bluuebunny/crossref_metadata_2025 huggingface dataset:
On the Application of Liapunov’s Direct Method to Linear Lumped-Parameter Elastic Systems
Authors: Walker J. A.
Published: November 2010

A specialized Liapunov functional is presented for stability analysis of linear lumped-parameter elastic systems involving completely general types of forces not explicitly dependent on time. This functional appears to have the simplest possible form capable of providing necessary and sufficient stability conditions for virtually all such systems. Complete analyses are carried out for systems with and without velocity-dependent forces. Simple approaches are given for investigating systems involving “arbitrarily small” and “arbitrarily large” velocity-dependent forces, as well as for determining whether and how the “size” and “structure” of the velocity-dependent forces affect stability. Applications are made to several examples.
Internal Hypersonic Flow
Authors: Lin T. C. , Rubin S. G.
Published: November 2010

Apart from method of characteristic calculations, there has been little analytical consideration of high-speed internal flows where transverse curvature and/or viscous-inviscid interaction are important. Molder [1] has carried out a numerical computation for internal conical flow using the inviscid Taylor-Macoll equations; however, a singular ray is encountered. Minassian [2] obtained an approximate inviscid solution for internal hypersonic flow; and Lee [3] has recently obtained some numerical solutions. The purpose of the present analysis is to investigate more general hypersonic internal flows with, and without, viscous interactions.
Propagation of Low-Frequency Elastic Disturbances in a Composite Material
Authors: Kohn W.
Published: November 2010

In the limit of low frequencies the displacement u(x, t) in a one-dimensional composite can be written in the form of an operator acting on a slowly varying envelope function, U(x, t): u(x, t) = [1 + v1(x)∂/∂x + …] U(x, t). U(x, t) itself describes the overall long wavelength displacement field. It satisfies a wave equation with constant, i.e., x-independent, coefficients, obtainable from the dispersion relation ω = ω(k) of the lowest band of eigenmodes: (∂2/∂t2 − c¯2∂2/∂x2 − β∂4/∂x4 + …) U(x, t) = 0. Information about the local strain, on the microscale of the composite laminae, is contained in the function v1(x), explicitly expressible in terms of the periodic stiffness function, η(x), of the composite. Appropriate Green’s functions are constructed in terms of Airy functions. Among applications of this method is the structure of the so-called head of a propagating pulse.
Free Vibration of a Disordered Periodic Beam
Authors: Lin Y. K. , Yang J. N.
Published: November 2010

Using a first-order perturbation procedure the statistical properties of the natural frequencies and their associated normal modes of a disordered N-span beam are investigated. Two types of disorder are considered: the random deviation of span length from an ideal design value and the random fluctuation of the bending stiffness along the beam. The grouping pattern of the natural frequencies is used to establish a perfect correlation among certain random natural frequencies; therefore, their relative position can never be reversed. For other natural frequencies a sufficiency condition for nonreversal of position order is given.
Impedance of Strip-Traveling Waves on an Elastic Half Space: Asymptotic Solution
Authors: Crandall S. H. , Nigam A. K.
Published: November 2010

The dynamic normal-load distribution across a strip that is required to maintain a plane progressive wave along its length is studied for the case where the strip is of infinite length and lies on the surface of a homogeneous isotropic elastic half space. This configuration is proposed as a preliminary idealized model for analyzing the dynamic interaction between soils and flexible foundations. The surface load distribution across the strip and the motion of the strip are related by a pair of dual integral equations. An asymptotic solution is obtained for the limiting case of small wavelength. The nature of this solution depends importantly on the propagation velocity of the strip-traveling wave in comparison with the Rayleigh wave speed, the shear wave speed and the dilatational wave speed. When the strip-traveling wave propagates faster than the Rayleigh wave speed, a pattern of trailing Rayleigh waves is shed from the strip. The limiting amplitude of the trailing waves is provided by the asymptotic solution.
Bounds on Plastic Strains and Displacements in Dynamic Shakedown of Work-Hardening Structures
Authors: Maier G. , Vitiello E.
Published: November 2010

Methods are established for the determination of upper bounds on plastic strains and displacements after the adaptation (shakedown) of elastoplastic systems subjected to varying loads and straining effects, in the presence of significant inertia and viscous damping forces. A broad class of piecewise liner hardening rules are covered. Discrete structural models and piecewise linear yield loci are assumed and, consequently, mathematical programming notions and techniques are used.
Analytic Treatment of Minimum Weight Design of Cantilevers
Authors: Brock J. E.
Published: November 2010

Minimum weight design is considered for cantilever beams which must sustain a concentrated moment and a concentrated force at the tip as well as their own distributed weight. An analytic solution is obtained for the case where the variation of cross section is such that section modulus varies as a power of cross-sectional area. Three cases, having practical importance, are studied in detail; two of these lead to nonlinear differential or integral relationships. Cases having more complicated laws of variation and other end conditions are discussed.
On Berger’s Method in the Nonlinear Theory of Plates
Authors: Schmidt R.
Published: November 2010

This Note develops a new perturbation method for the analysis of circular plates and membranes with finite axisymmetric deflections. The perturbation parameter involves Poisson’s ratio. Two equations of the resulting infinite system of linearized differential equations are identical with Berger’s equations.
A Simplified Approach to the Analysis of Large Deflections of Plates
Authors: Mazumdar J. , Jones R.
Published: November 2010

This paper uses the method of constant deflection contour lines [1–3] to analyze the nonlinear large deflections of thin elastic plates of arbitrary shape in a new fashion. As an illustration the case of an elliptical plate with edges constrained against motion in the horizontal direction is discussed.
Magnetically Induced Stress Waves in a Conducting Solid—Theory and Experiment
Authors: Moon F. C. , Chattopadhyay S.
Published: November 2010

The induction of stress waves by transient magnetic fields has been examined analytically for a conducting half space and experimentally for a cylindrical rod. The analytical model predicts both a body force generated compressional wave and a thermoelastic stress wave. The model shows the magnetic, temperature, and stress fields in the half space for various times after a prescribed magnetic field is applied at the boundary. In the experiment a transient, radial, magnetic field (up to 15 kilogauss) was applied to the end of a copper bar. The field was generated by discharging a small capacitor bank through a flat helical coil. The measured compressional stresses obtained in this manner were of the order of the measured magnetic pressure (B2/2μ0), at the end of the bar.
Interlaminar Stresses in Composite Laminates—An Approximate Elasticity Solution
Authors: Pipes R. B. , Pagano N. J.
Published: November 2010

An approximate elasticity solution is developed for the response of the finite-width, angle-ply composite laminate under uniform axial strain. The solution yields components of the displacement vector, strain tensor, and stress tensor in the form of sinusoidal-hyperbolic series. Results of the approximate solution are compared to numerical solutions of the exact equations for four-layer, symmetric laminate geometries. The nature of the boundary disturbance in the eight-layer laminate is also examined by the approximate solution.
Asymptotic Solutions for Orthotropic Nonhomogeneous Shells of Revolution
Authors: Fettahlioglu O. A. , Steele C. R.
Published: November 2010

Approximate closed-form solutions are obtained for the static stress and deformation as well as the stability of an orthotropic layered shell of revolution with properties which vary along the meridian and through the wall thickness. The shell is subjected to axisymmetrical load and temperature distributions. The nonlinear “prestress” or “pressurization” effect is taken into consideration. It is of interest that due to the nonhomogeneity of the shell wall significant bending stresses can occur far from support points. The asymptotic results agree with numerical values obtained from two computer programs using direct numerical methods, even for shells that are relatively shallow.
On Computation of the Motion of Elastic Rods
Authors: Nordgren R. P.
Published: November 2010

A computational method is developed for the finite-amplitude three-dimensional motion of inextensible elastic rods with equal principal stiffnesses. The method also applies to the two-dimensional motion of such rods with unequal principal stiffnesses. For these two classes of problems the equations of the classical theory of rods are reduced to a non-linear vector equation of motion together with the inextensibility condition and appropriate boundary and initial conditions. Consistent finite-difference approximations are introduced and a semi-explicit method of solution is devised. The approximate limitation for numerical stability of the method is shown to be the same as for the usual explicit method in linear beam dynamics. By way of example the method is applied to the free fall of a circular pipe through water onto a rigid plane from a suspended initial configuration.
Interaction Between a Circular Inclusion and an Arbitrarily Oriented Crack
Authors: Erdogan F. , Gupta G. D. , Ratwani M.
Published: November 2010

The plane interaction problem for a circular elastic inclusion embedded into an elastic matrix which contains an arbitrarily oriented crack is considered. Using the existing solutions for the edge dislocations [6] as Green’s functions, first the general problem of a through crack in the form of an arbitrary smooth arc located in the matrix in the vicinity of the inclusion is formulated. The integral equations for the line crack are then obtained as a system of singular integral equations with simple Cauchy kernels. The singular behavior of the stresses around the crack tips is examined and the expressions for the stress-intensity factors representing the strength of the stress singularities are obtained in terms of the asymtotic values of the density functions of the integral equations. The problem is solved for various typical crack orientations and the corresponding stress-intensity factors are given.
Large Deflections and Stability of Hingeless Circular Arches Under Interacting Loads
Authors: DaDeppo D. A. , Schmidt R.
Published: November 2010

The buckling behavior subsequent to large prebuckling deflections of hingeless circular arches subjected to a downward point load at the crown as well as their own dead weight is investigated on the basis of Euler’s nonlinear theory of the inextensible curved elastica. The theory used is exact in the sense that no restrictions are imposed on the magnitudes of deflections. Among others, interaction curves of the critical values of the two loads (i.e., stability boundaries) are plotted and examined. With the aid of these interaction curves, simple approximate formulas relating the two critical loads are established. It is found that nonshallow hingeless arches may buckle by either asymmetrical sidesway or symmetrical snap-through, depending on the relative magnitudes of the point load and the weight of the arch. The results of this study are essential if arches are to be tested near buckling loads, since it is difficult to eliminate the effect of own dead weight in experimental work.
Effect of Imperfections on the Plastic Buckling of Rectangular Plates
Authors: Neale K. W.
Published: November 2010

The effect of initial imperfections in geometry on the plastic buckling of simply supported compressed rectangular plates is examined. The analysis, which is based on the application of a Reissner-type variational principle, indicates that the buckling load can be highly imperfection-sensitive; and that a consideration of small imperfections in geometry could provide results which compare favorably with experimental data.
On the Significance of the Inclusion of the Effect of Transverse Normal Strain in Problems Involving Beams With Surface Constraints
Authors: Essenburg F.
Published: November 2010

The general problem of a beam of rectangular section with displacement components prescribed over portions of its top and bottom surfaces is considered. A beam theory which includes the effect of transverse normal strain (as well as the effect of transverse shear deformation) is developed and the advantages of applying this theory to the class of problems considered is examined by means of an example.
The Frictionless Contact Problem for an Elastic Layer Under Gravity
Authors: Civelek M. B. , Erdogan F.
Published: November 2010

The paper presents a technique for solving the plane frictionless contact problems in the presence of gravity and/or uniform clamping pressure. The technique is described by applying it to a simple problem of lifting of an elastic layer lying on a horizontal, rigid, frictionless subspace by means of a concentrated vertical load. First, the problem of continuous contact is considered and the critical value of the load corresponding to the initiation of interface separation is determined. Then the mixed boundary-value problem of discontinuous contact is formulated in terms of a singular integral equation by closely following a technique developed for crack problems. The numerical results include the contact stress distribution and the length of separation region. One of the main conclusions of the study is that neither the separation length nor the contact stresses are dependent on the elastic constants of the layer.
Wave Propagation in Layered Elastic Media
Authors: Christensen R. M.
Published: November 2010

The Boltzmann constitutive representation is shown to provide a consistent means of incorporating dispersion effects into the mathematical modeling of wave behavior in layered elastic media. Attention is restricted to long wavelength conditions, with the waves propagating normal to the planes of layering. Special forms of a general Boltzmann law are derived for the special cases of periodic layering and one dimensionally random layering. Although there is no attenuation of harmonic waves in the periodic media case, an analytical representation is obtained for the attenuation measure in random media.
A Continuous Prediction Method for Fully Developed Laminar, Transitional, and Turbulent Flows in Pipes
Authors: Wilson N. W. , Azad R. S.
Published: November 2010

A single set of equations is developed to predict the mean flow characteristics in long circular pipes operating at laminar, transitional, and turbulent Reynolds numbers. Generally good agreement is obtained with available data in the Reynolds number range 100 < Re < 500,000.
Weakening of an Elastic Solid by a Rectangular Array of Cracks
Authors: Delameter W. R. , Herrmann G. , Barnett D. M.
Published: November 2010

An infinite elastic solid containing a doubly periodic rectangular array of slitlike cracks is considered. The solid is subjected to a uniform stress resulting in a state of plane strain. The cracks are represented as suitable distributions of dislocations which are determined from a singular integral equation. This equation is solved numerically in an efficient manner using an expansion of the nonsingular part of the kernel in a series of Chebyshev polynomials. Values of the stress-intensity factors are presented, as well as the change in strain energy due to the presence of the cracks. Also, the effective elastic constants of a sheet having a rectangular array of cracks are given as functions of the crack spacing.
A Random Cell Model for Pressure Drop Prediction in Fibrous Filters
Authors: Yu C. P. , Soong T. T.
Published: November 2010

A filter model consisting of a random distribution of parallel fibers is proposed to account for nonuniform fiber spacings in a real filter. The average pressure drop across this filter is determined based upon a random cell model of hydrodynamics. The results are favorably compared with existing experimental data. The computation is also extended to the slip flow regime where the Knudsen number is not negligible.
Dynamic Buckling of Externally Pressurized Imperfect Cylindrical Shells
Authors: Lockhart D. , Amazigo J. C.
Published: November 2010

The dynamic buckling of imperfect finite circular cylindrical shells subjected to suddenly applied and subsequently maintained lateral or hydrostatic pressure is studied using a perturbation method. The geometric imperfections are assumed small but arbitrary. A simple asymptotic expression is obtained for the dynamic buckling load in terms of the amplitude of the Fourier component of the imperfection in the shape of the classical buckling mode. Consequently, for small imperfection, there is a simple relation between the dynamic buckling load under step-loading and the static buckling load. This relation is independent of the shape of the imperfection.
Forced Motions of Elastic Cylindrical Shells
Authors: Huang C. C.
Published: November 2010

A formal solution is presented for the dynamic boundary-value problem of the axially symmetric motion of finite, Timoshenko-type, isotropic, linearly elastic, cylindrical shells with time-dependent boundary conditions of any admissible combination, acted upon by time-dependent surface tractions with specified arbitrary initial conditions, obtained by using Herrmann-Mirsky shell theory and modal acceleration method. The method is applied to a simply supported shell subject to longitudinal tensile step forces at both ends. The transient response is studied in detail and the results predicted by the improved and the classical theories are compared.
A Spherical Model Calculation for Volumetric Response of Porous Rocks
Authors: Bhatt J. J. , Carroll M. M. , Schatz J. F.
Published: November 2010

The problem of external pressurization and release is solved for a hollow sphere of incompressible material obeying Coulomb’s law of failure. The resulting relations between the applied pressure and the porosity of the sphere are used in formulating constitutive relations for the volumetric response of porous rocks. The theoretical predictions are compared with experimental data for a sandstone and a tuff.
A Quest for Micropolar Elastic Constants
Authors: Gauthier R. D. , Jahsman W. E.
Published: November 2010

In contrast to a homogeneous isotropic elastic medium with only two elastic constants, a linear elastic micropolar solid is characterized by six such constants. To evaluate these constants it is necessary to solve selected boundary-value problems in terms of measurable surface tractions and displacements. Representative problems are tension and torsion of a circular cylinder and cylindrical bending of a rectangular plate. Analytical solutions to these static problems have been obtained, and to complement these solutions a combination of experiments was planned and a novel man-made micropolar solid was developed. The solid consisted of a composite material with aluminum shot uniformly distributed throughout an epoxy matrix. The shot, with an elastic modulus 20 times that of the matrix, was selected to represent rigid microelements embedded in a deformable medium and thereby model a micropolar solid. Static torsion tests revealed that the micropolar effects were masked by material inhomogeneity. It was concluded that, to within the resolution of the measurements, the special material developed here behaved as a classical elastic solid. Detection of possible micropolar phenomena will demand either higher resolution static measurements or a series of dynamic tests.
An Elastic-Plastic Constitutive Law for Sea Ice
Authors: Pritchard R. S.
Published: November 2010

The AIDJEX sea ice model is extended by a careful consideration of the deformation measured relative to a reference configuration which changes according to the plastic flow. This approach makes the strain more meaningful than it was previously. The kinematic relations properly allow both finite stretch and rotation. The resulting kinematic relations reflect the feeling that sea ice response is independent of any fixed reference configuration. This formulation has been achieved by writing an incremental kinematic relation using the Finger deformation tensor. A special relation is presented for the case when elastic strain is small, as with sea ice. The elastic response and yield criterion as well as the plastic flow rule remain unchanged from those presently in use. The flow rule is derived by maximizing the rate at which plastic work is done. This approach unifies the development and also helps us to study the material instabilities that occur when the material softens. The material model satisfies the principle of material frame indifference. The model has been subjected to known deformation histories and the response is satisfactory. In many cases the stress history is indistinguishable from that of the previously used elastic-or-plastic model.
On the Influence of Variations of Material Properties on Stress Wave Propagation Through Elastic Slabs
Authors: Lee E. H. , Budiansky B. , Drucker D. C.
Published: November 2010

The influence of variation of elastic properties through a plate on the propagation of elastic waves through it has been studied, with a view to investigating its ability to withstand impact. The relative merit of properties changes in a series of steps (graded material) or continuous variation (gradient material) is investigated. For an elastic slab with elastic modulus varying continuously but otherwise arbitrarily with depth, the magnitude of the stress wave front associated with an applied step surface pressure varies in proportion to ρ(x)c(x) where ρ is the density and c the elastic wave speed for dilatational waves. This magnitude grows indefinitely with increasing c(x). However, in the limit of a sudden change of properties as at an interface with a rigid body (c → ∞), the stress magnitude only doubles. This paradox is explained by noting a singular approach to the limit of the continuously varying case. A boundary layer consisting of a peak of high stress can occur for sharp changes of properties, which narrows as the gradient material approaches a graded one. The possible significance of this result to material damage under dynamic loading is discussed.
Measurements in a Turbulent Boundary Layer Over a d-Type Surface Roughness
Authors: Wood D. H. , Antonia R. A.
Published: November 2010

Mean velocity and turbulence intensity measurements have been made in a fully developed turbulent boundary layer over a d-type surface roughness. This roughness is characterised by regular two-dimensional elements of square cross section placed one element width apart, with the cavity flow between elements being essentially isolated from the outer flow. The measurements show that this boundary layer closely satisfies the requirement of exact self-preservation. Distribution across the layer of Reynolds normal and shear stresses are closely similar to those found over a smooth surface except for the region immediately above the grooves. This similarity extends to distributions of third and fourth-order moments of longitudinal and normal velocity fluctuations and also to the distribution of turbulent energy dissipation. The present results are compared with those obtained for a k-type or sand grained roughness.
A Practical Two Surface Plasticity Theory
Authors: Krieg R. D.
Published: November 2010

A plasticity theory is presented using the usual concept of a loading surface which moves and isotropically grows, but in addition uses a “limit surface” which grows and moves independently and encloses the loading surface. The plastic stiffness is a function of the distance between the surfaces at the loading point. Characteristics of the theory are a smoother transition between elastic and plastic regions on loading, an inherent Bauschinger effect, and more latitude on the description of hardening characteristics than the traditional methods used in structural codes. The full capability of the theory requires a memory of three vectors and three scalars, while some of the foregoing characteristics can be retained with only two vectors, the same as a traditional kinematic hardening model. The multiaxial theory is presented, particularized, specialized to uniaxial stress and the equations solved. The theory is compared to uniaxial stress experimental results.
Dynamic Response of Anisotropic Laminated Plates Under Initial Stress to Impact of a Mass
Authors: Sun C. T. , Chattopadhyay S.
Published: November 2010

The central impact of a mass on a simply supported laminated composite plate under initial stress is investigated. The contact force and the dynamic response of the plate are obtained by solving a nonlinear integral equation. The energy transferred from the mass to the plate during impact is also obtained by use of a normalized contact force. It is found that a higher initial tensile stress elevates the maximum contact force, but reduces the contact time, the deflection, and the stresses. It is also noted that a higher tensile initial stress results in less energy transfer from the striking mass to the plate.
Probability of First-Passage Failure for Nonstationary Random Vibration
Authors: Roberts J. B.
Published: November 2010

The problem of calculating the probability of first-passage failure, Pf, is considered, for systems responding to a short pulse of nonstationary random excitation. It is shown, by an analysis based on the “in and exclusion” series, that, under certain conditions, Pf tends to Pf*, the probability calculated by assuming Poisson distributed barrier crossings, as the barrier height, b, tends to infinity. The first three terms in the series solution provide bounds to Pf which converge when b is large. Methods of estimating Pf from these terms are presented which are useful even when the series is divergent. The theory is illustrated by numerical results relating to a linear oscillator excited by modulated white noise.
Limiting Performance Characteristics of Steady-State Systems
Authors: Wang B. P. , Pilkey W. D.
Published: November 2010

The problem of determining the limiting (or absolute optimum) performance of mechanical systems subject to steady-state loadings is considered. By replacing portions of a system by generic forces which can represent any configuration, the limiting performance characteristics of the system can be found using mathematical programming techniques. For the class of problems treated here, both performance index and constraints are composed of system response variables, such as displacements, velocities, and accelerations. Details of an efficient linear programming formulation of the problem are presented. In spite of the linear programming solution, no linearity restrictions are placed on the generic forces. Several examples are included.
Parametric and Combination Resonances of a Pipe Conveying Pulsating Fluid
Authors: Paidoussis M. P. , Sundararajan C.
Published: November 2010

In this paper we consider the dynamics of a pipe conveying fluid, when the flow velocity is harmonically perturbed about a mean value. Two methods of analysis are presented; Bolotin’s method, which can only give the boundaries of regions of parametric resonance, and a numerical Floquet analysis, which gives also the boundaries of combination resonance. A number of calculations for cantilevered pipes show that, generally, combination resonance is less important than parametric resonance, except for flow velocities near the critical (where the system loses stability in steady flow); parametric resonances are selectively associated with only some of the modes of the system, and combination resonances involve only the difference of the eigenfrequencies. For pipes clamped at both ends the behavior of the system is similar to that of a column subjected to a pulsating load; combination resonances in this case involve the sum of the eigenfrequencies.
On the Extension of Elastic Two-Ply Filament Yarns
Authors: Huang N. C.
Published: November 2010

This paper deals with the small extension of linearly elastic two-ply filament yarns. Each filament is treated as a long slender curved rod with circular cross section and helical configuration. Analysis is based on the linear theory of slender curved rods. Two problems are investigated, namely, the extension of a yarn with fixed ends and the extension of a yarn with free ends. In comparison with a previous study of a similar problem, it is found that the method adopted in this paper can provide more accurate results and better geometrical and physical insights into the problem. In this study, the yarn elongation and the filament stress are determined for yarns with various helical angles. The effect of the superposition of a twisting moment on the axial extension is also investigated.
Flexural Vibration of Segmented Elastic-Viscoelastic Sandwich Beams
Authors: Sandman B. E.
Published: November 2010

A pair of governing differential equations form the basis for the study of steady-state forced vibration of a sandwich beam with longitudinal nonuniformity in the stiffness and mass of the middle layer. The spatial solution for simply supported boundary conditions is obtained by a Fourier analysis of both material and kinematic variations. The solution is utilized in the numerical study of a sandwich beam with a segmented configuration of elastic and viscoelastic core materials. The results exemplify a tuned configuration of core segments for optimum damping of the first resonant mode.
On the Analysis of Residual Stresses Introduced in Sheet Metals by Thermal Shock Treatment
Authors: Hsu T. R. , Trasi S. R.
Published: November 2010

This paper presents a theoretical study of the residual stresses in a thin metal sheet with a circular hole subjected to an axially symmetric thermal shock over a concentric annular area. Quasi-static, uncoupled, thermoelastoplasticity theory incorporating the postulates of incremental plasticity theory is employed. The solution is sought through a numerical technique incorporating an iteration scheme and numerical integration. Several numerical examples are considered for a specific distribution and duration of the thermal shock and some optimization considerations are discussed.
Creep Buckling of Imperfect Columns
Authors: Huang N. C.
Published: November 2010

Problems in creep buckling of columns have generally been analyzed based on the assumption of small deflection. However, it is known that the critical time for creep buckling is determined by unbounded deflection or deflection rate. Thus a more rational consideration of creep buckling problems would necessarily include large deformation. In this paper, a study of the creep buckling of two simple columns with geometrical imperfections associated with finite deformations has been made. The material property of the column is considered to satisfy a power law for creep deformation and a generalized Ramberg-Osgood relation for noncreep deformation. It is found that creep buckling at a finite time would exist only when the magnitude of the load is between two bounds. If the load is greater than the upper bound, instantaneous buckling would occur. On the other hand, if the load is smaller than the lower bound, creep buckling would not occur at any finite time. Misleading conclusions on creep buckling caused by the small deflection assumption are also investigated.
A Random Cell Model for Predicting Filtration Efficiency of Fibrous Filters
Authors: Soong T. T. , Yu C. P.
Published: November 2010

With the use of the random cell model developed in a previous paper, an expression for predicting filter efficiency of a fibrous filter is obtained. Comparisons between theory and experiments are made. It is shown that the use of the random cell model also leads to a more realistic prediction of the filter efficiency, thus further enhancing utility of this model.
The Dynamic Response of an Elastic Half Space With an Overlying Acoustic Fluid
Authors: Bennett B. E. , Herrmann G.
Published: November 2010

A class of dynamic problems involving a semi-infinite elastic solid with an overlying semi-infinite acoustic fluid, subjected at the plane interface to arbitrary normal loading is investigated. A method of solution is proposed which reduces the class of problems under study to that in which the fluid is absent. This latter class has received considerable consideration in the past. A specific example is presented for an expanding disk-shaped load including numerical results for the subseismic range.
Partially Activated Human Skeletal Muscle: An Experimental Investigation of Force, Velocity, and EMG
Authors: Zahalak G. I. , Duffy J. , Stewart P. A. , Litchman H. M. , Hawley R. H. , Paslay P. R.
Published: November 2010

Experiments are described which establish quantitative relations between muscular force, contraction velocity, and the electrical activity of the muscle (as measured by the surface EMG) under conditions of steady motion. The six subjects who participated in these experiments were all athletes. Test results confirm that human skeletal muscle in vivo behaves differently when it is contracting under load than when it is extending under load. At maximum voluntary effort the force-velocity relation is similar to that found for excised, tetanized muscle (Hill’s equation). Antagonist activity was found to be low under all conditions of load and velocity. Simple equations are proposed to describe the observed force-velocity-activation relations. The parameters of these equations, which represent the apparent internal friction properties of the muscles, are evaluated and reported.
A Unified Model for Turbulent and Laminar Momentum Transfer: Channel Flow
Authors: Thomas L. C. , Kakarala C. R.
Published: November 2010

An analysis of fully developed, turbulent transitional flow between parallel plates is presented which is based on the modeling of the burst phenomenon. This analysis gives rise to predictions for the mean velocity profile which are in agreement with experimental data near the wall for transitional turbulent flow in a channel with large aspect ratio. Furthermore, predictions for the mean periodicity of wall turbulence are in basic agreement with available data for tube flow.
Hydrodynamic Pressure Field on a Slender Ship Moving Over a High-Frequency Wavy Shallow Bottom
Authors: Plotkin A.
Published: November 2010

The hydrodynamic pressure field for the unsteady subcritical potential flow of a slender ship moving over a wavy wall in shallow water is analyzed using perturbation techniques. For the case of wall wavelength much smaller than the ship length but larger than the transverse ship dimensions, a combination of the methods of matched asymptotic expansions and multiple scales is used to obtain the lowest-order effect of the bottom variation.
The Effect of Boundaries on the Stability of Inviscid Stratified Shear Flows
Authors: Einaudi F. , Lalas D. P.
Published: November 2010

The influence of the presence and position of solid boundaries on the stability of an inviscid, stratified shear flow, is examined numerically for the case of a hyperbolic tangent velocity profile and an exponentially decreasing density. The presence of solid boundaries is shown to stabilize short wavelengths and destabilize large wavelengths. Furthermore, extra unstable modes, not present in an infinite domain, are found for large wavelengths, both for symmetric and asymmetric boundaries. Finally, the validity of the principle of exchange of stability is examined, and it is shown to be unreliable even for the case of symmetric boundaries.
Wave Propagation in the Linear Theory of Elastic Shells
Authors: Cohen H.
Published: November 2010

The problem of wave propagation in elastic shells within the framework of a linear theory of a Cosserat surface is treated using the method of singular wave curves. The equations for determining the speeds of propagation and their associated wave mode shapes are obtained in a form involving the speeds of propagation in Cosserat plates and the curvature of the shell. A number of special cases in which the speeds and mode shapes simplify are considered. In particular, these special cases are shown to include as examples, certain systems of waves in elastic shells whose middle surfaces are the surface of revolution, the circular cylinder, the sphere, and the right helicoid.
Added Mass and Damping of a Vibrating Rod in Confined Viscous Fluids
Authors: Chen S. S. , Wambsganss M. W. , Jendrzejczyk J. A.
Published: November 2010

This paper presents an analytical and experimental study of a cylindrical rod vibrating in a viscous fluid enclosed by a rigid, concentric cylindrical shell. A closed-form solution for the added mass and damping coefficient is obtained and a series of experiments with cantilevered rods vibrating in various viscous fluids is performed. Experimental data and theoretical results are in good agreement.
An Energy Method Determination of Large Cable Dynamics
Authors: Carson W. W. , Emery A. F.
Published: November 2010

The free and forced vibrations of cable segments typical of a skyline logging cable system are analyzed by assuming that the vibrating cable segment maintains a catenary shape, and energy expressions are derived to implement the Lagrange equation of motion. The results of this method are compared with finite-difference results published in the senior author’s PhD thesis and the accuracy and usefulness of the approach applied to more complex cable configurations are discussed.
Narrow-Band Excitation of a Nonlinear Oscillator
Authors: Lennox W. C. , Kuak Y. C.
Published: November 2010

A nonlinear oscillator characterized by a hardening-type restoring force is excited by stationary narrow-band noise. The analysis is based on the concept of quasi-static amplitude and phase values which is exactly opposite to the stochastic or Markov approach with its associated Fokker-Planck equation. The approach, in effect, replaces a system with memory with one without memory. The existence of jumps is demonstrated and an expression for the probability of the occurrence of jumps is derived.
Free Vibration of Fluid-Coupled Coaxial Cylindrical Shells of Different Lengths
Authors: Au-Yang M. K.
Published: November 2010

This paper considers the free vibration of two coaxial cylinders with finite lengths immersed in a restricted fluid medium. The general coupled equations of motion are derived. Qualitative study of the governing differential equation shows that only modes of the cylinders with their axial mode numbers directly proportional to their lengths are coupled. For the uncoupled modes, each cylinder vibrates as if the other one is rigid, and the only effect of fluid loading is an apparent increase in its mass (virtual mass effect). The natural frequencies in the fluid can then be computed by including the virtual mass to its physical mass. Experimental results have been used to verify the analysis. Agreement between experimental and theoretical results is excellent.
Point Force Solution for an Infinite Transversely Isotropic Solid
Authors: Pan Y.-C. , Chou T.-W.
Published: November 2010

The solution for a point force applied at the interior of an infinite transversely isotropic solid is obtained by introducing three potential functions which govern the displacements. Unlike previous publications where the solutions are expressed in different forms depending on the conditions satisfied by the elastic constants, the present paper provides a systematic approach to obtain a unified solution which is applicable for all stable transversely isotropic materials. The expression obtained does not have the deficiency suffered by previous solutions, namely, each individual term in the present expression does not tend to infinity on the z-axis. Thus accurate numerical evaluation of the Green’s function can be directly performed without the need to resolve the singularity algebraically.
Experimental Solution of Flexed Plates by the Method of Caustics
Authors: Theocaris P. S. , Gdoutos E. E.
Published: November 2010

A new experimental technique based on the optical method of caustics for the determination of bending moments in laterally loaded plates is developed. The method involves the direct by the experiment calculation of the partial slopes of the flexed plate or the deflection of the plate in a power series form. Two particular cases were considered to show the potentialities of the method: the simply supported triangular plate bent by moments uniformly distributed along its boundary and the axisymmetric plates. In the latter case the method leads to the direct determination of the curvatures of the plate.
The Virtual Mass of a Sphere Moving Toward a Plane Wall
Authors: Jeffrey D. J. , Chen H.-S.
Published: November 2010

The axisymmetric potential flow past a sphere almost touching a plane wall is solved in closed form and the solution used to show that the Virtual mass of the sphere is finite This result clears up a difficulty uncovered in calculations by Small and Weihs.
Generalized Hydrodynamic Mass for Beam Mode Vibration of Cylinders Coupled by Fluid Gap
Authors: Au-Yang M. K.
Published: November 2010

The generalized hydrodynamic mass for the free vibration of two coaxial cylindrical shells coupled by a narrow fluid gap is derived by following a procedure similar to that mentioned in [1]; the end conditions of the shells are arbitrary. The equations are applied to evaluate the generalized hydrodynamic mass for the coupled beam mode vibration of two cylinders. Numerical examples that can be compared with experimental data are given for two specific cases. In both cases, agreement between computed and measured values is excellent. It is intended that the results of this study will be applied to the vibration analysis of nuclear reactor internal components.
A Mixed Method in Elasticity
Authors: Kameswara Rao N. S. V. , Das Y. C.
Published: November 2010

A mixed method for three-dimensional elasto-dynamic problems has been formulated which gives a complete choice in prescribing the boundary conditions in terms of either stresses, or displacements, or partly stresses and partly displacements. The general expressions for the responses of the elastic body have been derived in the form of transcendental partial differential equations of a set of initial functions, which can be evaluated in terms of the prescribed boundary conditions. The method so-formulated has been illustrated by applying it to the theory of plates. Only plates subjected to antisymmetric loads have been considered for illustration. Some examples of free and forced vibration of plates have been presented. Results are compared with solutions from existing theories.
Vibration of a Group of Circular Cylinders in a Confined Fluid
Authors: Chung Ho , Chen Shoei-sheng
Published: November 2010

This paper presents an analytical method for evaluating the hydrodynamic masses of a group of circular cylinders immersed in a fluid contained in a cylinder. The analysis is based on the two-dimensional potential flow theory. The fluid coupling effect among cylinders is taken into account; self and mutual-added masses for both inner and outer cylinders are evaluated. Based on the proposed method, the free vibration of two eccentric cylinders with a fluid-filled gap is analyzed as an example.
Elastodynamic Stress-Intensity Factors for a Semi-Infinite Crack Under 3-D Loading
Authors: Achenbach J. D. , Gautesen A. K.
Published: November 2010

Elastodynamic stress-intensity factors accompanying the three-dimensional steady-state elastodynamic response of an unbounded solid containing a semi-infinite crack, are investigated in this paper. Analytic solutions are obtained by application of the Fourier transform technique in conjunction with the Wiener-Hopf method. Two specific examples are worked out. For the diffraction of a plane longitudinal wave, which is incident under an arbitrary angle with the edge of the crack, explicit expressions are presented for the Modes I, II, and III stress-intensity factors. The variation of these quantities with the direction of the incident wave was worked out in detail, and the results are displayed in several figures. The second example deals with the elastodynamic field generated by the application of normal point loads of equal magnitude but opposite sense to the surfaces of the crack. For this case relatively simple approximate expressions are derived for the Mode I stress-intensity factor.
Analytical and Numerical Calculation of Stress-Intensity Factors in a Pressurized Cylindrical Shell With a Clamped Crack
Authors: Latta G. E. , Simmonds J. G. , Bradley M. R.
Published: November 2010

The primary goal of this paper is to compute the stretching stress-intensity factor at the tip of a crack in a pressurized cylindrical shell. Shallow shell theory is used and the governing equations are reduced to singular integral equations along the crack, following earlier work by Folias and Copley and Sanders. The solution of the integral equations depends on a dimensionless parameter λ proportional to the crack length divided by the square root of the thickness times the midsurface radius of curvature. Series solutions are obtained for λ < 1 and numerical solutions for 0 ≤ λ ≤ 10. The major contribution of the paper is an asymptotic solution as λ → ∞. To avoid an intractable double Weiner-Hopf problem, the edge of the crack is assumed to be clamped in such a way that it can expand tangentially but cannot rotate or displace perpendicular to the midplane.
A Simple Technique for the Minimum Mass Design of Continuous Structural Members
Authors: Foley M. , Citron S. J.
Published: November 2010

A technique for determining the minimum mass design of continuous structural members is presented. The method involves formulating the minimum mass design problem as an optimal control problem, transforming the differential equations modeling the member into a penalty function, and then representing the state variables in terms of a Ritz-type expansion and discretizing to reduce the original optimal control problem to a parameter optimization problem. The technique is applied to determine the optimal design of a simply supported beam with fixed fundamental frequency of free vibration and a fixed-free column with specified Euler buckling load.
Whirl Stability of the Pendulously Supported Flywheel System
Authors: Thomson W. T. , Younger F. C. , Gordon H. S.
Published: November 2010

The steady-state whirl-spin relationships for the pendulously supported flywheel with bearing flexibilities, stiff sections of shaft and gyroscopic action are derived and experimentally verified. Stable and unstable operations of the system are experimentally demonstrated, and damping necessary to stabilize an inherently unstable system is theoretically derived for two modes of bearing displacements.
The Critical Excitation of Nonlinear Systems
Authors: Drenick R. F.
Published: November 2010

The critical excitation of a mechanical system, in the terminology of this paper, is one that drives the system to a larger response peak than any other in some class of allowed excitations. The critical excitation is of interest in questions related to the reliability and safety because the magnitude of the response peak is frequently an indicator of the survivability of the system. The problem of finding it has been solved for linear systems some time ago. This paper deals with the generalization of the problem to nonlinear systems. It is shown that its solution is in many ways analogous to its earlier counterpart.