillating fluid in a U-shaped vertical tunnel have been measured. The drag, inertia, and the transverse force (lift) coefficients have been determined through the use of a Fourier analysis and found to depend on a period parameter. The results have shown that the transverse force on cylinders is as large as the in-line force and alternates at frequencies ranging from one to four times the driving frequency of the fluid within the range of subcritical Reynolds numbers encountered in the investigation.
The Behavior of a Two-Dimensional Wake in a Uniformly Sheared Turbulent Flow
Authors: Ahmad Q. A. , Luxton R. E. , Antonia R. A.
Published: November 2010

The behavior of a cylinder wake in a weak uniformly sheared external stream is studied. It is found that the departure of the wake from the linear velocity distribution of the external flow is approximately self preserving. There is a tendency for the wake to grow faster on the “high velocity” side (where ∂U/∂y has the same sign inside and outside the wake) than on the “low velocity” side (where the signs of ∂U/∂y are different). This result agrees with the limited evidence on the growth of boundary layers under a uniformly sheared free stream. The turbulence structures on the two sides of the wake appear to behave independently of each other.
Experiments on Supersonic Boundary-Layer Separation in Three Dimensions
Authors: Bachalo W. D.
Published: November 2010

A detailed experimental study of three-dimensional separation in supersonic flow is described. Three-dimensional wedges affixed to flat plates were used to generate the flow fields that were used to examine the relationship of cross flow to the extent of separation. Models with strong transverse pressure gradients resulted in a diminished extent of separation about the model plane of symmetry but demonstrated expansive growth of separation to a limit with distance from the plane of symmetry. A secondary flow region was found embedded in the separated flow.
Elastic-Plastic Analysis of an Infinite Sheet Having a Circular Hole Under Pressure
Authors: Hsu Y. C. , Forman R. G.
Published: November 2010

An exact elastic-plastic solution for the stresses in an infinite sheet having a circular hole subject to pressure is obtained on the basis of J2 deformation theory together with a modified Ramberg-Osgood law. The sheet is orthotropic but isotropic in its plane. The results are assessed on the basis of Budiansky’s criterion for the acceptability of J2 deformation theory. By using exact elastic-plastic stresses, the function connecting the pressure at the hole with the radial enlargement is obtained. Upon release of the pressure, residual stresses around the hole are produced.
Coefficient of Restitution Interpreted as Damping in Vibroimpact
Authors: Hunt K. H. , Crossley F. R. E.
Published: November 2010

During impact the relative motion of two bodies is often taken to be simply represented as half of a damped sine wave, according to the Kelvin-Voigt model. This is shown to be logically untenable, for it indicates that the bodies must exert tension on one another just before separating. Furthermore, it denotes that the damping energy loss is proportional to the square of the impacting velocity, instead of to its cube, as can be deduced from Goldsmith’s work. A damping term λxnx˙ is here introduced; for a sphere impacting a plate Hertz gives n = 3/2. The Kelvin-Voigt model is shown to be approximated as a special case deducible from this law, and applicable when impacts are absent. Physical experiments have confirmed this postulate.
Criteria for Analysis-Test Correlation of Structural Dynamic Systems
Authors: Chen J. C. , Wada B. K.
Published: November 2010

A rational criterion for structural dynamic analysis-test correlation has been established by using a matrix perturbation technique. This criterion can be used for the verification of an analytical model by the test results. Also, the same technique can be applied to update the analytical results by using the test results without repeating the entire analytical procedure. A sample problem has been used to demonstrate this technique. Very satisfactory results are obtained with only the first-order perturbation solution included for transient loading. For periodic loading, higher-order perturbation solutions are needed to achieve the same accuracy.
Extension of Lanczos’ Method of Fundamental Eigenvalue Approximation
Authors: Herman H.
Published: November 2010

A method introduced by Lanczos for the approximate determination of fundamental eigenvalues of one-dimensional continuous systems is extended to permit the determination of higher eigenvalues as well, and a modification is introduced which yields better accuracy for the same number of approximating equations. Illustrations are presented demonstrating applications of the method to systems with discontinuities and to the frequency determination in nonlinear oscillation problems.
Unsteady Cavity Flows: Oscillatory Flat Box Flows
Authors: O’Brien V.
Published: November 2010

The oscillatory cavity flows reported here are extensions of previously studied steady closed rectangular cavity flows (box flows). The periodic laminar incompressible flows are characterized by three numerical parameters, peak Reynolds number, a reduced frequency (or Stokes number) and the height-to-length ratio of the cavity. Depending on the height-to-length ratio, flow fields are obtained by finite-difference solutions or analytic solutions of the Navier-Stokes equation. The central portion of a flat cavity contains an oscillatory parallel flow. Experimental measurements corroborate the theory. Stokes number dependency and particularly differences from the corresponding steady flow (whose Stokes number is zero) are illustrated.
The Effect of Stress Concentrations on the Creep Rupture of Tension Panels
Authors: Hayhurst D. R. , Morrison C. J. , Leckie F. A.
Published: November 2010

The creep rupture behavior of metals at high temperatures is reviewed for constant homogeneous states of multiaxial stress. Currently used methods for estimating the creep rupture life of engineering structures are discussed. The rupture lives of plane stress tension plates containing discontinuities are predicted by the different methods. The estimates of life are compared with the results of experiments carried out on copper and aluminum plates. It is shown that the magnitudes of the elastic and steady-state stresses do not influence the rupture behavior of the tension plates examined. The redistribution of stress in the structures which occurs due to tertiary creep plays an important part in determining the rupture lives. A method of predicting lower bounds on the structural rupture lives is presented and shown to closely predict the results of experiments.
Stationary Temperature and Stress Fields in an Anisotropic Elastic Slab
Authors: Tauchert T. R. , Ako¨z A. Y.
Published: November 2010

The stationary temperature, displacement, and stress distributions in an anisotropic elastic slab undergoing generalized plane deformation are examined. A general representation for the thermal boundary conditions is used, which permits specification of surface temperature, heat input, thermal insulation, or convection at each boundary of the slab. The solution is valid for traction-free slabs having thermal and elastic anisotropy of the most general form. As an illustrative example, the temperature and stresses due to a uniform temperature rise over a portion of the boundary of a slab are computed.
Steady Laminar Flow in a Stationary Tank With a Spinning Bottom
Authors: Alonso C. V.
Published: November 2010

The steady incompressible viscous flow induced in a cylindrical tank by the rotation of its bottom was studied both theoretically and experimentally. The complete Navier-Stokes equations are expressed in terms of the tangential velocity, vorticity, and meridional stream function. The transformed equations are solved numerically using an alternating-direction implicit scheme and a nonuniform grid. The general validity of the numerical solution was demonstrated by the agreement between the computed and experimental results.
Analysis of Knuckle Region Between Two Smooth Shells
Authors: Ranjan G. V. , Steele C. R.
Published: November 2010

The stress analysis of a small knuckle region between two smooth shell segments is studied with the aid of an asymptotic expansion valid for small deviation from the nominal geometry. A simple design formula which includes the nonlinear prestress effect is obtained for the maximum stress in the knuckle portion. Graphs are presented from which stress concentration can be easily determined for a wide variation of parameters.
Dynamic Fracture of a Beam or Plate in Plane Bending
Authors: Freund L. B. , Herrmann G.
Published: November 2010

The dynamic fracture response of a long beam of brittle elastic material subjected to pure bending is studied. If the magnitude of the applied bending moment is increased to a critical value, a crack will propagate from the tensile side of the beam across a cross section. An analysis is presented by means of which the crack length and bending moment at the fracturing section are determined as functions of time after fracture initiation. The main assumption on which the analysis rests is that, due to multiple reflections of stress waves across the thickness of the beam, the stress distribution on the prospective fracture plane ahead of the crack may be adequately approximated by the static distribution appropriate for the instantaneous crack length and net section bending moment. The results of numerical calculations are shown in graphs of crack length, crack tip speed, and fracturing section bending moment versus time. It is found that the crack tip accelerates very quickly to a speed near the characteristic terminal speed for the material, travels at this speed through most of the beam thickness, and then rapidly decelerates in the final stage of the process. The results also apply for plane strain fracture of a plate in pure bending provided that the value of the elastic modulus is appropriately modified.
Effects of Flexible Mounting and Damping on the Synchronous Response of a Rotor-Shaft System
Authors: O¯ta H. , Kanbe Y.
Published: November 2010

Synchronous response of a rotor supported by a damped, flexibly mounted bearing is similar to the well-known one of a rectilinear vibratory system having two degrees of freedom, or a dynamic vibration absorber. Designing the flexible support with an appropriate combination of equivalently concentrated mass of pedestal, bearing support stiffness, and optimum damping, the peak amplitude of a rotor-shaft system is found to be kept nearly to the value of rotor eccentricity. Experimental results of rotor unbalance resonance coincide well with the analytical ones.
Statistical Analysis of Longevity of Prosthetic Aortic Valves
Authors: Ghista D. N. , Lin Y. K.
Published: November 2010

The analysis and procedure for obtaining the average fatigue damage rate, and hence a measure of longevity, of a prosthetic heart valve is presented. Design charts are developed to obtain measures of longevity of prosthetic heart valves, for various values of valve geometry characterizing parameter, valve’s in vivo pressure loading characteristics and the fatigue properties of the valve material. Such design charts can be updated when more reliable information about the fatigue properties of valve material (in a physiological fluid environment) becomes available.
Wave Propagation in a Chemically Reacting, Linear Elastic Sphere
Authors: Nunziato J. W. , Wheeler L. T.
Published: November 2010

Of concern is the response induced in a chemically reacting elastic sphere by a spatially uniform applied surface pressure. The analysis, which is carried out in the context of a linearized theory, is concentrated mainly on the behavior during the time it takes for a pulse to travel from the surface to the center. An interesting interplay is described which develops between the dominance of mechanical effects near the center and possible chemical-reaction effects near the surface.
Stresses in Ventricular Wall
Authors: Demiray H.
Published: November 2010

Assuming an idealized geometry, i.e., a spherical geometry, for the left ventricle, the ventricular wall stresses and elastic stiffness are investigated by use of a finite elasticity theory. The values of material constants are obtained via comparison of analytical results with experiments. The numerical calculations indicate that the endocardial layers experience very large tangential stress gradients which may be the cause of ischemia of left ventricle.
Experiments on Parametric Resonance of Pipes Containing Pulsatile Flow
Authors: Paidoussis M. P. , Issid N. T.
Published: November 2010

This paper describes an experimental investigation of the stability of elastic pipes containing water flow, the velocity of which is perturbed harmonically about a mean value. Parametric and combination resonances were found to occur over specific ranges of pulsation amplitudes and frequencies, and of flow rates. The critical values of pulsation frequency and amplitude for the onset of instability are compared with theory, and agreement is found to be generally fairly good.