bluuebunny/crossref_metadata_2025 huggingface dataset:
Parametric Resonance Oscillations of Flexible Slender Cylinders in Harmonically Perturbed Axial Flow—Part 2: Experiments
Authors: Paidoussis M. P. , Issid N. T. , Tsui M.
Published: July 2009

This paper examines experimentally the dynamical behavior of a flexible slender cylinder in axial flow, perturbed harmonically in time. Parametric resonance oscillations were found to exist over certain ranges of frequencies and amplitudes of flow-velocity perturbations. The most prominent of the resonances, in these experiments, were associated with the second-mode principal primary resonance, and were studied extensively. Agreement with theory was found to be quite good.
Approximation of the Strain Field Associated With an Inhomogeneous Precipitate—Part 1: Theory
Authors: Johnson W. C. , Earmme Y. Y. , Lee J. K.
Published: July 2009

Two independent methods are derived for the calculation of the elastic strain field associated with a coherent precipitate of arbitrary morphology that has undergone a stress-free transformation strain. Both methods are formulated in their entirety for an isotropic system. The first method is predicated upon the derivation of an integral equation from consideration of the equations of equilibrium. A Taylor series expansion about the origin is employed in solution of the integral equation. However, an inherently more accurate means is also developed based upon a Taylor expansion about the point of which the strain is to be calculated. Employing the technique of Moschovidis and Mura, the second method extends Eshelby’s equivalency condition to the more general precipitate shape where the constrained strain is now a function of position within the precipitate. An approximate solution to the resultant system of equations is obtained through representation of the equivalent stress-free transformation strain by a polynomial series. For a given order of approximation, both methods reduce to the determination of the biharmonic potential functions and their derivatives.
Transient Response of a Finite Crack in a Strip With Stress-Free Edges
Authors: Itou S.
Published: July 2009

We have considered the problem of determining the dynamic stress distribution in an infinitely long isotropic homogeneous elastic strip containing a Griffith crack which is perpendicular to the edges of the strip. The crack is opened by internal pressure with the Heaviside function time-dependence. By using the Fourier and Laplace transforms, we can solve the problem with a set of dual integral equations in the Laplace transform domain. These equations are solved using the Schmidt method. The Laplace inversion of the stress-intensity factor is carried out numerically.
Resolution of a Core Problem in Wound Rolls
Authors: Yagoda H. P.
Published: July 2009

Previous misunderstandings about the behavior of stresses in the vicinity of the core of wound rolls are resolved through the development of an explicit closed-form analytical solution for the radial and circumferential stresses which are generated during winding; the solution holds in the general case of variable winding tension. Asymptotic series are derived and then employed to compute profiles of stresses within the wound material for several cases of practical interest. A parametric analysis of the influence of core elasticity on structural integrity of the roll underscores the indispensable support provided by the core at the inner boundary of the roll. Results show that the circumferential stress in the vicinity of the core strongly depends on core stiffness. A relation that is derived between interlayer pressure and circumferential stress at the core boundary may be useful as a guide in core design and in preventing roll collapse.
A Thermomechanical Example of Auto-Oscillation
Authors: Panek Carl
Published: July 2009

A system which progresses repeatedly through a cyclic sequence of physical configurations (continuous or discrete), in the absence of any periodic excitation, is said to be in the state of auto-oscillation. In this paper the author examines a thin thermoelastic rod projecting from the warmer of two parallel rigid walls, their separation being slightly wider than the length of the rod. Assuming heat transfer by conduction only, it is found that for certain combinations of physical parameters the rod does auto-oscillate (repeatedly makes and breaks contact with the cooler wall at finite frequency) provided that part of the rod near the cooler wall has a nonpositive thermal coefficient of expansion. This last condition is absolutely necessary since otherwise one encounters certain thermomechanical pathologies. The only other way that these pathologies could be eliminated would be to employ the concept of imperfect contact as suggested by Barber, which may also be interpreted as allowing heat transfer by radiation.
A Theory of Cell-to-Cell Mapping Dynamical Systems
Authors: Hsu C. S.
Published: July 2009

The method of point-to-point mappings has been receiving increasing attention in recent years. In this paper we discuss instead dynamical systems governed by cell-to-cell mappings. The justifications of considering such mappings come from the unavoidable accuracy limitations of both physical measurements and numerical evaluation. Because of these limitations one is not really able to treat a state variable as a continuum of points but rather only as a collection of very small intervals. The introduction of the idea of cell-to-cell mappings has led to an algorithm which is found to be potentially a very powerful tool for global analysis of dynamical systems. In this paper an introductory theory of cell-to-cell mappings is offered. The theory provides a basis for the algorithm presented in [14]. In the first half of the paper we discuss the analysis of cell-to-cell mappings in their own right. In the second half the cell-to-cell mappings which are obtained from point-to-point mappings by discretization are examined in order to see what properties of the point mapping systems are preserved in the discretization process.
Force of Extraction for a Cylinder Buried in Sand
Authors: Cowin S. C. , Trent L. E.
Published: July 2009

Lower bounds are derived for the force needed to extract a cylinder from a larger cylinder when the annular region between the two cylinders contains a granular material.
Propagation of Elastic Pulses and Acoustic Emission in a Plate—Part 2: Epicentral Responses
Authors: Ceranoglu A. N. , Pao Yih-Hsing
Published: July 2009

In the first part of this paper expressions for Green’s dyadics in terms of the generalized ray integrals for both unbounded and bounded media were given. In this part Cagniard’s method is applied to obtain the transient response along the epicentral points of an elastic plate. Numerical results are shown for a concentrated force, a single-couple, a double force, a double-couple without moment and a center of rotation up to 10 transit time required for the longitudinal (P)-wave to cross the thickness of the plate.
Stability Theorems for Multidimensional Linear Systems With Variable Parameters
Authors: Shrivastava S. K.
Published: July 2009

Two equivalent theorems governing stability of multidimensional linear systems with variable parameters are derived which generalize some of the existing stability theorems. Illustrations include damped, gyroscopic, circulatory systems with varying parameters.
Pendulum With a Rotational Vibration
Authors: Schmidt B. A.
Published: July 2009

This work involves a pendulum made up of a mass, a pivoted weightless rod, and a spring. The mass is constrained to maintain its axial position on the rod, but is allowed to move rotationally on the rod under the influence of the spring. The pivot is vibrated rotationally at a high frequency about a vertical axis. It is found that, in some conditions, the vibration causes new stable equilibrium positions.
How to Optimally Support a Plate
Authors: Yang W. H.
Published: July 2009

In practical applications, plates are often not supported along their boundaries. Properly located interior supports can greatly increase the load-carrying capacity of a plate. The optimal locations of N point symmetrical support for a uniformly loaded circular plate are calculated to substantiate the claim. The solutions are obtained for 1 ≤ N ≤ ∞ under the theory of limit analysis of plates. The collapse load in each case is maximized by a search for the optimal support location.
Dynamic Analysis of Explosive-Metal Interaction in Three Dimensions
Authors: Johnson G. R.
Published: July 2009

This paper demonstrates the capability to perform three-dimensional computations for explosive-metal interaction problems with complex sliding surfaces. An analysis is performed for an explosive device which accelerates a metal liner known as a self-forging fragment. Results are presented to show the effects of off-center detonation, asymmetric liner thickness, and asymmetric explosive density for an otherwise axisymmetric device. These three-dimensional conditions have little effect on the linear velocities, but they do introduce significant angular velocities to the self-forging fragment. Unlike projectile-target impact computations, which require only a single sliding surface between the projectile and the target, the explosive devices have multiple, intersecting, three-dimensional sliding surfaces between the expanding explosive gases and the various metal portions of the devices. Included are descriptions of the specialized “search routines” and the “double-pass” approach used for the explosive-metal interfaces.
The Rate (Time)-Dependent Behavior of Ti-7Al-2Cb-1Ta Titanium Alloy at Room Temperature Under Quasi-Static Monotonic and Cyclic Loading
Authors: Kujawski D. , Krempl E.
Published: July 2009

Uniaxial tests using a servocontrolled testing machine and strain measurement at the gage length were performed on a high-strength, low-ductility Titanium alloy. Tests involved monotonic and cyclic loadings with strain rates between 2 × 10−8 to 10−3 s−1, stress rates from 10−1 to 102 MPa s−1, repeated changes in strain rates, and short-term relaxation and creep tests. The inelastic behavior is strongly rate-dependent. Ratchetting is shown to increase as the stress rate decreases. No strain-rate history effect was found. A unique stress-strain curve is ultimately reached for a given strain rate irrespective of prior history as long as only positive stresses are imposed. In the plastic range the relaxation drop in a given time period depends only on the strain rate preceding the test and is independent of the actual stress and strain.
Unsteady Hydromagnetic Flow Near a Moving Porous Plate
Authors: Tokis J. N. , Pande G. C.
Published: July 2009

Unsteady two-dimensional flow of a viscous incompressible and electrically conducting fluid near a moving porous plate of infinite extent in presence of a transverse magnetic field is investigated. Solution of the problem in closed form is obtained with the help of Laplace transform technique, when the plate is moving with a velocity which is an arbitrary function of time and the magnetic Prandtl number is unity. Three particular cases of physical interest are also discussed.
Viscoelastic Analysis of Adhesively Bonded Joints
Authors: Delale F. , Erdogan F.
Published: July 2009

In this paper an adhesively bonded lap joint is analyzed by assuming that the adherends are elastic and the adhesive is linearly viscoelastic. After formulating the general problem a specific example for two identical adherends bonded through a three parameter viscoelastic solid adhesive is considered. The standard Laplace transform technique is used to solve the problem. The stress distribution in the adhesive layer is calculated for three different external loads namely, membrane loading, bending, and transverse shear loading. The results indicate that the peak value of the normal stress in the adhesive is not only consistently higher than the corresponding shear stress but also decays slower.
Instability of a Transversely Isotropic Elastic Slab Subjected to Axial Loads
Authors: Kurashige M.
Published: July 2009

After obtaining the relations between incremental stresses and incremental strains, we analyzed the instability problem stated in the title on the basis of Biot’s mechanics of incremental deformations. The slab, made of a hypothetical transversely isotropic compressible elastic material, is assumed to be stronger in its transverse direction than in its axial direction. The analysis shows that, no matter what the anisotropy strength of the slab is or its thickness is, it can become unstable under tension as well as under compression. The critical load is higher for the stronger anisotropy in the compressive case, while it is lower for the stronger anisotropy in the tensile case. In other words, the reinforcement in the “wrong” direction weakens the slab under tension with respect to its stability. Furthermore, the weakly anisotropic slab can become unstable only after the axial resultant force reaches its maximum, while the strongly anisotropic slab can lose its stability before the force reaches its maximum.
Acceleration of Unbalanced Rotor Through the Resonance of Supporting Structure
Authors: Victor F. , Ellyin F.
Published: July 2009

The dynamic response of a simple beam excited at its midspan by the action of a turbomachine secured to it, is investigated in detail. The forcing function includes transients at startup or shutdown. Effects of the shear deformation, rotatory inertia, and the internal viscous damping, which may depend on the frequency, are considered individually as well as in combined forms. The results indicate that the maximum amplitude of vibration is highly dependent on the acceleration rate through the critical frequency. There is also an apparent shift in its position as compared to the classical resonance frequency. Influences of shear deformation and rotatory inertia are significant when the supporting structure (or foundation) is relatively massive.
A Numerical Study of Nonaxisymmetric Stokesian Flow in a Circular Tube
Authors: Strigberger J. , Plotkin A.
Published: July 2009

A numerical study of the nonaxisymmetric Stokesian flow of a Newtonian fluid in a rigid circular tube of fixed radius has been performed. The analysis presented here is an integral part of the problem of modeling the flow of blood near the ostia of the intercostal arteries of rabbits in order to study a possible factor in the initiation of atherosclerosis. The method of lines is used to reduce the mathematical problem to one of solving a system of first-order ordinary differential equations along lines parallel to the tube axis. Solutions are obtained analytically using matrix eigenvalue techniques for the first two Fourier components of the flow and the accuracy of the numerical method is verified by suitable comparison with the results of independent computations.
An Analysis of Power Law Viscous Materials Under a Plane-Strain Condition Using Complex Stream and Stress Functions
Authors: Lee Y. S. , Smith L. C.
Published: July 2009

The equilibrium and compatibility equations for nonlinear viscous materials described by the power law are solved by introducing the complex stream and stress function. The stresses, strain rates, and velocities derived from the summation form of the stream function and the product form of the stress function are identical to the results obtained from the axially symmetric field equation. The stream function solution is used in the deformation analysis of a viscous hollow cylindrical inclusion buried in an infinitely large viscous medium assuming an equal biaxial boundary stress. The stream function approach is used in determining the stress-concentration factor for a cavity in a viscous material subject to the identical boundary biaxial stress. The results agree with the results of Nadai. The effect of the strain-rate-hardening exponent, the geometry of the inclusion, and the material constants on the hoop stress-concentration factor in the interface between the inclusion and the matrix are discussed.
An Analysis of Contact Between a Pair of Surface Asperities During Sliding
Authors: Lisowski Z. , Stolarski T.
Published: July 2009

An analysis of friction junction formed by a pair of interacting hemispherically shaped surface asperities was carried out. Depending on the maximum geometrical interference of the asperities junction deformation can be elastic or plastic. Elastic junctions were analyzed using Hertz solution. Depending on whether the junction is welded or nonwelded it was assumed that the interfacial shear stress is constant and equal to or less than the bulk shear strength of the weaker material. Solution for the case of plastic junction was approximated by Green’s slip-line field solution.
Stability of Thermoelastic Contact for the Aldo Model
Authors: Barber J. R.
Published: July 2009

A perturbation method is used to investigate the stability of a simple one-dimensional rod model of thermoelastic contact which exhibits multiple steady-state solutions. A thermal contact resistance is postulated which is a continuous function of the contact pressure or separation. It is found that solutions involving substantial separation and/or contact pressures are always stable, but these are separated by unstable “imperfect contact” solutions in which one of the rods is very lightly loaded or has a very small separation. The results can be expressed in terms of the minimization of a certain energy function.
Diffraction of Elastic Waves by a Surface Crack on a Plate
Authors: Kundu T. , Mal A. K.
Published: July 2009

The interaction of time harmonic elastic waves with an edge crack in a plate is studied. The crack is assumed to be normal to the plate surface and its depth small compared to plate thickness. Only plane strain deformations are considered. The incident waves are assumed to be either plane body waves (compressional (P) or inplane shear (SV)) of arbitrary angle of propagation or surface Rayleigh waves propagating at right angles to the crack. For each incident wave type the complete high frequency diffracted field on the plate surface is calculated. Solution is obtained by the application of an asymptotic theory of diffraction. Application to ultrasonic inspection techniques is indicated.
Plane Elastic Waves Generated by Dynamical Loading Applied to Edge of Circular Hole
Authors: Moodie T. B. , Haddow J. B. , Mioduchowski A. , Tait R. J.
Published: July 2009

The generalized plane stress, or plane strain, elastodynamic problem of an unbounded body, subjected to sudden application of tractions at the surface of a circular hole, is considered. In general this problem involves three independent variables, two spatial coordinates, and time, but it is shown how the method of characteristics, for one spatial variable and time, can be applied when the dependent variables are expanded as Fourier series in terms of the polar angle θ. A numerical procedure is proposed for the method of characteristics and numerical results are obtained for a specific example.
Loss of Contact in the Vicinity of a Right-Angle Corner for a Simply Supported, Laterally Loaded Plate
Authors: Keer L. M. , Mak A. F.
Published: July 2009

The solutions to problems of laterally loaded, simply supported rectangular plates are classical ones that can be found in standard textbooks. It is found that forces directed downward must be present to prevent the corners of the plate from rising up during bending. The objective of the present analysis is to determine the extent to which such a plate will rise if the corner force is not present and the plate is unilaterally constrained. Rather than determine the solution for a rectangular plate, we consider a laterally loaded, simply supported plate which occupies a quarter space region. The plate is unilaterally constrained and may rise at the corner due to an absence of restraining force there. Using integral transform techniques appropriate to the quarter space for elastic plates, the region of lost contact is determined for a general loading. The special loading due to a concentrated force is given as an example.
Steady Motion of an Elastic Beam Across a Rigid Step
Authors: Adams G. G. , Manor H.
Published: July 2009

An infinite elastic beam moves at constant speed across a frictionless rigid step. Steady-state solutions are obtained in closed form using both Euler-Bernoulli and Timoshenko beam models. With step height and speed as parameters, the noncontact regions, mode shapes, and foundation reactions are determined. The results show interesting qualitative as well as quantitative differences between the behavior of the Euler-Bernoulli and Timoshenko beams.
Optimum Pulse Control of Flexible Structures
Authors: Masri S. F. , Bekey G. A. , Caughey T. K.
Published: July 2009

A simple yet efficient active control method is presented for reducing the oscillations of distributed parameter systems subjected to arbitrary dynamic environments. Following determination that some specified response threshold has been exceeded, an open-loop control pulse is applied. The optimum pulse characteristics are determined analytically so as to minimize a non-negative cost function related to the structure energy. The proposed control method is shown to be reliable in consistently mitigating the response of realistic multidegree-of-freedom systems, whether linear or nonlinear, subject to arbitrary stochastic or deterministic excitation.
A Generalized Theory of Cell-to-Cell Mapping for Nonlinear Dynamical Systems
Authors: Hsu C. S.
Published: July 2009

The simple theory of cell mapping and the associated algorithm presented in [1, 2] have been found to form a very effective tool for the global analysis of nonlinear systems. In this paper we generalize the theory by allowing the mapping of a cell to have multiple image cells with appropriate individual mapping probabilities. This generalized theory will be able to deal with very fine and complicated global behavior patterns, if they exist, in a more attractive way without having to utilize extremely small cell sizes. It is found that such a generalized cell mapping can be identified with a Markov chain and the well-developed mathematical theory of Markov chains can be immediately applied. Similar to the simple theory of [1], the generalized cell mapping theory is also eminently suited as a theoretic base for computer alogorithms which will be needed when dealing with systems involving a very large number of cells.
Buckling of Polar Orthotropic Annular Plates Under Uniform Inplane Compressive Forces
Authors: Ramaiah G. K.
Published: July 2009

The problem of buckling of polar orthotropic annular plates under various types of inplane compressive forces along the radial edges has been analyzed in detail by the Rayleigh-Ritz method for eight different combinations of clamped, simply supported, and free boundary conditions. Accurate estimates of critical buckling loads have been obtained for various values of hole ratios and for various values of rigidity ratios. The numerical results are presented in the form of data sheets for direct use by the design engineers.
Note on a Paper by Liu on the Scattering of Water Waves by a Pair of Semi-Infinite Barriers
Authors: Rawlins A. D.
Published: July 2009

Recently, a problem, whose solution was well known in exact form, has been analyzed by Liu (Scattering of Water Waves by a Pair of Semi-Infinite Barriers, ASME Journal of Applied Mechanics, Vol. 42, 1975, p. 777), by the method of matched asymptotic expansions. From the known exact solution a simple expression is obtained for the transmission coefficient. The exact expression for the transmission coefficient when expanded for low frequency incident waves differs from Liu’s result, and therefore casts doubt on Liu’s analysis and physical conclusions.
Optimal Isolation of a Single-Degree-of-Freedom System With Quadratic-Velocity Damping
Authors: Alley T. L.
Published: July 2009

The response of a mass isolated by a linear spring and a quadratic-velocity damper subjected to a step-and-decay velocity input at the base is found in closed form. This solution leads immediately to the optimal isolation system for this input. The parameters of the optimal isolation system are given by a simple formula.
A Surface Integral Numerical Solution for Laminar Developed Duct Flow
Authors: Khader M. S.
Published: July 2009

A surface integral numerical solution for laminar developed flow in ducts of arbitrary shape cross sections is presented. The method is general for any two-dimensional duct with simple or multiple connected regions cross section. The solutions provide information for velocity distribution, friction factor, and wall shear stress. As an application of the present method, solutions for flow in circular and rectangular ducts are obtained. These solutions are used to compare the obtained results and the corresponding exact analytical solutions. Moreover, in order to illustrate the general use of the present scheme, a solution for the case of circular duct containing rod clusters is obtained. The method proved to have several interesting features and advantages over other conventional numerical and analytical techniques.
Calculation of the Response of an Impulsively Excited Oscillator in an Infinite Acoustic Fluid
Authors: Clark A. V. , Whitman A. M.
Published: July 2009

The response of an impulsively excited single-degree-of-freedom oscillator submerged in an infinite acoustic fluid is considered. The character of the response is determined by the quantity ka; k is the wave number associated with the in-vacuo natural frequency of the oscillator, and a is a characteristic structural dimension. For low-frequency oscillators (ka ≪ 1), the response consists of two parts. The first is the usual hydrodynamic solution in which the effect of the fluid on the structure is that of an added mass. The second is much smaller (of order ka) and is significant only in a “boundary layer” in time of order a/c, with c the fluid sonic velocity. For high-frequency oscillators (ka ≫ 1), the principal effect of the fluid is a decay of oscillator vibration due to sound radiation.
Elastohydrodynamic Analysis of Head to Flexible Disk Interface Phenomena
Authors: Licari J. P. , King F. K.
Published: July 2009

The finite-element and finite-difference techniques are used to develop an analytical model which describes the interaction between a magnetic recording head and a flexible disk. The finite-element approach is used to describe disk deformation. Both disk bending stiffness and stiffness effects due to disk rotation are included. The finite-difference scheme is used to solve the Reynold’s or lubrication equation which describes the flow interaction between head and disk. The procedure used to couple the two numerical models into a complete head-to-disk interface simulator is outlined. Accuracy of the simulator is verified experimentally, and results of studies showing the sensitivities of various parameters are given.
Energy-Release Rate in Elastic-Plastic Fracture Problems
Authors: Aoki S. , Kishimoto K. , Sakata M.
Published: July 2009

It is shown that the energy-release rates associated with the translation, rotation, self-similar expansion and distortion of the fracture process region are expressed by the newly introduced integrals, Jˆ, Lˆ, Mˆ, and Iˆ. These integrals can be defined even if there exist plastic deformation, thermal strains, body forces, and inertia forces. They include as special cases the J, L, and M integrals which have been defined by Knowles and Sternberg and discussed by Budiansky and Rice.
The Penny-Shaped Crack and the Plane Strain Crack in an Infinite Body of Power-Law Material
Authors: He M. Y. , Hutchinson J. W.
Published: July 2009

A study is carried out of the problem of a penny-shaped crack in an infinite body of power-law material subject to general remote axisymmetric stressing conditions. The plane strain version of the problem is also examined. The material is incompressible and is characterized by small strain deformation theory with a pure power relation between stress and strain. The solutions presented also apply to power-law creeping materials and to a class of strain-rate sensitive hardening materials. Both numerical and analytical procedures are employed to obtain the main results. A perturbation solution obtained by expanding about the trivial state in which the stress is everywhere parallel to the crack leads to simple formulas which are highly accurate even when the remote stress is perpendicular to the crack.
The Rolling Contact of Two Elastic-Layer-Covered Cylinders Driving a Loaded Sheet in the Nip
Authors: Soong T.-C. , Li C.
Published: July 2009

A circular stress function is used for the steady rolling contact of two cylinders. Each cylinder has an elastic layer bonded to a hard core, and an elastic thin sheet is compressed in the contact arc and being driven by the system. An asymmetric stress distribution is caused by a pushing or pulling force acting at the tail end of the sheet. The effect of the normal load and the tail force on the speed ratios of the two cylinders and the sheet, and also the local slippage in the contact arc are studied by enforcing the exact conditions at the contact zone. The resulting equations are solved by the collocation method and an iterative procedure which stepwisely unlocked the nonslip contacting points whenever the calculated interface shear exceeds the local Coulomb friction.
The Deformation of a Thin, Incomplete, Elastic Ring in a Frictional Channel
Authors: Benson R. C.
Published: July 2009

The deformation of a thin, incomplete, elastic ring being pushed through a frictional channel is analyzed. The problem is formulated using the nonlinear theory of the elastica and it is found that, depending on the channel geometry, either two deformed shapes for the ring are possible, or else no solution is possible. The results are applied to the design of machines such as plain-paper copiers, self-threading tapes, and sewing machines.
Optimization in a Class of Hole Shapes in Plate Structures
Authors: Dhir S. K.
Published: July 2009

An analytical/numerical procedure has been developed which yields the optimum geometry for a constrained hole shape in a large plate under prescribed boundary stresses at infinity. The optimality criterion is based on the minimization of a certain stress integral taken around the hole boundary. Muskhelishvili’s method is used to first obtain the symbolic stress expressions for a given mapping function with unknown coefficients. These stress expressions are then squared and integrated around the hole boundary to obtain the stress integral. A sample problem is worked out in detail to demonstrate this procedure. The optimum shape of a square-like (double-barrel shape) hole with rounded corners was determined by restricting the mapping function to only one specific unknown coefficient. Modification of this shape by introduction of an additional term is also discussed. Numerical stress-concentration values for this case are compared with those from other sources. Most of the algebraic and numerical calculations presented in this paper were performed using MACSYMA, a symbolic manipulation package developed at M.I.T. and in regular use at the David W. Taylor Naval Ship R&D Center.
Transverse Vibrations of Beams, Exact Versus Approximate Solutions
Authors: Hutchinson J. R.
Published: July 2009

An exact solution for the natural frequencies of vibration of a finite length free-free beam with a circular cross section is found and compared to approximate solutions. This exact solution is a series solution of the general linear elasticity equations which converges to correct natural frequencies. Correctness of the frequencies is established by comparison to previous experiments. Comparison of the exact to approximate solutions is made with the Pochhammer-Chree approximation, the Timoshenko beam approximation and the Pickett approximation. The comparisons clearly show the range of applicability of the approximate methods as well as their accuracy. The correct shear coefficient for use in the Timoshenko beam approximation is investigated and conclusions which differ with, yet at the same time complement, those of previous researchers are reached.
Resonant Whirling of Aircraft Propeller-Engine Systems
Authors: Crandall S. H. , Dugundji J.
Published: July 2009

At a critical speed, a light aircraft can experience severe vibrations in steady flight in which the propeller blades vibrate at one frequency while the engine block vibrates at a lower frequency. A model is presented which explains this phenomenon. A three-bladed propeller-engine system is considered to have six rigid-body degrees of freedom plus six blade vibration degrees of freedom. This system is analyzed and simplified by introducing a constraint based on observation of the flight phenomenon. Multiblade coordinates are introduced and a linear eigenvalue problem is derived which describes whirling motions of the engine coupled to progressive waves of blade deformation which circle the propeller disk. These whirling motions are excited by harmonics of the transverse forces on the engine due to the explosive gas pressures in the cylinders. The effects of varying the propeller blade pitch angle are studied and a high-speed instability mechanism is examined.
Nonlinear Breaking of Wave Fronts in a Vibrationally Relaxing Gas
Authors: Shyam R. , Sharma V. D. , Menon V. V.
Published: July 2009

Using the method of characteristics, some explicit criteria for the nonlinear breaking of wave fronts in a plane, cylindrically or spherically symmetric flows of a vibrationally relaxing gas are obtained. It is shown that except a spherically converging compressive wave, all compressive waves break only when the initial discontinuity at the wave-head exceeds a critical value, and the effects of vibrational relaxation and that of the wave front curvature are to increase the time of their breaking. It is found that the stabilizing influences of vibrational relaxation and that of the wave front curvature are not strong enough to overcome the breaking tendency of a spherically converging compressive wave; in fact, in contrast to a cylindrically converging wave, it always breaks down before the formation of a focus, no matter how small be the initial discontinuity at the wave-head.
Transverse Impact on Fluid-Filled Cylindrical Tubes
Authors: Katsamanis F. , Goldsmith W.
Published: July 2009

An analytical and experimental study was conducted regarding the effects produced by transverse impact of spherical steel projectiles on circular elastic tubes either empty or else containing stationary or flowing fluids. Similar tests were also executed on acrylic (PMMA) tubes that exhibit viscoelastic behavior. Transients were generated by pneumatically propelled 12.7 mm (1/2 in.) and 4.8 mm (3/16 in.) diameter projectiles striking the midpoint of two types of 3 m long 2024-T3 aluminum tubes with an outer diameter of 25.4 mm and wall thicknesses of 2.41 and 1.25 mm, respectively, and PMMA tubes with outer diameters of 34.93 and 31.75 mm and wall thicknesses of 3.17 and 1.58 mm, respectively. The targets were ballistically suspended by means of strings, and filled either with distilled water or a high-density capacitor fluid, Fluorinert. Most of the tests were performed with stationary liquids when the tube ends were stoppered; in some of the experiments, laminar flow in the hollow cylinders was produced by means of a blood pump. The initial and final projectile velocities were measured by means of a set of two multiple coils wound around an acrylic tube through which the striker passed; the impact force was determined from a sandwiched quartz crystal arrangement placed ahead of the contact point on the targets. Axial and hoop strain histories were ascertained by means of foil strain gages mounted at two stations on the outer hollow cylinder surface. Antisymmetric strain records were compared with the predictions of a modified Timoshenko-beam model; good agreement was noted between these results, particularly for the case of thick-walled tubes.
Stability Analysis of an Extrapolated Force Correction Method for Nonlinear Structural Dynamics
Authors: Trujillo D. M.
Published: July 2009

In this paper, conditions for the unconditional stability of an extrapolated force correction method have been identified. The analysis assumed a nonlinear elastodynamic system for which energy is conserved. Some numerical examples are included to demonstrate the performance of the method.
A Generalized Hill’s Method for the Stability Analysis of Parametrically Excited Dynamic Systems
Authors: Noah S. T. , Hopkins G. R.
Published: July 2009

A method is described for investigating the stability of the null solution for a general system of linear second-order differential equations with periodic coefficients. The method is based on a generalization of Hill’s analysis and leads to a generalized Hill’s infinite determinant. Following a proof of its absolute convergence, a closed-form expression for the characteristic infinite determinant is obtained. Methods for the stability analysis utilizing different forms of the characteristic determinant are discussed. For cases where the instabilities are of the simple parametric type, a truncated form of the determinant may be used directly to locate the boundaries of the resonance regions in terms of appropriate system parameters. The present generalized Hill’s method is applied to a multidegree-of-freedom discretized system describing pipes conveying pulsating fluid. It is demonstrated that the method is a flexible and efficient computational tool for the stability analysis of general periodic systems.
Laminar Flow Along a Porous Vertical Wall
Authors: Verma P. D. , Sarangi K. C. , Ariel P. D.
Published: July 2009

The behavior of boundary layer thickness, film thickness is investigated for steady laminar flow along a porous vertical wall. Using a sixth-degree velocity profile the resulting equation from the Von Karman integral equation has been integrated numerically. The boundary layer thickness, film thickness are shown graphically for different values of suction parameter λ1 = v0h0/ν and a dimensionless parameter φ=3νu0gh021/2.
Antiplane Eigenstrain Problem of an Elliptic Inclusion in an Anisotropic Half Space
Authors: Masumura R. A. , Chou Y. T.
Published: July 2009

The antiplane eigenstrain problem of an elliptic inclusion in an anisotropic semi-infinite medium is investigated. Expressions for the stresses and elastic energy have been developed using the line force concept and superposition of the image field. It is shown that in the presence of a free surface the stresses inside the inclusion are not constant. In addition, the elastic energy of the system is reduced as the inclusion approaches the free surface.
Unconventional Internal Cracks, Part 1: Symmetric Variations of a Straight Crack
Authors: Wu C. H.
Published: July 2009

The composite mapping function of successive mappings by rational functions is rational but may have poles at more than one location. This method may be exploited to generate many, many new but unconventional cracks for which the associated elasticity problems may be solved exactly. Two families of cracks are examined in detail in this paper. A few more cases will be reported in a follow-up paper.
The Linear Magnetoelastic Problem of Two Coplanar Griffith Cracks in a Soft Ferromagnetic Elastic Strip
Authors: Shindo Y.
Published: July 2009

Following a linear theory for soft ferromagnetic elastic solids, we consider the problem of determining the stress-intensity factors in an infinite strip of a soft ferromagnetic elastic material containing two coplanar Griffith cracks. We assume that the solid is a homogeneous and isotropic one and it is permeated by a uniform magnetostatic field normal to the cracks surfaces and that the cracks are opened by a constant internal pressure. By the use of Fourier transforms we reduce the problem to that of solving two simultaneous triple integral equations. These equations are reduced to a singular integral equation of the first kind. By expanding the solution into the form of the product of the series of Chebyshev polynomials of the first kind and their weight function, the singular integral equation is further reduced to the infinite system of algebraic equations for the determination of the unknown coefficients. Numerical calculations are carried out and the influence of the magnetic fields on the stress-intensity factors is graphically shown in detail.
Use of Jˆ-Integral in Dynamic Analysis of Cracked Linear Viscoelastic Solids by Finite-Element Method
Authors: Kishimoto K. , Aoki S. , Sakata M.
Published: July 2009

A computational method using the path (area)-independent Jˆ-integral is developed to analyze viscoelastic problems. Since the displacement field near the crack tip of a viscoelastic solid is dependent upon the complete past history of the dynamic stress-intensity factors, the Jˆ-integral is represented by a hereditary integral of the dynamic stress-intensity factors. We assume that the stress and strain rates vary in proportion to time during each increment of time and derive a formula to obtain the current value of the dynamic stress-intensity factor from the time increment of the Jˆ-value. Both pure and mixed mode problems of a suddenly loaded crack are analyzed by making use of the formula together with the conventional finite-element method. In order to demonstrate the capability and reliability of the present method, problems of a center crack and an oblique crack in viscoelastic rectangular plates are solved.
Application of the Line-Spring Model to a Cylindrical Shell Containing a Circumferential or Axial Part-Through Crack
Authors: Delale F. , Erdogan F.
Published: July 2009

In this paper the line-spring model developed by Rice and Levy is used to obtain an approximate solution for a cylindrical shell containing a part-through surface crack. It is assumed that the shell contains a circumferential or axial semi-elliptic internal or external surface crack and is subjected to a uniform membrane loading or a uniform bending moment away from the crack region. To formulate the shell problem, a Reissner type theory is used to account for the effects of the transverse shear deformations. The stress intensity factor at the deepest penetration point of the crack is tabulated for bending and membrane loading by varying three-dimensionless length parameters of the problem formed from the shell radius, the shell thickness, the crack length, and the crack depth. The upper bounds of the stress intensity factors are provided by the results of the elasticity solution obtained from the axisymmetric crack problem for the circumferential crack, and that were found from the plane strain problem for a circular ring having a radial crack for the axial crack. Qualitatively the line-spring model gives the expected results in comparison with the elasticity solutions. The results also compare well with the existing finite element solution of the pressurized cylinder containing an internal semi-elliptic surface crack.
Torque on Eccentric Spheres Flowing in Tubes
Authors: To¨zeren H.
Published: July 2009

The steady flow of an eccentric sphere in a circular cylindrical tube filled with viscous fluid is considered as a regular perturbation of the axisymmetric problem. A sequence of boundary value problems are formulated involving Stokes equations and some linear boundary conditions. Solution of the first-order problem yields the leading term in the perturbation series of the torque on the sphere.
Bounds on the Transverse Effective Conductivity of Computer-Generated Fiber Composites
Authors: McCoy J. J.
Published: July 2009

Using trial functions that are motivated by single-body calculations, we have derived bounds on the effective transverse thermal conductivity of a fiber composite. These bounds incorporate both fiber area fraction information and some information of the configurational statistics. Simplified expressions for the bounds are obtained for the limits of widely differing conductivity values for the constitutent phases, and of a dilute suspension. The bounds are made specific for a given computer-generated fiber composite and these specific bounds are compared with the best available bounds that require area fraction information alone. The conclusions reached are that configuration statistics are significant for effective property calculations for moderately dense composites for component conductivity values that differ by some one to two orders of magnitude, or greater. Further, the bounds based on the single-body calculation are reasonably close for component conductivity values that differ by some two orders of magnitude, or less.
Disturbance at a Frictional Interface Caused by a Plane Elastic Pulse
Authors: Comninou Maria , Barber J. R. , Dundurs John
Published: July 2009

We consider a plane pulse striking the frictional interface between two elastic solids which are held together by compressive applied tractions and sheared. The pulse causes a disturbance involving separation or slip between the bodies, which propagates along the interface at supersonic speed. The extent of these zones is determined using a convenient graphical representation and the interface tractions are given in closed form. It is found that the results change qualitatively when the coefficient of friction exceeds a critical value.
A Further Examination on the Application of the Strain Energy Density Theory to the Angled Crack Problem
Authors: Chang K. J.
Published: July 2009

The strain energy density theory (the S-theory) has been examined. Two points that may lead to confusion have been discussed when the S-theory is employed in the study of the angled crack problem. Predictions for the biaxial tension configuration based on the S-theory compared with one based on the maximum strain criterion are presented. Use of the ratio of core region radius as a material parameter in the S-theory is also questioned.
Stability of Nonparallel Developing Flow in an Annulus to Asymmetric Disturbances
Authors: Garg V. K.
Published: July 2009

Linear spatial stability of the nonparallel developing flow in a concentric annulus shows that the asymmetric disturbance with an azimuthal wave number equal to unity is more unstable than the axisymmetric disturbance at all axial locations. Also, in the near entry region, the critical Reynolds number corresponding to the parallel flow theory is as much as three times that due to the nonparallel theory for some values of the annular diameter ratio.
Transient Response of a Fluid-Saturated Poroelastic Layer Subjected to a Sudden Fluid Pressure Rise
Authors: Kurashige M.
Published: July 2009

The transient response of a fluid-saturated poroelastic layer resting on a very porous rigid foundation and subjected to a sudden fluid pressure rise on its upper surface is analyzed on the basis of Biot’s theory of poroelasticity. Compaction of the layer and fluid outflux from its bottom surface are calculated for five typical poroelastic materials: alundum and Ohio sandstone saturated with water, compact bone, and Albany felt and polyurethane foam filled with silicone fluid. For each of these materials, the numerical results are compared with those estimated by the “incompressible model” as well as the “rigid skeleton model” in order to examine the validity of these models.
Effective Longitudinal Young’s Modulus of Misoriented Short Fiber Composites
Authors: Takao Y. , Chou T. W. , Taya M.
Published: July 2009

This paper examines the effective longitudinal Young’s modulus of composites containing misoriented short fibers. The analysis is based on the Eshelby’s equivalent inclusion method and the average induced strain approach of Taya, Mura, and Chou. The present approach is unique in that it takes into account the interactions among fibers at different orientations. Numerical results are presented to demonstrate the effects of fiber elastic property, aspect ratio, volume fraction, and orientation distribution function on composite Young’s modulus. Fiber orientation distribution has a more significant effect on composite longitudinal Young’s modulus than fiber volume friction, within the range examined.