bluuebunny/crossref_metadata_2025 huggingface dataset:
Scattering of a Plane Elastic Wave From Objects Near an Interface
Authors: Bennett Stephen B.
Published: November 2010

The displacement field generated by the reflection and refraction of plane (time harmonic) elastic waves by finite obstacles of arbitrary shape, in the neighborhood of a plane interface between two elastic media, is investigated. The technique employed allows a consistent formulation of the problem for both two and three dimensions, and is not limited either to boundary shapes which are level surfaces in appropriate coordinate systems, i.e., circular cylinders, spheres, etc., or to closed boundary curves or surfaces. The approach is due to Twersky, and has been applied to many problems of the scattering of electromagnetic waves. The method consists of expressing the net field due to all multiple scattering in terms of the field reflected from each boundary in isolation when subjected to an incident plane elastic wave. Thus the technique makes use of more elemental scattering problems whose solutions are extant. By way of illustration, a numerical solution to the scattering of a plane elastic wave by a rigid circular cylindrical obstacle adjacent to a plane free surface is considered.
External Excitation of Planar Jets
Authors: Rockwell D. O.
Published: November 2010

A planar jet was subjected to transverse periodic disturbances of appropriate dimension-less frequency such that the vortex growth of the jet could be controlled for a wide range of jet Reynolds number (1860 to 10,800). Changes in the apparent time mean characteristics of the jet in its initial formation region, due to the applied disturbances, are related to the behavior of vortices. The processes of vortex formation, growth, and coalescence in the initial formation region are portrayed. The alterations of these processes as a function of the dimensionless applied disturbance are classed into regimes identified with respect to the natural breakdown state of the jet.
A Comparison of Flow and Deformation Theories in a Radially Stressed Annular Plate
Authors: Chen P. C. T.
Published: November 2010

Two mathematically consistent solutions to the strains and displacement in a partly plastic, annular plate stressed by internal pressure are obtained according to the deformation theory of Hencky and to the flow theory of Prandtl-Reuss. In both cases, the material is assumed to be elastic, perfectly plastic and obeying the Mises yield condition. It is shown that one solution is expressed in closed form and the other, in terms of simple integrals. A quantitative comparison of two theories is given and the effect of compressibility is discussed.
Flow Near the Stagnation Point of a Body Which Undergoes a Sudden Change in a Steady Stream
Authors: Nanbu K.
Published: November 2010

Unsteady laminar boundary layers near the stagnation point of a body which undergoes a sudden change in a steady stream are analyzed by the method of successive approximations. It is shown that the second approximation which includes the effect of nonlinear convective terms of the equations of motion improves remarkably the first-order theory by the earlier investigators. Also, it seems that when the body is started with velocity increasing gradually with increasing time, the small-time solution obtained thus connects smoothly with the existing large-time solution.
Swirling Laminar Pipe Flow of Suspensions
Authors: Tung S. K. , Soo S. L.
Published: November 2010

Vortex pipe flow of suspensions with laminar motion in the fluid phase is treated. The pipe consists of two smoothly joined sections, one stationary and the other rotating with a constant angular velocity. The flow properties of the fluid phase are determined by solving the complete Navier-Stokes equations numerically. The governing parameters are the flow Reynolds number and swirl ratio. Subsequent numerical solution to the momentum equations governing the particulate phase provides for both particle velocity and concentration distributions.
Breakdown of the Laminar Flow Regime in Permeable-Walled Ducts
Authors: Sparrow E. M. , Beavers G. S. , Chen T. S. , Lloyd J. R.
Published: November 2010

The stability of laminar flow in a parallel-plate channel having one permeable bounding wall is investigated by means of linear theory. The analysis takes account of the coupling of the disturbance fields in the channel and in the permeable material and of velocity slip at the surface of the permeable wall. Complementary experiments are performed in which the breakdown of the laminar regime in flat rectangular ducts is identified from pressure-drop measurements and from flow visualization studies. The experiments cover the range of slip velocities from 15–30 percent of the mean velocity and, in addition, the case of zero slip (impermeable walls). In the slip range of the experiments, the instability Reynolds number results of both analysis and experiment lie below the corresponding values for the case of the impermeable-walled duct. Furthermore, in this range, the instability Reynolds numbers are rather insensitive to variations in the slip velocity. Quantitative agreement between analysis and experiment was found to be somewhat better in the slip range than for the impermeable-walled duct.
Boundary-Layer Separation From Downstream Moving Boundaries
Authors: Telionis D. P. , Werle M. J.
Published: November 2010

The laminar boundary-layer equations for incompressible flow with a mild adverse pressure gradient were numerically solved for flows over downstream moving boundaries. It was demonstrated that the vanishing of skin friction in this case is not related to separation.2 Indeed the integration proceeds smoothly through a point of vanishing skin friction and further downstream a Goldstein-type singularity appears at a station where all the properties of separation according to the model of Moore, Rott, and Sears are present. It is also numerically demonstrated that the singular behavior is not uniform with n, the distance perpendicular to the wall, but it is initiated at a point away from the wall leaving below a region of nonsingular flow. The foregoing points provide numerical justification of the general theoretical models of unsteady boundary-layer separation suggested by Sears and Telionis.
First-Order Frequency Effects in Supersonic Panel Flutter of Finite Cylindrical Shells
Authors: Holt M. , Lee T. M.
Published: November 2010

An improved calculation of the supersonic panel flutter characteristics of a thin cylindrical shell of finite length is presented. The aerodynamic load is determined with account taken of first-order terms in vibration frequency, and when this is introduced into the elastic shell equation an integro differential equation results. An equivalent eigenvalue problem is set up by applying Galerkin’s method to this equation. The flutter boundary, for given Mach number and circumferential mode n, corresponds to the shell thickness ratio at which the real part of any one of the eigenvalues first becomes non-negative. It is found that the most severe flutter condition, for given Mach number, occurs for a circumferential mode n = 7. The present calculations exclude second-order frequency terms in the elastic part of the flutter equation, even though they may have a first-order effect. A subsequent calculation referred to here shows that these terms indeed have no significant influence on the first-order analysis.
Steady Motion of a Plate on an Elastic Half Space
Authors: Oien M. A.
Published: November 2010

The response of a smooth Bernoulli-Euler plate of finite width and infinite length in contact with an elastic half space to incident plane harmonic waves propagating normally to the infinite axis of the plate is considered. Upon expanding the motion of the plate in a series of vibrational modes, approximate solutions for the response of the plate and the elastic half space are obtained separately using the Bubnov-Galerkin method. Numerical results are presented illustrating the general nature of the response of the plate and showing that individual vibrational modes of the plate are not excited to resonance.
Buckling of Continuously Supported Beams
Authors: Murthy G. K. N.
Published: November 2010

The buckling of infinite beams continuously supported by a semi-infinite elastic continuum is investigated. The buckling loads were determined when the beam rests on a two-dimensional elastic continuum and also when the foundation extends beyond the width of the beam. The effect of the outside foundation is shown by comparing the obtained buckling loads.
On the Stress Analysis of Creeping Structures Subject to Variable Loading
Authors: Ponter A. R. S.
Published: November 2010

In earlier papers [13, 14] displacement and deformation bounds were derived for a structure composed of an elastic, perfectly plastic, time-hardening viscous material. Here the upper and lower work bounds are discussed for a body subject to cyclic loading. It is shown that the optimal bounds may be interpreted as the asymptotic states when the cycle time is very small and very large compared with a characteristic time of the material. The time scales which occur in practice are discussed, and a simple worked example is presented.
A Necessary Condition for the Nonoccurrence of von Mises Yielding in Impulsively Loaded Plates
Authors: Simmonds J. G.
Published: November 2010

For an elastically isotropic plate subject to an arbitrary impulsive load and boundary conditions which prevent rigid-body motion and do no work, it is shown that a necessary condition for the nonoccurrence of plastic yielding according to the von Mises criteria is that T(0) < 2/3 V(1 – ν)E−1σ02, where T(0) is the initial kinetic energy imparted by the impulse, V is the volume of the plate, ν is Poisson’s ratio, E is Young’s modulus, and σ0 is the yield stress of the plate material in a simple tension test.
Acceleration Wave Propagation in a Nonlinear Viscoelastic Solid
Authors: Walsh E. K. , Schuler K. W.
Published: November 2010

In this study the growth and decay of one-dimensional acceleration waves in nonlinear viscoelastic solids are considered. The conditions governing the growth and decay, including the concept of a critical acceleration level derived by Coleman and Gurtin, are discussed in terms of certain relevant material functions. It is shown that these material functions can be determined from the results of experimental shock wave-propagation studies. The experimental methods used to generate and observe acceleration waves in solids are discussed and applied to the propagation of acceleration waves in the polymer, polymethyl methacrylate (PMMA). It was found that the conditions derived by Coleman and Gurtin accurately predict the experimentally observed behavior of acceleration waves in PMMA.
A Dynamic Shell Theory Coupling Thickness Stress Wave Effects With Gross Structural Response
Authors: Benzley S. E. , Hutchinson J. R. , Key S. W.
Published: November 2010

A theory for thick cylindrical shells is presented that couples the early time thickness stress wave propagation with higher-order shell theory equations. The formulation completely describes the continuum response in the thickness direction for “early time” considerations while representing the circumferential response with a high-order circumferential displacement assumption. Late time (structural response) equations are developed to continue the analysis after thickness effects are no longer important. The finite-element method is used to obtain solutions of the theory. Calculations are presented which show that thickness stress need not be included for cylindrical shells with h/R ratios less than 0.2.
Snapping of Low Pinned Arches on an Elastic Foundation
Authors: Simitses G. J.
Published: November 2010

The problem of a low half-sine pinned arch under a quasi-statically applied half-sine load is considered. The low arch is resting on an elastic foundation. Critical loads are obtained by investigating the stability of the equilibrium positions by considering all possible modes of deformation. It is assumed that the behavior of the arch is linearly elastic up to the critical load. The entire range of values for the modulus of the foundation is considered. The results are presented graphically as either critical load (snap-through) or classical buckling load (stable bifurcation) versus the rise parameters for a large number of values of the modulus of foundations. This investigation presents an interesting model for stability studies, because, depending on the value of the rise parameter and the modulus of the foundation, the load-deflection curve exhibits the possibilities of the top-of-the-knee buckling, snap-through buckling through unstable bifurcation, and classical buckling (stable bifurcation).
Stresses in a Perforated Wedge
Authors: Ling Chih-Bing , Hsu Chang-Ming
Published: November 2010

This paper presents a method of solution for an infinite wedge containing a symmetrically located circular hole. The solution is formulated separately according to the given in-plane edge tractions being even or odd with respect to the axis of the wedge. In either case, the stress function is constructed as the sum of four parts of biharmonic functions, two in the form of integrals and the other two in the form of series, in addition to a basic stress function for an otherwise unperforated wedge. The four parts as a whole give no traction along the edges and no stress at infinity of the wedge. Together with the basic stress function, the boundary conditions of no traction at the rim of hole are adjusted. Complex expressions are used in adjusting the boundary conditions. Finally, numerical examples are given for illustration.
Solution of Plane Problems of Elasticity Utilizing Partitioning Concepts
Authors: Bowie O. L. , Freese C. E. , Neal D. M.
Published: November 2010

A partitioning plan combined with the modified mapping-collocation method is presented for the solution of awkward configurations in two-dimensional problems of elasticity. It is shown that continuation arguments taken from analytic function theory can be applied in the discrete to “stitch” several power series expansions of the stress function in appropriate subregions of the geometry. The effectiveness of such a plan is illustrated by several numerical examples.
A Technique for Increasing the Accuracy of the Numerical Inversion of the Laplace Transform With Applications
Authors: Berger B. S. , Duangudom S.
Published: November 2010

A technique is introduced which extends the range of useful approximation of numerical inversion techniques to many cycles of an oscillatory function without requiring either the evaluation of the image function for many values of s or the computation of higher-order terms. The technique consists in reducing a given initial value problem defined over some interval into a sequence of initial value problems defined over a set of subintervals. Several numerical examples demonstrate the utility of the method.
An Energy Assessment for Liquids in a Filled Precessing Spherical Cavity
Authors: Vanyo J. P.
Published: November 2010

Experimental results and analytical approximations for energy dissipation due to liquids in a filled precessing spherical cavity are presented. The range of physical parameters include kinematic viscosities from 1 to 1000 centistokes, half coning angles from 5/8 to 10 deg, precession speeds from 0.15 to 200 rpm, and spin speeds (relative to the precessing frame) of from 7.5–900 rpm. These parameters and the associated energy dissipation rates, as low as 10−4 watts, place the results in the region of direct applicability to spinning satellite stability problems. A dimensionless parameter related to an Ekman number is used to correlate energy dissipation rates with laminar, intermediate, and fully turbulent flows. The reduced data are integrated with data from other sources and used to develop equations in dimensionless form for the experimental and analytical results. The results, while not defining details of fluid motion, place experimental bounds on the integrated shear stress at the cavity wall for analytical models.
On Finite Elastic-Plastic Deformation of Metals
Authors: Naghdi P. M. , Trapp J. A.
Published: November 2010

This paper is concerned with a special class of response functions for some of the constitutive equations in the nonlinear isothermal theory of elastic-plastic materials. Detailed attention is given to the development of special forms for the free energy and the stress response, motivated mainly by the mechanical behavior of ductile metals in the plastic range and in the presence of finite strains. After obtaining a properly invariant representation for the free energy response (and hence also for the stress) as a function of certain (easily interpretable) measures of deformation, the results are specialized to isotropic materials and are expressed in terms of the invariants of kinematic measures. Some special cases are elaborated upon and, by way of illustration, the influence of plastic deformation on the material properties of the stress response in a simple tension test is discussed.
Impulsive Motion in a Particle-Fluid Suspension Including Particulate Volume, Density, and Migration Effects
Authors: Di Giovanni P. R. , Lee S. L.
Published: November 2010

Based on expansions for small and large times, velocity and particulate volume distributions are obtained from the approximate continuum representation of a suspension of uniformly distributed small spherical solid particles for flow induced by impulsive motion of an infinite flat plate. Included in the analysis are major effects of the fractional particulate volume, which is assumed to vary due to the inclusion of the particle slip-shear lift force, as well as a generalized drag interaction force. For both small and large times, the lift force results in an accumulation of particles near the wall. Motion in the horizontal direction is determined in terms of modified similarity variables for large and small times indicating an increase or decrease in the viscous boundary layer for small times depending on the fractional volume of particles, and an increase or decrease for large times depending on whether the particles are lighter or heavier than the fluid. To the zeroth order, the skin friction on the wall is shown to increase or decrease for small times depending on whether the ambient fractional particulate volume is greater or less than 1/4. For large times the friction increases for heavy particles and decreases for light particles. Finally, by using the modified Rayleigh’s method, an estimate is made for boundary-layer flow past a semi-infinite flat plate.
The Dynamic Behavior of Articulated Pipes Conveying Fluid With Periodic Flow Rate
Authors: Bohn M. P. , Herrmann G.
Published: November 2010

The plane motion of two rigid, straight articulated pipes conveying fluid is examined. In contrast to previous work, the flow rate is not taken as constant, but is allowed to have small periodic oscillations about a mean value, as would be expected in a pump-driven system. It is shown that in the presence of such disturbances, both parametric and combination resonances are possible. When the system can also admit loss of stabilty by static buckling or by flutter, it is found that the presence of small periodic disturbances constitutes a destabilizing effect. Floquet theory and converging infinite determinant expansions are used to illustrate a basic difference between systems which lose stability by divergence and those that lose stability by flutter. An algebraic criterion is obtained for the minimum amplitude of flow rate oscillation required for the system to be affected by the presence of small disturbances.
Time-Harmonic Waves Propagating Normal to the Layers of Multilayered Periodic Media
Authors: Nayfeh Adnan H.
Published: November 2010

The dispersion relation is derived for time-harmonic waves propagating normal to the layers of a multilayered periodic composite. The known relations for the homogeneous and the bilaminated media are deduced as special cases. Mixture mass density and elastic modulus are defined in the limit as the ratio of the incident wavelength to the microdimension of the composite approaches infinity.
Stress Amplification in a Ring Caused by Dynamic Instability
Authors: Lindberg H. E.
Published: November 2010

An analysis is presented for stress amplification in a ring caused by the dynamic instability of symmetric in-and-out breathing oscillations, which results in energy transfer to flexural modes. Stress amplification is shown to depend on a ring stability parameter p that is proportional to the unperturbed hoop strain and inversely proportional to the thickness-to-radius ratio. The analysis is a generalization of earlier work by Goodier and McIvor. They showed that, with p tacity assumed small, stress is amplified by approximately the factor 6, independent of the wave number of the flexural mode into which the breathing energy is transferred. The present analysis shows that for large p (increased instability), higher-order nonlinear terms must be included in the differential equations in order to give bounded solutions. With these terms included, stress amplification departs from 6 as p is increased, the peak compressive stress becoming larger and the peak tensile stress becoming smaller. With damping also included, the amplification approaches unity (no amplification) as p approaches zero, and passes through a maximum as p is increased. An experimental example of flexural fracture caused by such amplification is given.
On the Adhesive Contact of Two Coaxial Cylindrical Shells
Authors: Kulkarni S. V. , Frederick D.
Published: November 2010

The adhesive contact problem of two coaxial cylindrical shells of identical layers is investigated in detail. A shear deformation theory is used to derive the governing differential equations. The inner shell is subjected to a constant pressure and an initial separation between the inner and outer shells is specified. It is recommended that the elasticity theory be used to solve the problem exactly primarily because the edge effects as obtained from the shell theory tend to distort the actual behavior of the radial displacement and the surface stresses. The variation of the contact pressure and the interlaminar shear stress for different shell parameters are also studied.
Geometry of a Bulged Diaphragm
Authors: Kular G. S. , Hillier M. J.
Published: November 2010

It is shown that the shape of the bulge deviates significantly from that of a spherical cap due to bending effects at the periphery. This result is independent of the state of anisotropy and will be significant when attempting to predict the critical strain at necking.
Elastic Layer Pressed Against a Half Space
Authors: Tsai K. C. , Dundurs J. , Keer L. M.
Published: November 2010

The paper considers the elastic layer which is pressed against a half space by loads that are not necessarily symmetric about the center of the loaded region. It is shown that the receding contact between the two bodies can be treated by means of superposition, leading to two homogeneous Fredholm integral equations for auxiliary functions that are directly related to the contact tractions. The determination of the extent of contact and the shift between the load and contact intervals can be viewed as an eigenvalue problem of the homogeneous integral equations. Specific numerical results are given for two types of triangular loads, and a comparison is made with certain symmetric loads.
Displacements and Stresses in a Two-Dimensional Wedge-Shaped Medium
Authors: Teng Y.-C. , Kuo J. T.
Published: November 2010

This paper deals with two-dimensional wedge problems in elastostatics—a single wedge and a welded multiwedge of arbitrary wedge angles and different elastic constants subjected to an inclined line load on the free surface of the wedge; and a single wedge subjected to an Nth multipole line load on the free surface of the wedge. The general expressions of stresses and displacements are obtained, neglecting body forces, in terms of Papkovitch functions. By satisfying the boundary conditions of the wedge problems, the formal solutions of stresses and displacements are obtained. The stresses and displacements for r < r0 and r > r0, where r0 is the position of load in r-direction, are evluated separately by means of the residue theorem. As examples, numerical results are obtained for several particular cases.
Lower Bounds to the Nth Eigenvalue of the Helmholz Equation Over Three-Dimensional Regions of Arbitrary Shape
Authors: Pnueli D.
Published: November 2010

A method is presented to compute a lower bound to the nth eigenvalue of the Helmholtz equation over three-dimensional regions. The shape of the regions is arbitrary and only their volume need be known.
The Stress Response of an Elastic Surface to a High-Velocity, Unlubricated Punch
Authors: Gerstle F. P. , Pearsall G. W.
Published: November 2010

Medium to high velocity linear sliding contact is modeled as the response of an elastic half space to an unlubricated punch, moving at constant speed. The stresses in the half space are derived explicitly, using the singular integral equation technique pioneered by Muskhelishvili. The solution is shown to satisfy all necessary mathematical and physical conditions, including an accurate prediction of the Rayleigh surface wave velocity. The normal stresses are evaluated and plotted to demonstrate the interplay between friction and inertial effects at various velocities.
A Multiparameter Perturbation Approach for the Vibration of Plates Subject to Arbitrary, Independent, In-Plane Loads
Authors: Bassily S. F. , Dickinson S. M.
Published: November 2010

A multiparameter perturbation approach for the solution of a class of differential equations is developed and is applied to the study of the vibration of rectangular plates under arbitrary in-plane loading fields describable by linear combinations of two or more independent loading parameters. The solution takes the form of a power series involving all the independent loading parameters and is valid over whole ranges of those parameters. Numerical results for fully clamped plates subject to uniform, combined, direct, and shear in-plane loads are presented in order to demonstrate the utility of the approach.
Free Vibrations of Longitudinally Stiffened Cylindrical Shells
Authors: Wang J. T. S. , Rinehart S. A.
Published: November 2010

This study is concerned with the free-vibration characteristics of thin cylindrical shells reinforced by longitudinal stringers for any edge boundary conditions. The structural system is treated as an isotropic cylinder interacting with a set of discrete thin-walled stringers. Frequencies of simply supported shells obtained according to the present analysis compare favorably with Ritz solution and existing experimental data. For mode shapes, the present analysis often yields much better results than Ritz solution. Numerical results for frequencies and mode shapes for clamped-clamped cylindrical shells are included, and frequencies of a shell with very flexible stiffeners compare favorably with frequencies of an unstiffened shell.
A Quantitative Model for Partially Activated Skeletal Muscle
Authors: Paslay P. R. , Clamann H. P. , Soechting J. F. , Stewart P. A. , Zahalak G. I. , Duffy J.
Published: November 2010

Most current knowledge concerning the mechanical behavior of skeletal muscle has been obtained from experiments in which the muscle is impulsively activated (twitch) or maximally activated (tetanus). In living organisms, however, muscle usually functions under conditions of gradually varying partial activation. In the present work equations are derived for partially activated whole muscle which relate the force exerted by the muscle, its contraction, velocity of contraction, and level of neural activation. This is accomplished by considering the sarcomere as the basic contractile unit; by describing its behavior according to a model due to Hill [8]; and predicting muscle behavior by integrating from the sarcomere through the fibril and the fiber to the whole muscle. When this is done it turns out that the model muscle is rather more complex than anticipated. The results should prove useful in modeling skeletal muscle for clinical purposes.
Water Jet Impact Damage at Convex, Concave, and Flat-Inclined Surfaces
Authors: Vickers G. W.
Published: November 2010

Results showing the damage arising from water jet impact on convex, concave, and flat-inclined polymethylmethacrylate targets are presented and discussed. The direction and distribution of surface cracks and pits within the zone of impact are related to liquid flow during the impact and the essential features of the damage are analyzed in terms of stress wave phenomena.
Plastic Analysis of Fiber-Reinforced Shells of Revolution
Authors: Bachrach B. I. , Lance R. H.
Published: November 2010

The yield surface for a shell of revolution which is loaded axisymmetrically and made of an anisotropic plastic material which obeys the maximum shear stress theory of Lance and Robinson is developed in this paper. The material is a model of a ductile matrix reinforced unidirectionally with ductile fibers. The principal axes of the material are assumed to be aligned with the principal axes of stress in the shell. Using the developed yield surface, the complete solution for the problem of plastic analysis of a shallow conical shell with circumferential reinforcement loaded by an axismmetric lateral force applied to a rigid central boss is obtained.
Shear Constraint and Macroscopic Fracture Criteria for Ductile Metals
Authors: Kaplan M. A. , Rowell G. A.
Published: November 2010

The role of material constraint in the shear fracture of ductile metals is investigated by means of a series of torsion and internal pressure tests on aluminum alloy tubing combined with analytical descriptions of the stress states at fracture. These descriptions include work hardening and, in the case of a tube under internal pressure, account for the nonaxisymmetric deformations that always precede fracture. The results, which indicate that shear fracture initiation depends on conditions at points far removed from the initiation site when the maximum shear stress vector there is directed through the interior of the body, are supported by the results of tensile tests on plates with shallow notches. These latter experiments are also used to show that tensile and shear fracture are governed by independent fracture criteria. A continuum fracture theory for ductile metals, based on the concepts of material constraint and independent fracture criteria, is proposed. The theory predicts fracture in terms of the stress state. A critical analysis of the theory is provided along with examples of fracture phenomena which the theory predicts, but which are not explained by existing theories.
Finite Width Foil Bearing With Light Loading
Authors: Langlois W. E.
Published: November 2010

The paper describes and illustrates a procedure for computing the deflection of a foil bearing due to a finite width bump when the load is light enough that perturbations of the foil position can be ignored insofar as solution of the Reynolds equation is concerned.
Consistent Formulation of Sound Radiation From Arbitrary Structure
Authors: Engblom J. J. , Nelson R. B.
Published: November 2010

A refined and efficient approach is presented for determining the radiated sound pressure levels in an infinite acoustic medium produced by a closed structure undergoing harmonic vibratory motion. Refined acoustic and equilibrium relationships are developed and quadratic approximations are used to define the acoustic variables on the radiating surface. Efficiencies are inherent in the modal approach utilized to define an equilibrium relationship and in the treatment of improper integral forms. Examples include the special problem of a finite cylindrical cavity for which uniform radial velocity is specified. Also investigated is a thin elastic sphere for which particular modes of vibration are specified.
A General Approximation Theory for Mechanism Synthesis
Authors: Gupta K. C. , Roth B.
Published: November 2010

It is shown how to determine those points, in a system under planar motion, which have trajectories which over a given range best approximate circles and straight lines. These points are best approximations in the sense of having a minimum error-norm. In this work a general norm is used which results in an approximation theory which includes the least-square and mini-max approximations as special cases. Several special motions are considered in detail, and some applications to linkage design are given.
Solute Distribution in the Flow in a Channel Bounded by Porous Layers: A Model of the Lung
Authors: Fung Y. C. , Tang H. T.
Published: November 2010

The tracer (indicator-dilution) technique is often used to measure the volume of interstitial water in the lung tissue. The basic hypotheses required for the validity of the formula: volume = flow × (mean transit time) are reviewed. One of the conditions is that, at a steady state, the average concentration of the tracer over the entire system be equal to the concentration at the sampling site. It is shown that if a tracer (such as THO) is permeable through the membrane that separates the blood from the tissue space, which in turn is limited by an impermeable wall, then, at a steady state, the concentration of that tracer is uniform in both compartments. If a tracer is confined to the vascular space by a semipermeable membrane, then its concentration is nonuniform, but the average value meets the requirement of the tracer-volume formula.
Longitudinal Dispersion of Tracer Particles in the Blood Flowing in a Pulmonary Alveolar Sheet
Authors: Fung Y. C. , Tang H. T.
Published: November 2010

The analysis of G. I. Taylor on the dispersion of solutes in a circular cylindrical tube is extended to the case of flow in a channel bounded by porous layers. Creeping flow in the channel and the porous layers stimulates the blood flow in the alveolar sheets of the lung. Overall perturbation on the longitudinal dispersion due to the porous layers is evaluated. It is shown that the mean coefficient of apparent diffusivity is smaller in a channel bounded by porous layers than that in a channel with impermeable walls for the case that the channel walls are permeable to solvent but not to tracer. For the case that channel walls are permeable to both solvent and tracer, the mean coefficient of apparent diffusivity is nearly the same as that of a channel with impermeable walls.
Influence of Stored Angular Momentum on the Modal Characteristics of Spacecraft With Flexible Appendages
Authors: Hughes P. C. , Sharpe H. N.
Published: November 2010

The attitude dynamics and control of flexible spacecraft are more clearly understood if the natural frequencies of oscillation are known for these spacecraft. The influence of stored angular momentum hs (for example, dual-spin vehicles, or vehicles with a momentum wheel) on these natural frequencies is determined in terms of the appendage characteristics, the inertia distribution, and hs. Primary emphasis is placed on general qualitative results. The discussion is illustrated with an example.
Wave Propagation and Parametric Instability in Materials Reinforced by Fibers With Periodically Varying Directions
Authors: Schoenberg M. , Weitsman Y.
Published: November 2010

This paper concerns the propagation of plane harmonic waves in an infinite fiber-reinforced elastic medium. The composite material is represented by an equivalent homogeneous transversely isotropic matter whose preferred directions coincide with the orientations of the fibers. The fibers are assumed to wobble periodically about a dominant direction, all fibers being parallel to each other. This wobbliness endows the material with a structural periodicity which generates dispersion at all frequencies and instability for various frequency bands. The zones of instability are analyzed in some detail.
Behavior of Dynamical Systems Governed by a Simple Nonlinear Difference Equation
Authors: Hsu C. S. , Yee H. C.
Published: November 2010

Many dynamical systems and mechanics problems are governed by nonlinear difference equations. These equations have also been used increasingly to model problems in population dynamics, economics, and ecology. In this paper we study systems governed by the nonlinear difference equation (4). The locally asymptotically stable periodic solutions are investigated and the global behavior of the system for different values of the system parameter and for different initial conditions is examined. Although the equation is a simple one, the general pattern of its solution is surprisingly complex and seems to have implications in many fields.
Strain-Rate Effect in the Endochronic Theory of Viscoplasticity
Authors: Lin H.-C. , Wu H.-C.
Published: November 2010

An explicit function of material parameter β1 is proposed to accommodate the strain-rate effect in the endochronic theory of viscoplasticity developed by Valanis. The strain-rate effects are treated in a manner that includes strain-rate history dependence. The theoretical stress-strain curves at constant strain rates are presented and compared with the existing experimental data. Based on this constitutive equation, the solution of one-dimensional plastic wave propagation in thin rods is obtained for annealed aluminum and copper. The theoretical strain-time profiles are in qualitative and quantitative agreement with the experimental results. It has been shown theoretically that the consideration of the strain-rate effect in the endochronic theory lowers the final constant strain states in the strain-time profiles.
On the Influence of the Geometry of the Foundation on Its Impulse Response
Authors: Umek A.
Published: November 2010

The influence of the foundation geometry on the antiplane impulse response of an embedded foundation is the topic. The foundations of a semicircular and a rectangular cross section are selected as characteristic examples. First, the impulse response for the semicylindrical foundation is obtained from its admittance derived by Luco and Trifunac. Then it is compared with the impulse response of the rectangular foundation as obtained by Thau and Umek. On the basis of this comparison it can be concluded, that the foundation geometry does not decisively influence its antiplane impulse response.
Dynamic Behavior of Ideal Fibre-Reinforced Rigid-Plastic Beams
Authors: Jones Norman
Published: November 2010

Theoretical solutions are developed herein for the dynamic plastic structural response of some ideal fibre-reinforced (strongly anisotropic) beams with boundary conditions and external dynamic loadings which can be reproduced easily and reliably in a laboratory. The theoretical behavior of these beams is also compared to the corresponding dynamic response of beams which are made from a rigid perfectly plastic isotropic material. Generally speaking, it appears that the permanent transverse deflections and response durations of ideal fibre-reinforced beams loaded dynamically are less than the corresponding values for similar rigid perfectly plastic isotropic beams.
The Energy Stability Limit for Flow in a Curved Channel
Authors: Jankowski D. F. , Takeuchi D. I.
Published: November 2010

The energy stability limit is calculated for flow in a curved channel due to a pressure gradient acting around the channel. The energy limit is found among transverse disturbances and is of the same order for all channel radius ratios. The difference between the previously available linear limit and the energy limit increases dramatically as the instability mechanism changes, with radius ratio, from centrifugal force to viscosity in the limiting plane Poiseuille flow case.
The Turbulent Boundary Layer Near a Corner
Authors: Shafir M. , Rubin S. G.
Published: November 2010

Turbulent boundary-layer behavior in the vicinity of a right-angle corner formed by intersecting flat plates is considered. Due to interference effects a secondary flow is induced. Numerical solutions are obtained for the main stream and secondary motion. Models with and without intermittency factors are considered. It is shown that the secondary motion is significantly different for laminar and turbulent conditions. Similar behavior has previously been observed experimentally.
Low Knudsen Number Creeping Motion of Two Touching Spheres
Authors: Reed L. D. , Morrison F. A.
Published: November 2010

The creeping motion of an aerosol aggregate composed of two touching spheres is investigated. A continuum-slip theory, suitable for small values of Knudsen number, is developed. The drag on a pair of equal spheres moving along their line of centers is determined. For vanishing Knudsen number, this drag reduces to Faxe´n’s result. Theoretical results for the effect of small Knudsen number are compared with an approximate expression based on calculations for separated spheres.
A Theoretical and Experimental Investigation of Creep Problems With Variable Temperature
Authors: Ponter A. R. S. , Walter M. H.
Published: November 2010

Rapid cycling solutions are presented for a simple two-bar structure subjected to variable temperature. Three constitutive relationships are considered, nonlinear viscous, strain-hardening and Bailey-Orowan models which describe differing aspects of the creep of metals. It is shown that the solutions for the viscous and strain-hardening relations are essentially similar and possess distinct reference stress histories over ranges of the governing parameters. The presence of recovery in the Bailey-Orowan model causes a distinctly different mode of behavior. Experimental results on a simulated two-bar structure are presented, under conditions where the strain-hardening hypothesis may be expected to be most relevant. Good agreement is obtained between theory and experiment although the presence of anelastic creep, with a short time scale, tends to reduce the effective thermoelastic stresses.
The Vibration of an Elliptic Ring Membrane
Authors: Ozkul A. G. , Chen Y.
Published: November 2010

The vibration of an elliptic ring clamped along two confocal ellipses was studied by McLachlan some time ago. Due to complexities in the computations of Mathieu functions, numerical results were not available. In this Note the fundamental frequencies of clamped ring membranes with a fixed area enclosed between two confocal ellipses of various eccentricities are computed. Results are presented in a tabulated form.
The Influence of Heating on the Stability of Laminar Boundary Layers Along Concave Curved Walls
Authors: Kahawita R. , Meroney R.
Published: November 2010

This paper considers the effect of heating on Taylor-Go¨rtler vortices in laminar boundary layers. The effect of higher-order terms and the normal velocity component of the primary flow in the stability calculations has been demonstrated. The findings indicate that terms involving the higher-order effects of curvature as well as the normal component of the primary flow become increasingly important at small wave numbers. The effect of heating is to stabilize the flow to disturbances of long lateral wavelength but has a destabilizing effect on short wavelength disturbances.
Solution Bounds for Transient Vibration Problems
Authors: McDaniel T. J. , Testa F. J. , Babu P. V. Thangam
Published: November 2010

The theory of differential inequalities is applied to systems of nonlinear differential equations of the initial value type. Established bounding theorems are used to construct bounds on the solution of these equations and to develop an iterative procedure for improving these bounds. The methods are illustrated by constructing upper and lower solution bounds for one and two-degree-of-freedom dynamic systems.
An Alternative Representation of the Elastic-Viscoelastic Correspondence Principle for Harmonic Oscillations
Authors: Dasgupta G. , Sackman J. L.
Published: November 2010

An alternative representation of the elastic-viscoelastic correspondence principle is derived for solids with identical damping characteristics in bulk and shear undergoing steady-state harmonic motion. This form is particularly useful when the elastic solution of the mechanical system is not available in closed form but is known only numerically, say as a tabular list. The analyticity property of the frequency response function is utilized to formulate a Dirichlet problem in the lower half of the complex plane with the elastic solution on the real line supplying the boundary data. The expression for the viscoelastic frequency response function is then obtained as an infinite integral in which the elastic frequency response and the viscoelastic parameters constitute the integrand. This integral may be evaluated numerically by quadrature to any desired degree of accuracy by suitably increasing the range of integration and employing a finer mesh. Any isolated singularity in the elastic response, like poles at the resonant frequencies, can be very accurately handled by using exact complex integration in the sense of Cauchy principal value. A simple example is presented to illustrate an application of this alternative formulation.
Flow-Induced Bending of Rectangular Plates
Authors: Kim Y. T. , Scarton H. A.
Published: November 2010

An analysis of flow-induced bending of rectangular plates simply supported on two sides and free on the leading and trailing edges, with viscous entry flows differing in flow rate on top and bottom, is presented. Viscous shear is shown to be important in modifying the plate deflection near the leading edge. The flow rate is maximized and deflection minimized by using relatively small length-to-width ratios. The results are directly applicable to stacked rectangular fuel-bearing plates in nuclear reactors.
Stress-Induced Radial Pressure Gradients in Liquid-Filled Multiple Concentric Cylinders
Authors: Munro M. , Piekarski K.
Published: November 2010

The concept of liquid-filled multiple concentric cylinders under compressive axial loading is investigated. An analytical model to predict the hydrostatic pressures in the liquid regions is formulated. It is found that upon loading a radially decreasing pressure gradient in the liquid layers is produced. The values of hydrostatic pressure from an experimental model comprising aluminum cylinders filled with hydraulic oil show good agreement with those predicted by the analytical model.
Edge Effect Influence on Magnetoelastic Buckling of Rectangular Plates
Authors: Dalrymple J. M. , Peach M. O. , Viegelahn G. L.
Published: November 2010

This paper extends the Moon-Pao theoretical treatment of the buckling of a rectangular beam of infinite length l and infinite width w to the case (a) l infinite, w finite, and the case (b) l finite, w infinite. Then an approximate formulation is used to obtain a lower bound to the critical buckling field for the case (c) l finite, w finite. It is concluded that finite specimen size alone cannot account for the discrepancy between the Moon-Pao theory and experiments.
Large Deflection of a Rectangular Plate Resting on a Pasternak-Type Elastic Foundation
Authors: Ghosh P. K.
Published: November 2010

The problem of large deflection of a rectangular plate resting on a Pasternak-type foundation and subjected to a uniform lateral load has been investigated by utilizing the linearized equation of plates due to H. M. Berger. The solutions derived and based on the effect of the two base parameters have been carried to practical conclusions by presenting graphs for bending moments and shear forces for a square plate with all edges simply supported.