bluuebunny/crossref_metadata_2025 huggingface dataset:
Flow Due to Eccentric Rotating a Porous Disk and a Fluid at Infinity
Authors: Erdogan M. Emin
Published: November 2010

An exact solution of the steady three-dimensional Navier-Stokes equations is obtained for the case of flow due to noncoaxially rotations of a porous disk and a fluid at infinity. It is shown that for uniform suction or uniform blowing at the disk an asymptotic profile exists for the velocity distribution.
Small Bubble Motion in an Accelerating Liquid
Authors: Morrison F. A. , Stewart M. B.
Published: November 2010

Low Reynolds number bubble motion in accelerating liquids is analyzed. Because of motion of the bubble surface, the flow about a bubble differs from the flow surrounding a rigid particle. A governing relation, equivalent to the Basset-Boussinesq-Oseen equation for rigid particle motion, is developed. Response characteristics of the bubble are presented. Bubble behavior is found to differ significantly from rigid particle behavior.
The Stability of a Spinning Elastic Disk With a Transverse Load System
Authors: Iwan W. D. , Moeller T. L.
Published: November 2010

This paper presents results of an investigation on the effect of a transverse load on the stability of a spinning elastic disk. The disk rotates at constant angular velocity and the load consists of a mass distributed over a small area of the disk, a spring, and a dashpot. The equation of motion for the transverse vibration of the disk is written as a system of linear ordinary differential equations with constant coefficients. The analysis indicates that the disk system is unstable for speeds in a region above the critical speeds of vibration of the spinning disk due to the effects of load stiffness. The mass and damping of the load system cause a terminal instability and other instabilities occur as a result of modal interaction.
The Dynamics of Discus Throw
Authors: Soong T.-C.
Published: November 2010

The analysis contains the derivation and a solution method for six nonlinear differential equations of motion which describe the c.g. position and orientations of the principal axes of a spinning discus moving in air. The aerodynamic pressure on the discus is obtained from existing experimental data on inclined plates and disk-shaped bodies; the effect on the moment due to the spinning motion is derived from the classical hydrodynamics of a rotating ellipsoid in a flow field. A case study, analyzed in the context of the 1972 World Olympics discus throw (which recorded 64.39 m or 211 ft 3 in.), showed that a fast-spinning discus will go farther than one not spinning by 13.8 m in this range. The optimum angle and optimum initial discus inclination are 35° and 26°. This combination of angles is found to be superior to the commonly accepted combination of 35° and 35°. The 35°/26° combination produced a gain in distance of 1.55 m over the 35° /35° combination. The results of the analyses presented here, including the effect of wind, agree closely with the experience of expert discus throwers.
Transient Boundary Layers Between Porous Plates
Authors: Fiveland W. A. , Lu P.-C.
Published: November 2010

Analysis is made of a transient, fully developed, laminar flow of an incompressible fluid in a porous, parallel-plate channel. The crossflow through the plates is uniform, but is allowed to vary with time. In addition to a pressure gradient due to pumping, the flow is also under the inducement of the motion of one of the plates. Numerical results are obtained through the (final or nonfinal) use of the finite Fourier sine transform. Asymptotic flow patterns showing transient boundary layers are investigated. Finally, the formation of the flow from the start is described in physical terms.
Saint-Venant’s Principle and the Torsion of Thin Shells of Revolution
Authors: Horgan C. O. , Wheeler L. T.
Published: November 2010

This paper is concerned with obtaining stress estimates for the problem of axisymmetric torsion of thin elastic shells of revolution subject to self-equilibrated end loads. The results are obtained in the form of explicit pointwise stress bounds exhibiting an exponential decay with distance from the ends, thus supplying a quantitative characterization of Saint-Venant’s principle for this problem. In contrast to arguments using energy inequalities, here we apply a technique, recently developed by the authors, based on the maximum principle for second-order uniformly elliptic equations.
Axial Impact of Twisted Wire Cables
Authors: Phillips J. W. , Costello G. A.
Published: November 2010

The nonlinear, coupled equations of motion governing the axial and rotational displacements of a straight, single lay, twisted wire cable are presented. Linearization of the equations of motion allows a solution by Laplace transforms which is valid for arbitrary initial and boundary conditions. The longitudinal impact of a finite-length cable fixed at one end is considered in detail, and numerical results for this case are presented.
Flutter of Articulated Pipes at Finite Amplitude
Authors: Rousselet J. , Herrmann G.
Published: November 2010

The plane motion of an articulated pipe made of two segments is examined and the flow velocity at which flutter manifests itself is sought. The pressure in the reservoir feeding the pipe is kept constant. In contrast to previous works, the flow velocity is not taken as a prescribed parameter of the system but is left to follow the laws of motion. This approach requires a nonlinear formulation of the problem and the equations of motion are solved using Krylov-Bogoliubov’s method. A graph of the amplitude of the limit cycles, as a function of the fluid-system mass ratio, is presented and conclusions are drawn as to the necessity of considering nonlinearities in the analysis.
Critical Velocity for Collapse of Viscoplastic Cylindrical Shells Without Buckling
Authors: Florence A. L. , Abrahamson G. R.
Published: November 2010

Successful operation of many practical devices that involve high-speed implosion of shells of circular cross section requires a stable collapse motion. In this paper, the dynamic buckling of imploding viscoplastic cylindrical shells is analyzed, and critical velocities are determined for which amplification factors of initial departures from circularity are 10, 100, and 1000.
On Wake-Induced Flutter of a Circular Cylinder in the Wake of Another
Authors: Tsui Y. T.
Published: November 2010

Two-dimensional stability of leaward cylinder in the wake of fixed windward cylinder is studied within the framework of quasi-static aerodynamic theory at both subcritical and supercritical flow region. Routh-Hurwitz stability criterion is employed. Two important points are clarified: 1. The wake-induced flutter is symmetric with respect to the horizontal line if there is no xy (refer to Fig. 1) static coupling. When coupled, the wake symmetry preserves provided the sign of static coupling is changed. This finding is supported by recent experimental data [7] and is in contrary with previous results [4–6]. 2. For the uncoupled case, vertical and horizontal frequency coalescence does not necessarily imply no oscillation. This is in variance with previous studies [2, 3, 34]. The region of instability is related to four physical variables: vertical to horizontal natural frequency ratio κ = ωy/ωx = (Kyy/Kxx)1/2, static coupling coefficient ε = Kxy/Kxx, cylinder spacing to diameter ratio d/c and flow characteristics. Some highlights of numerical results [1] are as follows: (a) The region of instability roughly lies between 0 < |ε| < 0.1 and 0.8 ≤ κ ≤ 1.2. (b) The region of instability enlarges as |ε| increases from zero to 0.8 when everything else is kept fixed. (c) For both subcritical and supercritical flow, the region of instability shrinks as d/c varies from 10–16 when keeping all other factors fixed. (d) The region of instability shrinks as the flow changes from subcritical to supercritical when everything else remains unchanged.
The Problem of Internal and Edge Cracks in an Orthotropic Strip
Authors: Delale F. , Erdogan F.
Published: November 2010

The plane elastostatic problem of internal and edge cracks in an infinite orthotropic strip is considered. The problems for the material types I and II are formulated in terms of singular integral equations. For the symmetric case the stress-intensity factors are calculated and are compared with the isotropic results. The results show that because of the dependence of the Fredholm kernels on the elastic constants in the strip (unlike the crack problem for an infinite plane) the stress-intensity factors are dependent on the elastic constants and are generally different from the corresponding isotropic results.
Transient Response of Three-Layered Rings
Authors: Sagartz M. J.
Published: November 2010

Hamilton’s principle is used to derive equations of motion for a linear elastic three-layered ring. The theory includes the effects of shear deformation and rotatory inertia in each layer and radial strain effects in the middle layer. A convenient computational technique is developed for transient response evaluation. A companion experimental study was conducted using two different rings. Both rings had aluminum inner and outer layers, but each had a different low-modulus middle layer. Radial impulse loads distributed as a cosine over half the ring circumference, were applied to the outer ring surface, and the transient response was monitored with strain gages mounted on the aluminum layers. Measured strain-time histories were compared with theoretical calculations, and good agreement was obtained.
Experimental Investigations of Steady and Pulsatile Laminar Flow in a 90° Branch
Authors: Mark F. F. , Bargeron C. B. , Deters O. J. , Friedman M. H.
Published: November 2010

Velocity measurements are reported for steady and unsteady flow in a rectangular cross-section Y-branch of high aspect ratio. Good agreement is found between the experimental results and two-dimensional calculations. Emphasis is placed on flow velocities near and parallel to the outer wall inasmuch as their gradients are proportional to wall shearing stress which may be of influence in atherogenesis. Large variation in flow velocities and hence shearing stress are found in the immediate vicinity of the corner. The results in this region could support theories which propose either high or low shearing stress as an important consideration in the etiology of arteriosclerosis.
Saint-Venant’s Principle and End Effects in Anisotropic Elasticity
Authors: Choi I. , Horgan C. O.
Published: November 2010

The purpose of this paper is to draw attention to the fact that the routine application of Saint-Venant’s principle in the solution of elasticity problems involving highly anisotropic or composite materials is not justified in general. This is illustrated in the context of the plane problem of elasticity for an anisotropic rectangular strip loaded only on the short ends. For highly anisotropic transversely isotropic materials, the slow decay of end effects is demonstrated using a method involving self-equilibrating eigenfunctions. For a graphite/epoxy composite, for example, the characteristic decay length is shown to be approximately four times that for an isotropic material. The results have implications in the accurate measurement of mechanical properties of anisotropic materials.
Antiplane Strain Problems of an Elliptic Inclusion in an Anisotropic Medium
Authors: Yang H. C. , Chou Y. T.
Published: November 2010

The antiplane strain problem of an elliptic inclusion in an anisotropic medium with one plane of symmetry is solved. Explicit expressions of compact form are obtained for the elastic field inside the inclusion, the stress at the boundary, and the strain energy of the system. The perturbation of an otherwise uniform stress field due to an elliptic inhomogeneity is studied, and explicit solutions are given for the extreme cases of an elliptic cavity and a rigid elliptic inhomogeneity. It is found that both the stress magnification at the edge of the inhomogeneity and the increase of strain energy depend only on the component P23A of the applied stress for an elongated cavity; and depend only on the component E13A of the applied strain for a rigid line inhomogeneity.
A Parabolic Theory of Stress Wave Propagation Through Inhomogeneous Linearly Elastic Solids
Authors: McCoy J. J.
Published: November 2010

A theory, in the form of a coupled system of reduced parabolic wave equations (equations (42)), is developed for stress wave propagation studies through inhomogeneous, locally isotropic, linearly elastic solids. A parabolic wave theory differs from a complete wave theory in allowing propagation only in directions of increasing range. Thus, when applicable, it is well suited for numerical computation using a range-incrementing procedure. The parabolic theory considered here requires the propagation directions to be limited to a cone, centered about a principal propagation direction, which might be described as narrow-angled. Further, the theory requires that the effects of diffraction, refraction, and energy transfer between the dilatational and distortional modes are gradual enough that coupling between them can be ignored over a range of several wavelengths. Precise conditions for the applicability of the theory are summarized in a series of inequalities (equations (44)).
Transient Response of a Shear Beam to Correlated Random Boundary Excitation
Authors: Masri S. F. , Udwadia F.
Published: November 2010

The transient mean-square displacement, slope, and relative motion of a viscously damped shear beam subjected to correlated random boundary excitation is presented. The effects of various system parameters including the spectral characteristics of the excitation, the delay time between the beam support motion, and the beam damping have been investigated. Marked amplifications in the mean-square response are shown to occur for certain dimensionless time delays.
The Interface Crack
Authors: Comninou Maria
Published: November 2010

It is known that oscillatory singularities appear in problems involving interface cracks that are assumed to have open tips. An unsatisfactory aspect of the oscillatory singularities is that they lead to overlapping of the crack faces. The interface crack in a tension field, originally treated by England among others, is thus reconsidered on the basis that the crack is not completely open and that its faces are in frictionless contact near the tips. The formulation leads to a pair of coupled singular integral equations. The singularities, no longer oscillatory, exhibit some unusual features and indicate that the spreading of the interface crack in a tension field is intimately connected with failure in shear. A new stress-intensity factor is obtained and compared to the stress-intensity factors for the completely open crack.
An Approximate Method of Analysis of the Transmission of Elastic Waves Through a Frictional Boundary
Authors: Miller R. K.
Published: November 2010

An approximate analytical method is presented for determining the transmission and reflection of elastic waves at a frictional boundary. The method is applied to the case of plane harmonic shear waves normally incident on a Coulomb friction boundary between semi-infinite elastic media. The accuracy of the method is determined by comparison of approximate and exact solutions in a numerical example.
A High-Order Theory of Plate Deformation—Part 2: Laminated Plates
Authors: Lo K. H. , Christensen R. M. , Wu E. M.
Published: November 2010

The high-order theory of plate deformation developed in Part 1 of this work is extended here to model the behavior of laminated plates. Through comparison with elasticity solutions, it is shown the present theory correctly models effects not attainable from the classical theory.
Nonlinear Behavior of Flutter Unstable Dynamical Systems With Gyroscopic and Circulatory Forces
Authors: Sethna P. R. , Schapiro S. M.
Published: November 2010

Postflutter behavior of nonlinear discrete dynamical systems having a combination of gyroscopic and circulatory forces are studied. The study leads to Hopf bifurcations. The method of analysis is based on the method of Hopf and the method of integral manifolds. The results of the analysis are applied to an example and the accuracy of the analysis is checked against numerical solutions of the equations of motion.
Cumulative Fatigue by Fracture Mechanics
Authors: Hobbacher A.
Published: November 2010

Cumulative fatigue properties can be explained by the propagation of a preexisting crack. The power law of crack propagation is made dimensionless in order to execute crack propagation calculations without the knowledge of fracture mechanics parameters of the microcrack. The relative parameters are easily derived from constant amplitude test S-N curves.
Experiments on Strain Rate History and Temperature Effects During the Plastic Deformation of Close-Packed Metals
Authors: Senseny P. E. , Duffy J. , Hawley R. H.
Published: November 2010

A study is presented on the influence of strain rate and strain rate history on the flow stress of several metals. Experiments were performed on specimens of four polycrystalline metals: 1100-0 aluminum, OFHC copper, AZ31 B magnesium, and commercially pure zinc. The experiments involve, the use of a modified Kolsky bar to increase abruptly the imposed strain rate, initially 2 × 10−4 s−1, by a factor of more than 106. Tests were performed at selected temperatures in the range T ≤ (1/2)Tm. The results include complete stress-strain curves for deformation at constant strain rates as well as for deformation involving a sharp increment in strain rate. The difference in flow stress at a given value of strain for stress-strain curves obtained at constant but different strain rates provides one measure of the influence of strain rate on the flow stress. However, the results of the incremental strain rate experiments show that both strain rate and strain rate history contribute to this difference in flow stress. Hence, interpretation of both the incremental and the constant strain rate tests offers a means for distinguishing between the effects of strain rate as opposed to those of differences in strain rate history.
Magnetoelastic Interaction of a Soft Ferromagnetic Elastic Solid With a Penny-Shaped Crack in a Constant Axial Magnetic Field
Authors: Shindo Y.
Published: November 2010

The fundamental equations for soft ferromagnetic elastic materials of multidomain structure are derived in cylindrical coordinates. The basic theory used is one of Pao and Yeh [3] and the soft ferromagnetic elastic solids are considered to be composed of materials with isotropic, cubic or uniaxial symmetry. Using the fundamental equations, the axisymmetric problem for an infinite body with a penny-shaped crack in a constant axial magnetic field is investigated. A solution for the infinite solid is obtained by the method of two simultaneous dual integral equations. The magnetoelastic stresses and the Maxwell stresses are expressed in closed forms. By referring to a set of polar coordinates r1 and θ1 measured from the crack periphery, the dependence of the local stresses on r1 and θ1 is also determined in closed elementary form. As in the classical case, the stresses possess the familiar inverse square-root singularity at the crack boundary. The stress-intensity factor, however, is found to depend on the magnetic field. When the magnetic field reaches a critical value, the surface of a crack is unstable. The effect of magnetic fields on the stresses and the stress-intensity factor, and a comparison of the plane strain and axisymmetric solutions are shown graphically.
Finite-Element Methods for Nonlinear Elastodynamics Which Conserve Energy
Authors: Hughes T. J. R. , Caughey T. K. , Liu W. K.
Published: November 2010

A modification of the trapezoidal rule is presented which results in physically appropriate energy growth characteristics for nonlinear transient analysis. In particular, when external forces are absent, energy conservation is attained for nonlinear elastodynamics and unconditional stability is thereby automatically achieved. Implementation aspects and numerical examples in support of the theory are described.
Nonlinear Flexural Vibration of an Elastic Ring
Authors: Maewal A.
Published: November 2010

Nonlinear free vibration of a thin, elastic, circular ring is analyzed using an asymptotic technique and results are compared with previous solutions obtained through the Galerkin method.
Fluid Dynamics of the Elliptic Porous Slider
Authors: Watson L. T. , Li T. Y. , Wang C. Y.
Published: November 2010

Fluid cushioned porous sliders are useful in reducing the frictional resistance of moving objects. This paper studies the elliptic slider. After a transformation of variables, the Navier-Stokes equations reduce to a nonlinear two-point boundary-value problem. This boundary-value problem was solved by a homotopy-type method, which did not require a good initial approximation to the solution. The problem was solved for several Reynolds numbers and ellipse eccentricities. Lift and drag calculations show that an elliptic porous slider should be operated along the minor axis.
The Second Law of Thermodynamics and Cyclic Processes
Authors: Green A. E. , Naghdi P. M.
Published: November 2010

This paper is concerned with the implications of a modified form of an inequality proposed recently by Green and Naghdi [3] in regard to the classical statements of the second law of thermodynamics associated with cyclic thermomechanical processes. The results obtained are compared with corresponding previous studies by Fosdick and Serrin [1] and by Truesdell [2] who employ the Clausius-Duhem inequality. Our development also employs an alternative definition to that used in [1, 2] for the quantity of heat absorbed or emitted by a body.
Buckling of Short Cylinders Under Combined Loading
Authors: Tennyson R. C. , Booton M. , Chan K. H.
Published: November 2010

This report presents theoretical and experimental data on the buckling of short, homogeneous, isotropic circular cylinders subjected to simultaneous loading of axial compression and hydrostatic pressure. Of major significance is the drastic change from “concave” to “convex” interactive behavior as the Z parameter is decreased. This phenomenon is demonstrated for both clamped and simply supported boundary conditions.
A General Mode Approach to Nonlinear Flexural Vibrations of Laminated Rectangular Plates
Authors: Chia C. Y. , Prabhakara M. K.
Published: November 2010

This paper is concerned with an analytical investigation of free flexural large-amplitude vibrations of rectangular composite plates. Solutions of the dynamic von Karman-type equations of these plates in conjunction with different boundary conditions are obtained by use of generalized double Fourier series and the method of harmonic balance. Numerical calculations for multimode vibrations of unsymmetric cross-ply and angle-ply plates having various material properties and lamination geometry were performed for all-clamped and all-simply supported stress-free edges. The present results indicate that the effect of coupling of vibrating modes on nonlinear frequencies is not appreciably significant for isotropic plates but considerably significant for composite plates, especially for clamped high-modulus laminates.
Numerical Analysis of Time-Dependent Inelastic Deformation in Metallic Media Using the Boundary-Integral Equation Method
Authors: Mukherjee S. , Kumar V.
Published: November 2010

A numerical analysis procedure using the boundary-integral equation method is presented for the solution of problems of time-dependent inelastic deformation in planar metallic bodies. The formulation allows the use of both classical creep theories as well as newer theories of inelastic deformation using state variables. Numerical results are presented for plane stress problems using either the power law equations of creep or the state variable theory due to Hart. Comparison of BIE and analytical methods for simple problems shows good agreement. Other features of the numerical solutions of more complicated problems are discussed in the paper.
Resonant Excitation of a Spinning, Nutating Plate
Authors: Klahs J. W. , Ginsberg J. H.
Published: November 2010

The equations of motion governing the three-dimensional finite-amplitude response of a plate in arbitrary space motion are derived and shown to lead to dynamic coupling between the transverse and in-plane displacement. A general method of solution for such problems is demonstrated in an example involving a simply supported rectangular plate spinning about an axis parallel to an edge and nutating through a small angle. The method involves an asymptotic expansion using the derivative expansion version of the method of multiple time scales, in conjunction with the Galerkin method. A critical spin rate leading to the loss of stability in divergence is determined. Then, a numerical example of resonant excitation of one principal coordinate demonstrates that the nonlinear response resembling the one obtained from linear theory may lose stability in favor of a second response in which several principal coordinates are mutually excited. Consideration of the interaction between in-plane and transverse displacements is shown to be crucial to the prediction of this “unusual” response.
Amplitude Modulation of a Forced System by Parameter Variation
Authors: Eisinger K. , Merchant H. C.
Published: November 2010

Classical (primary) parametric amplification is reviewed. This phenomenon is known to occur for a parametric variation with a frequency of twice that of a harmonic input in the neighborhood of a system’s characteristic frequency. A higher-order phenomenon that is identified as secondary parametric amplification (or attenuation), is discussed in detail and solutions related to Mathieu’s equation are presented. Its occurrence is characterized by a frequency of the parametric variation that is of the order of 2α/n (where n = 1, 2, 3, …, and α is the undamped characteristic frequency of the system) and a harmonic input of a much lower frequency. The amplification (or attenuation) resulting from the secondary parametric amplification phenomenon is manifested in an overmodulated response that must be low-pass filtered to recover the desired low frequency response.
Inviscid Solution for the Problem of Free Overfall
Authors: Chow W. L. , Han T.
Published: November 2010

The flow problem of free overfall has been examined through hodograph transformations. It has been found that even with strong influence of the gravitational field, the stream function can be solved in the hodograph plane through numerical calculations. The velocity functions of the two free streamlines must be determined through iterations and it has been found that this iterative process is rapidly convergent. Favorable agreement of the results with the experimental data substantiates the fact that this method is effective in dealing with flow problems strongly influenced by gravitation. Comparison of results of calculations with analytical results by Clarke for the case of supercritical approach flow is also presented.
Transient Interaction of a Circular Plate and a Fluid Medium
Authors: Berglund J. W.
Published: November 2010

The transient dynamic response of an elastic circular plate subjected to a suddenly applied pressure is determined for several edge boundary conditions. The plate boundary is attached to a semi-infinite, radially rigid tube which is filled with an acoustic fluid, and pressure is applied to the in-vacuo side of the plate. The transient solution is determined by using a technique in which the plate is subjected to a periodic pressure function constructed of appropriately signed and time-shifted Heaviside step functions, and by relying on a physical mechanism which returns the plate and fluid near the plate to an unstrained state of rest between pulses. The plate response is presented for a number of radius-to-thickness ratios and edge boundary conditions when interacting with water. Comparisons are also made with solutions obtained using a plane wave approximation to the fluid field.
Approximate Methods for Calculating Heated Water Laminar Boundary-Layer Properties
Authors: Harpole G. M. , Berger S. A. , Aroesty J.
Published: November 2010

The integral method of Thwaites, for computing the primary parameters of laminar boundary layers with constant fluid properties, is extended to heated boundary layers in water, taking into account variable fluid properties. Universal parameters are correlated from numerical solutions of heated water wedge flows for use with the integral method. The method shows good accuracy in a test with the Howarth retarded flow. The Lighthill high Prandtl number approximation is extended to permit computation of the Nusselt number for boundary layers with variable fluid properties. Nusselt numbers computed for the Howarth flow are close to the exact numerical solutions, except near separation.
Vortex-Induced Oscillations: A Selective Review
Authors: Sarpkaya T.
Published: November 2010

This paper reviews the vortex-induced oscillations in a few specific fundamental cases. Research topics discussed are vortex shedding from a stationary bluff body; consequences of the synchronization phenomenon; wake-oscillator models; added mass, damping, and dynamic response measurements; flow-field models and the discrete-vortex method; mechanism of synchronization; and, finally, in-line oscillations. Because of the selective nature of the review, a fairly comprehensive listing of recent contributions to the literature on these and related aspects of flow-induced oscillations research is an essential part of the exposition.
Some Observations on the Yoshimura Buckle Pattern for Thin-Walled Cylinders
Authors: Foster C. G.
Published: November 2010

A great deal of the behavior of thin-walled cylindrical shells loaded in axial compression can be explained by considering the Yoshimura buckle pattern as a three-dimensional space frame and observing the collapse of that space frame.
Limit Point Buckling Loads of Axially Compressed, Circular Cylindrical Shells—The Effect of Nonlinear Material Behavior
Authors: Nimmer R. P. , Mayers J.
Published: November 2010

The elasto-plastic buckling and postbuckling of imperfect, thin, circular cylindrical shells in axial compression is studied with the use of a mechanism model specifically designed to achieve an accurate representation of the developable polyhedral surface of Yoshimura. The formulation makes it possible to study the influence of asymmetric imperfection patterns of significantly larger amplitudes than previously treated. Elasto-plastic effects are included using a deformation theory of plasticity and Reissner’s variational principle. Material-sensitive load-shortening curves are obtained exhibiting initial-maximum values for the average axial stresses of imperfect shells that tend toward vanishingly small magnitudes with increasing radius-to-thickness ratio and attendant imperfections.
Buckling of a Stochastically Imperfect Finite Column on a Nonlinear Elastic Foundation: A Reliability Study
Authors: Elishakoff Isaac
Published: November 2010

The paper is concerned with the problem of buckling of finite columns with initial imperfections, resting on a “softening” nonlinear elastic foundation. The approach is probabilistic. The initial imperfections are assumed to be Gaussian random fields with given mean and autocorrelation functions, and the problem is solved by the Monte Carlo Method. For each realization of the initial imperfection function, the buckling load was found through transformation of the two-point nonlinear boundary-value problem into an initial-value problem and results were used in constructing the empirical reliability function at the specified load (relative number of columns with buckling loads exceeding this specified load). Numerous results are presented with regard to the influence of the parameters of the columns on their imperfection sensitivity.
A Nonparametric Identification Technique for Nonlinear Dynamic Problems
Authors: Masri S. F. , Caughey T. K.
Published: November 2010

A nonparametric identification technique is presented that uses information about the state variables of nonlinear systems to express the system characteristics in terms of orthogonal functions. The method can be used with deterministic or random excitation (stationary or otherwise) to identify dynamic systems with arbitrary nonlinearities, including those with hysteretic characteristics. The method is shown to be more efficient than the Weiner-kernel approach in identifying nonlinear dynamic systems of the type considered.
The Pressure Ratio in the Theory of Bin Pressures
Authors: Cowin S. C.
Published: November 2010

The pressure ratio K0 is assumed to be a constant in the theory developed by Janssen for determining the pressures imparted by a granular material to its container. Recently it was shown that K0 can be defined less restrictively as the ratio of the perimeter average of the horizontal stress acting on the vertical wall of the container to the cross-sectional average of the vertical stress in the granular material at the same depth in the container. Three results concerning K0 are presented in this paper. First, it is shown that the essential result of Janssen, namely that the vertical and horizontal stresses have a constant bound at great depths, also holds in the case when the bulk density and the pressure, ratio are bounded by linear functions of the average vertical stress. Second, it is shown that a formula relating K0 to the Poisson’s ratio of the granular material is not correct, in general. Third, bounds on K0 are obtained using the Mohr-Coulomb yield condition for the granular material.
Analysis of Properties of Fiber Composites With Anisotropic Constituents
Authors: Hashin Z.
Published: November 2010

Expressions and bounds for the five effective elastic moduli of a unidirectional fiber composite, consisting of transversely isotropic fibers and matrix, are derived on the basis of analogies between isotropic and transversely isotropic elasticity equations. Application of results for determination of the five elastic moduli of graphite fibers is discussed. Effective thermal expansion coefficients are derived on the basis of a general theorem. Effective conductivities, dielectric constants, and magnetic permeabilities are derived by use of certain mathematical analogies.
Green’s Functions for Two-Phase Transversely Isotropic Materials
Authors: Pan Y.-C. , Chou T.-W.
Published: November 2010

Closed-form solutions are obtained for the Green’s function problems of point forces applied in the interior of a two-phase material consisting of two semi-infinite transversely isotropic elastic media bonded along a plane interface. The interface is parallel to the plane of isotropy of both media. The solutions are applicable to all combinations of elastic constants. The present solution reduces to Sueklo’s expression when the point force is normal to the plane of isotropy and (C11C33)1/2 ≠ C13 + 2C44 for both phases. When the elastic constants of one of the phases are set to zero, the solution can be reduced to the Green’s function for semi-infinite media obtained by Michell, Lekhnitzki, Hu, Shield, and Pan and Chou. The Green’s function solution of Pan and Chou for an infinite transversely isotropic solid can be reproduced from the present expression by setting the elastic constants of both phases to be equal. Finally, the Green’s function for isotropic materials can also be obtained from the present solution by suitable substitution of elastic constants.
Penetration of a Half Space by a Rectangular Cylinder
Authors: Eringen A. Cemal , Balta F.
Published: November 2010

The stress and displacement fields are determined in an elastic half space loaded by a rectangular frictionless, rigid block normally at its surface. The semi-infinite solid is considered to be an elastic solid with nonlocal interatomic interaction. The field equations of the nonlocal elasticity and boundary conditions are employed to treat this contact problem. Interestingly the classical stress singularity at the edges of the block are not present in the nonlocal solutions. Consequently the critical applied load for the initiation of penetration of the rigid cylinder into the semi-infinite solid can be determined without recourse to any criterion foreign to the theory. The stress field obtained is valid even for penetrators of submicroscopic width.
On the Determination of Stresses, Displacements, and Stress-Intensity Factors in Edge-Cracked Sheets With Mixed Boundary Conditions
Authors: Torvik P. J.
Published: November 2010

The stresses and displacements in a finite, isotropic, elastic sheet containing a single edge crack are considered. Solutions are constructed through superposition of the solutions due to Williams. Variational principles are used to obtain solutions for mixed boundary conditions on the edge of a sheet containing a single, straight, unloaded edge crack. Trial solutions are constructed by expanding stresses and displacements in series of Williams’ solutions and a procedure for determining the coefficients for the best finite expansion is developed through the use of Reissner’s principle. The method is applicable to any combination of prescribed displacements and prescribed tractions on the boundary. The method is used to determine the stress-intensity factor for a rectangular edge-cracked sheet with two edges free of traction and a prescribed extension of the ends. Values of KI and compliance are given for various aspect ratios and crack lengths.
Rolling Element Bearing Vibration Transfer Characteristics: Effect of Stiffness
Authors: While M. F.
Published: November 2010

Vibration transmission through rolling element bearings was investigated in order to aid signal interpretation for use in machinery condition monitoring studies. The relationship between bearing nonlinear stiffness and frequency response function was derived for bearings of types commonly used in rotating machinery. By considering the contact deformation of individual elements the stiffness characteristic for a complete bearing was evaluated for the case of a radially applied load. Variation in stiffness of the complete bearing as elements moved through the load zone was calculated for bearings of a specified type and size. These values were also used to dynamically model typical rolling element bearing nonlinear behavior. Derived nonlinear stiffness coefficients were substituted into the equations of motion for a model bearing. Solution was obtained by digital integration, and the bearing frequency response function was then evaluated for discrete increments of static loading. Rolling element bearing frequency response was found to be very dependent on load. For operation under light load the bearings had especially strong nonlinear vibration transfer characteristics. At this operating condition a small increase in radial load produced a significant change in the bearing transfer characteristic (due to an increase in resonance frequency).
A Rigid Punch Bonded to a Half Plane
Authors: Adams G. G.
Published: November 2010

The well-known solution for a rigid punch bonded to an elastic half plane has oscillatory singularities at the corners of the punch. It is shown here that the resulting displacement of the free surface of the half plane actually spirals in upon itself and is therefore physically inadmissible. The problem of a flat punch with sloped sides is then formulated and a solution obtained which does not have an oscillatory singularity. The limit is taken as the punch sides become perpendicular with its base. This leads to square root singularities in the shear stress and to logarithmic singularities in the normal stress along the bond.
The Role of Saint Venant’s Solutions in Rod and Beam Theories
Authors: Parker D. F.
Published: November 2010

Within small displacement linear elasticity, Saint Venant derived semi-inverse solutions for bending and torsion of rods and beams. The resulting linear expressions for bending moments and torque in terms of curvatures and torsion are often taken to be those required by elastica theory in describing general configurations of rods and beams. It is here shown, by using a perturbation procedure based on an appropriate scaling of axial variations, that Saint Venant’s solutions combine naturally with elastica theory to describe configurations involuing large rotations and displacements. Also it is shown that the classical solution for beam flexure is essentially a bending solution with varying curvature. The contribution involving the bending function is, for general beam loading, only part of the first-order correction.
Axisymmetric Creep Buckling of Circular Cylindrical Shells in Axial Compression
Authors: Murakami S. , Tanaka E.
Published: November 2010

Creep buckling of axially compressed circular cylindrical shells with axisymmetric initial imperfection is discussed with special emphasis on the general features of its unstable process. An elastic-creep material obeying the isotropic elastic law and the time-hardening creep law of Mises-Mises type is assumed. The analysis is performed quasi-statically on the basis of the variational principle of Reissner’s type and the finite deformation theory in Lagrangean formulation. In order to minimize the number of parameters necessary for specifying the problem, the basic equations are expressed in terms of nondimensional equations. An approximate expression for the limit time of creep buckling is also given for wide range of the parameters.
Numerical Solution of the Beam Equation With Nonuniform Foundation Coefficient
Authors: Lentini M.
Published: November 2010

A new method for computing the solutions of the beam equation is given for the case of the problem of a pile. The method could be used for other problems where it is necessary to solve boundary-value problems for ordinary differential equations over semi-infinite intervals.
Ligament Strain in the Human Knee Joint
Authors: Edwards R. G. , Lafferty J. F. , Lange K. O.
Published: November 2010

The kinematics of the human knee joint and the strain of the ligaments as a function of flexion are determined analytically and experimentally. The experimental results were obtained in 13 tests of four knee joints in which the strain in each of the two collateral and two cruciate ligaments was measured with mercury strain gauges while the tibia was rotated through a flexion angle of 130 deg. The values of the relative ligament strain obtained from the analytical model are in good agreement with the experimental results.
Experimental Investigation of Discrete Frequency Noise Generated by Unsteady Blade Forces
Authors: Lipstein N. J. , Mani R.
Published: November 2010

A critical experiment was designed and carried out to study discrete frequency noise generation from an axial flow compressor row. The experiments were carried out in a small-scale Freon loop. Two arrays of rods were introduced upstream of a single compressor rotor so as to cause acoustic modes oriented approximately normal and parallel to the blade force. R. Mani’s analysis of the coupling of unsteady forces to acoustic modes was applied to these experimental results. Good agreement was obtained.
Annular Two-Phase Flow—Part 2: Additional Effects
Authors: Wallis G. B.
Published: November 2010

The theory of Part 1 is modified by taking additional phenomena into account. The liquid film, the gas core, and the interface are considered separately. The effects of entrainment, compressibility, liquid and gas Reynolds numbers, shear-stress distribution, relative velocity, and the various types of interfacial waves are discussed.
Active Control of Machine-Tool Chatter
Authors: Nachtigal C. L. , Cook N. H.
Published: November 2010

Regenerative chatter is recognized as one of the primary performance limitations of a machine tool. In the past much attention has been focused on minimizing this problem by improving the dynamic compliance of the structure. These approaches have been of a passive nature, such as increasing the structural damping, increasing the rigidity, addition of a vibration absorber, etc. The present work is one of two known basic contributions to the literature in the field of active chatter control. This paper includes an analysis of a machine tool equipped with an active chatter control system. In addition, experimental results are presented for such a control system applied to an engine lathe. The analysis, verified by the experimental results, indicated significant improvements in production rate, in transient response, and in static stiffness.
An Efficient, Computer-Oriented Method for Stability Analysis of Large Multivariable Linear Systems
Authors: Wright W. C. , Kerlin T. W.
Published: November 2010

A computer-oriented procedure for efficient stability analysis of very large systems was developed by modifying a method due to Mikhailov. The method allows pure time delays in the system model. The state variable model of the system is used, and the computational procedure is tailored to take advantage of the sparesness of the system matrices that are applicable for many systems. The practicality of the procedure has been demonstrated in the analysis of several systems, the largest of which consisted of a 553rd order model of a multistage flash evaporator plant.
Methods of Predicting the Tip Clearance Effects in Axial Flow Turbomachinery
Authors: Lakshminarayana B.
Published: November 2010

Using the author’s earlier flow model for the tip clearance flow, an expression is derived for the decrease in stage efficiency due to tip clearance. The analysis which includes all the dominant flow and blade parameters that affect the flow in the clearance region is compatible with fundamental physical principles, though not precise mathematically. The predictions agree closely with several compressor, fan, pump, and turbine data available. An alternate model which takes into account the presence of the vortex core is proposed. The theoretical treatment of the flow, more complete than hitherto available, predicts blade-to-blade variation in outlet angles accurately and stagnation pressure losses qualitatively. The predictions are compared with various experimental data available in the literature.
Fluid Flow Phenomena in Dusty Air
Authors: Boyce M. P. , Blick E. F.
Published: November 2010

The purpose of this study was to obtain extensive experimental data on the effect of skin-friction drag by suspending solid particles in air. The investigation was divided into two parts: The first study consisted of obtaining extensive experimental data on the pressure gradients (which are proportional to skin friction) encountered in circular pipes when a mixture of air with solid particles suspended in it flows through the pipe. The second part deals with the skin friction as measured on a flat plate placed flush with the floor of a wind tunnel having a dusty sub-layer. These studies involved a large range of Reynolds numbers, particle sizes, and weight-flow ratios. A theory is also presented to try and explain some of the complex flow phenomena encountered in a two-phase flow system.
The Management of Pressure and Other External Factors in the Prevention of Ischemic Ulcers
Authors: Newell P. H. , Thornburgh J. D. , Fleming W. C.
Published: November 2010

The primary external causes of ischemic ulcers or bedsores are (a) pressure, (b) abrasion with associated shear deformations, (c) moisture, and (d) lack of cleanness. These disturbances perturb the microcirculation and inhibit the mass transport necessary to support local metabolism. These external factors can be managed through engineering analysis and design. A technique has been developed to measure the pressure distributions between the body and various support systems without perturbing the pressure distribution using a thin, pliable, pneumatic-cell, pressure-sensor. Data are presented for several existing support devices, and design requirements have been determined for an external support system for the chronically ill and debilitated which will periodically relieve and redistribute external pressures and prevent the formation (and aid in treatment) of ischemic ulcers. The design is based primarily on the physiologically allowable time-at-pressure data and the anatomy.