bluuebunny/crossref_metadata_2025 huggingface dataset:
Rotational Sliding of Rubber: Second-Order Stresses, Seizure, and Buckling
Authors: Gent A. N. , Henry R. L.
Published: July 2009

Measurements are described of the frictional torque required to make a flat-ended rubber cylinder, bonded at one end to a flat metal plate, rotate about the cylinder axis when the other end is pressed against a flat Plexiglas surface. The contact pressure is found to increase on rotation, by an amount proportional to the square of the torsional deformation of the cylinder. The frictional torque then tends toward extremely large values (seizure) when the imposed compression approaches a critical level of about 20 percent, as predicted by theory. The rubber cylinder then transforms to a nonuniform state of deformation in which parts of the curved surfaces are drawn into contact with the Plexiglas surface. Sliding continues in this torsionally buckled state, at relatively low pressures and torques.
The Interaction Between a System of Circular Punches on an Elastic Half Space
Authors: Gladwell G. M. L. , Fabrikant V. I.
Published: July 2009

Galin derived an expression for the pressure produced under a rigid circular punch by the application of a concentrated load at another point of the half space. This result is used to derive approximate relationships among the forces, moments, and indentations for a system of punches on an elastic half space. The results are compared with a number of earlier approximate solutions.
Nonlinear Oscillations of Laminated, Anisotropic, Rectangular Plates
Authors: Reddy J. N. , Chao W. C.
Published: July 2009

A finite-element analysis of the equations governing the large-amplitude, free, flexural oscillations of laminated, anisotropic, rectangular plates is presented. The equations account for transverse shear strains as well as large rotations. Numerical results of nonlinear fundamental frequencies are presented for rectangular plates of both angle-ply and cross-ply constructions. The effects of amplitude, boundary conditions, transverse shear, aspect ratio, orientation of layers, and materials anisotrophy on natural frequencies are investigated. The present finite element results agree with other approximate solutions available in the literature.
The Axisymmetrical Steady-State Response of Internally Damped Annular Double-Plate Systems
Authors: Irie T. , Yamada G. , Muramoto Y.
Published: July 2009

The axisymmetrical steady-state response of an internally damped, annular double-plate system interconnected by several springs uniformly distributed along concentric circles to a sinusoidally varying force is determined by the transfer matrix technique. Once the transfer matrix of an annular plate has been determined analytically, the response of the system is obtained by the product of the transfer matrices of each plate and the point matrices at each connecting circle. By the application of the method, the driving-point impedance, transfer impedance, and force transmissibility are calculated numerically for a free-clamped system and a simply supported system.
On the Mean Reynolds Equation in the Presence of Homogeneous Random Surface Roughness
Authors: Phan-Thien N.
Published: July 2009

Assuming that the surface roughness is of small amplitude and can be modeled by a homogeneous random function in space, the classical Reynolds equation is averaged using a method due to J. B. Keller. The mean Reynolds equation is accurate up to terms of 0(ε2), where ε is the dimensionless amplitude of the surface roughness and has a nonlocal character. Furthermore, by exploiting the slowly varying property of the mean film thickness, this nonlocal character is eliminated. The resulting mean Reynolds equation depends on the surface roughness via its spectral density and, in the limits of either parallel or transverse surface roughness, it reduces to Christensen’s theory.
One Solution of Three-Dimensional Boundary Value Problems in the Couple-Stress Theory of Elasticity
Authors: Kishida M. , Sasaki K. , Hanzawa H.
Published: July 2009

This paper describes a numerical approach for elastic boundary value problems in the linear, couple-stress theory on the basis of the “indirect fictitious-boundary integral method.” In this approach we introduce appropriate potentials corresponding to those for a concentrated force and a couple in an infinite medium, and reduce the problem to solving the simultaneous Fredholm type integral equations of the first kind. As an example, the stress concentration problem is analyzed for a circular cylinder with a semicircular annular groove under uniaxial tension. The results are obtained for various values of parameters such as Poisson’s ratio ν, characteristic length l, and the ratio ηr of bending, twisting moduli.
The Contact of a Cuspidal Crack
Authors: Wu C. H.
Published: July 2009

A simplified airfoil mapping is used to define a cuspidal crack. The objective is to investigate the effects of compressive loads on an infinite solid containing crack-like flaws. Such an objective cannot be achieved by using the conventional line crack to characterize the flaws. The associated contact problem is solved exactly by assuming that the contact region is small in comparison to the crack length. It is shown that the well-known Barenblatt model is just the present contact problem in reverse. Moreover, a specific functional form is determined to describe the so-called cohesive force which was assumed to be a material function by Barenblatt.
On Stochastic Dynamics of an Embedded Rigid Cylinder
Authors: Beltzer A. , Parnes R.
Published: July 2009

Multidegree-of-freedom vibrations are considered for a rigid cylinder embedded in an isotropic elastic medium that is subjected to random propagating disturbances. The numerical results obtained enable one to select values of parameters of the system which would provide desirable motions of the inclusion.
Edge Effect in the Bending of Inextensible Plates
Authors: Kuznetsov E. N.
Published: July 2009

In the uniaxial bending of an elastic plate, a boundary layer develops along each free edge in the form of a small ripple in the deformed midsurface. The layer provides a smooth transition from the zero transverse bending moment at the edge to the required value in the plate interior. For an inextensible plate, the formation of this type of a boundary layer is impossible. An alternative mechanism for providng this transition is identified and investigated.
Similarity Analysis of Gas-Liquid Spray Systems
Authors: Yeung W.-S.
Published: July 2009

This paper discusses the fluid mechanics of the droplet-dispersed region of a liquid-spray system. Similarity solutions are sought under various assumptions for two types of common spray: the conical spray and the flat spray. Following the classical approach of Schlichting, for turbulent jet analysis, we obtain a similarity solution for the flat spray under the condition that the droplet motion is not influenced by gravity and interfacial drag. The solution is quite realistic from a physical standpoint. Finally, comparison between the theory and limited experimental data was found to give good agreement.
A Model of the Turbulent Burst Phenomenon: Fully Developed Transitional Turbulent Flow Between Parallel Plates
Authors: Thomas L. C. , Kadry H. M.
Published: July 2009

An analysis is presented for fully developed transitional turbulent flow between parallel plates that features the use of a turbulent burst model for the important wall region. Model closure is accomplished by the specification of the mean burst frequency and, for moderate to high Reynolds numbers, by matching with a classical eddy viscosity model for the turbulent core. Predictions obtained for friction factor and mean velocity distribution are compared with experimental data for fully developed transitional turbulent flow in a channel with large aspect ratio. Predictions are also developed for the eddy viscosity within the wall region for transitional turbulent conditions.
Conservation Laws and Material Momentum in Thermoelasticity
Authors: Francfort G. , Golebiewska Herrmann A.
Published: July 2009

The main goal of this paper is to construct a Lagrangian function such that not only the well-known equations of thermoelasticity, but also material conservation laws can be derived. As action variables, the position x of a material particle and a scalar function η related to temperature are used. The material momentum for thermoelasticity is derived. Here, by contrast to the purely elastic case, the material momentum depends on a time interval rather than on an instant of time. The balance of material momentum is integrated over time to produce a relation reminiscent of the impulse-momentum equation in classical mechanics.
The Stefan Problem With an Imperfect Thermal Contact at the Interface
Authors: Tao L. N.
Published: July 2009

The Stefan problem in a semi-infinite region with arbitrarily prescribed initial and boundary conditions, subject to a condition of the mixed type at the interface is investigated. To establish the exact solution of the problem, some new basic solutions of the heat equation are offered. Their mathematical properties are also supplied. The exact solutions of the temperatures in both phases and of the interfacial boundary are derived in infinite series. The existence and uniqueness of these series are considered and proved. It is also shown that these series are absolutely and uniformly convergent. Some concluding remarks about the differences between the present problem and the classical Stefan problem are given. Also the effect of a density discontinuity at the interface is discussed.
Plastic Stress Intensity Factors for Small Scale Yielding in Antiplane Shear by Caustics
Authors: Theocaris P. S. , Razem C. I.
Published: July 2009

The KIII-stress intensity factor in an edge-cracked plate submitted to antiplane shear may be evaluated by the reflected caustic created around the crack tip, provided that a purely elastic behavior exists at the crack tip [1]. For a work-hardening, elastic-plastic material, when stresses at the vicinity of the crack tip exceed the yield limit of the material, the new shape of caustic differs substantially from the corresponding shape of the elastic solution. In this paper the shape and size of the caustics created at the tip of the crack, when small-scale yielding is established in the vicinity of the crack tip, were studied, based on a closed-form solution introduced by Rice [2]. The plastic stress intensity factor may be evaluated from the dimensions of the plastic caustic. Experimental evidence with cracked plates made of opaque materials, like steel, corroborated the results of the theory.
Surface Instability and Splitting in Compressed Brittle Elastic Solids Containing Crack Arrays
Authors: Keer L. M. , Nemat-Nasser S. , Oranratnachai A.
Published: July 2009

Surface instability in brittle solids may occur at relatively small values of the inplane compressive force if the solid contains shallow cracks parallel to its free surface. The instability may produce surface damage by spallation. Similarly, the buckling load of a longitudinally compressed strip that contains an array of central cracks is affected to a great extent by the size and the relative spacing of these cracks. The instability in this case may result in longitudinal splitting of the strip. To illustrate these phenomena, the compression of an elastic half space and a layer, each containing an array of coplanar equally spaced cracks, is studied for a special class of hypoelastic materials, and the corresponding weakening due to cracks is analytically estimated.
Radiation From Expanding Circular Dislocation Loops and Elastic Precursor Decay
Authors: Markenscoff X. , Clifton R. J.
Published: July 2009

The solution is given for a circular dislocation loop that instantaneously begins to expand by gliding in its plane at constant velocity. The material is assumed to be elastic and isotropic. The solution, expressed as an integral over the loop and over previous times, is evaluated explicitly near the wavefront. This wavefront solution is used to derive an expression for the decay in amplitude of an elastic plane wave propagating in the direction perpendicular to the plane of the loop due to the radiation of elastic waves from the expanding loops. By superimposing the effects of many loops set in motion as the plane wavefront passes, a relation is derived for the decay of the front of the plane wave. This precursor decay relation is found to be the same as obtained previously for infinitely long, straight dislocations based on consideration of either elastic waves radiated from discrete dislocations or energy dissipated in an elastic/viscoplastic continuum model of the material. Thus, dislocation line curvature can apparently be regarded as unimportant in the attenuation of the amplitude of the wavefront. Because detectors have finite rise times, measured precursor amplitudes are indicative of wave amplitudes at small but finite times Δt after the wavefront arrives. Evaluation of the effects of dislocation line curvature on wave amplitudes behind the wavefront requires the consideration of higher order terms in Δt which are neglected in the present analysis.
A Probabilistic Theory of Nonlinear Dynamical Systems Based on the Cell State Space Concept
Authors: Hsu C. S.
Published: July 2009

Developed in the paper is a probabilistic theory for nonlinear dynamical systems. The theory is based on discretizing the state space into a cell structure and using the cell probability functions to describe the state of a system. Although the dynamical system may be highly nonlinear the probabilistic formulation always leads to a set of linear ordinary differential equations. The evolution of the probability distribution among the cells can then be studied by applying the theory of Markov processes to this set of equations. It is believed that this development possibly offers a new approach to the global analysis of nonlinear systems.
A Theory of Substructure Modal Synthesis
Authors: Kubomura K.
Published: July 2009

A theory is presented for representing the displacements of a substructure finite-element mathematical model with a reduced number of degrees of freedom. A first or second-order approximation is used for the substructure’s modal coordinates associated with significantly larger or smaller eigenvalues than the system eigenvalues of excitation. The derived representations of the substructure displacements are capable of employing any type of substructure natural mode; free-free, cantilever or hybrid mode, and of retaining the dynamic behavior of any frequency range. It is shown that the present representations compute the system eigenvalues of interest with satisfactory accuracy, and it appears that the second-order approximation methods compute the system eigenvalues with greater accuracy than the first-order methods.
Natural Frequencies of Out-of-Plane Vibration of Arcs
Authors: Irie T. , Yamada G. , Tanaka K.
Published: July 2009

The natural frequencies of out-of-plane vibration based on the Timoshenko beam theory are calculated numerically for uniform arcs of circular cross section under all combination of boundary conditions, and the results are presented in some figures.
Stability of the Vibrations of a Parameter-Excited System
Authors: Gu¨rgo¨ze M.
Published: July 2009

The subject of this Brief Note is to introduce a special parameter-excited system with two degrees of freedom, which has its principal instability region at ω ≈ ω0 instead at ω ≈ 2ω0. It consists of a horizontal plate with a fixed pin and a slotted rigid bar on it, in which the bar can rotate and translate with respect to the plate. The stability of its vibrations is investigated for the case in which the plate is harmonicaly excited in its own plane. Starting with the Mathieu differential equation, which governs the rotational vibrations, it is possible to predict the excitation frequencies, which must be avoided, to ensure the stability.
T-Matrix Approach to Scattering of Elastic (SH-) Waves by an Inclined Surface Void
Authors: Tsao S. J. , Varadan V. V. , Varadan V. K.
Published: July 2009

This study is concerned with the T-matrix method to solve the scattering of SH-waves by an inclined surface-breaking void in a homogeneous elastic half space. Additional complications arising from the inclination of the surface cavity have been overcome by using suitable basis functions for the surface displacements in the T-matrix method and the method of images. Numerical results are presented for elliptical cavities for two different angles of inclination, two aspect ratios for various angles of incidence, observation, and frequency. The T-matrix results are compared with the results obtained from a hybrid finite-element wave-expansion method.
Instabilities of a Finitely Deformed Fiber-Reinforced Elastic Material
Authors: Triantafyllidis N. , Abeyaratne R.
Published: July 2009

The instabilities of a finitely deformed Blatz-Ko material reinforced with fibers in a single direction (an anisotropic, nonlinearly elastic material) are examined. The loading is one of plane strain uniaxial stress with the load axis being inclined with respect to the fiber direction. In general one finds a critical applied stress (or stretch) at which surface instabilities of the body occur. This is then followed by a shear band-type instability. For a certain range of fiber orientations these instabilites appear a maximum stress level has been reached. It has also been found that when the fiber direction approaches the loading axis, the material is stabilized in tension but destabilized in compression.
Delamination Buckling and Growth in Laminates
Authors: Bottega W. J. , Maewal A.
Published: July 2009

The phenomenon of delamination buckling and growth in a compressively loaded, two-layer circular plate is analyzed. Geometrical nonlinearity is included in the model in order to determine the effect of postbuckling stiffness on the delamination growth process, and the influence of imperfections in the form of transverse loads is also examined.
Component Mode Analysis of Nonlinear, Nonconservative Systems
Authors: Tongue B. H. , Dowell E. H.
Published: July 2009

In this paper a method for attacking coupled linear-nonlinear problems is developed. This method allows one to express the equations of motion with a number of equations proportional to the number of nonlinear constraints on the system rather than to the number of linear modes of the system. Both steady state and transient solutions are investigated for a system possessing cubic nonlinearities.
Stability of Nonparallel Developing Flow in a Pipe to Nonaxisymmetric Disturbances
Authors: Garg V. K.
Published: July 2009

Linear spatial stability of the nonparallel developing flow in a rigid circular pipe has been studied at several axial locations for nonaxisymmetric disturbances. The main flow velocity profile is obtained by Hornbeck’s finite-difference method assuming uniform flow at entry to the pipe. The method of multiple scales is used to account for all the nonparallel effects. It is found that the nonparallel developing flow is most unstable to nonaxisymmetric disturbances with azimuthal wave number n equal to unity. Axisymmetric disturbances are, however, more unstable than nonaxisymmetric disturbances with n ≥ 2 except in the near-entry region. The results show that the parallel flow theory overpredicts the critical Reynolds number by as much as 136.5 percent in the near entry region for the n = 1 disturbance. The present results compare well with the available experimental data.
Cumulative Effect at the Soil Surface Due to Shear Wave Propagation
Authors: Zak M.
Published: July 2009

A cumulation of the shear strain energy at the soil surface as a response to underground shear excitations is considered. It is shown that this effect is caused by the vanishing shear modulus at the soil surface. The corresponding mathematical model is presented by a linear hyperbolic equation with variable coefficients. The uniqueness and stability of the solutions are analyzed.
The Penny-Shaped Interface Crack With Heat Flow, Part 1: Perfect Contact
Authors: Martin-Moran C. J. , Barber J. R. , Comninou M.
Published: July 2009

A solution is given for the thermal stresses due to a penny-shaped crack at the interface between dissimilar materials loaded in tension for the case where the heat flux is into the material with higher distortivity. Regions of separation and perfect thermal contact are developed at the crack faces. A harmonic potential function representation is used to reduce the problem to a three-part boundary value problem which is formulated as a pair of coupled Abel integral equations using the method of Green and Collins. These equations are further reduced to a single Fredholm equation which is solved numerically. Results are presented illustrating the effect of heat flux and applied tractions on the contact radius and the stress intensity factors for various combinations of material constants. The effect of heat flux is profoundly influenced by the relative signs of Dundurs constant β and a constant γ describing the mismatch of distortivities. If the more distortive material is also the more rigid, the contact region at the crack face is reduced by heat flow; otherwise it is increased. In the latter case, solutions involving separation are obtained even for applied compressive tractions if the latter is within a certain range. The solution also exhibits nonuniqueness in this range.
Stress Distributions for a Quarter Plane Containing an Arbitrarily Oriented Crack
Authors: Keer L. M. , Lee J. C. , Mura T.
Published: July 2009

A solution for an elastic quarter plane containing an arbitrarily oriented crack is presented. The problem is formulated by means of Mellin integral transforms and reduced to a system of two coupled singular integral equations where the unknown quantities are the dislocation densities that characterize the crack. Numerical solutions are investigated for various orientations of the cracks. In each case the stress intensity factors are computed for the different parameters.
Unified Approach to the Solution of Problems of Unsteady Laminar Flow in Long Pipes
Authors: Letelier S. M. F. , Leutheusser H. J.
Published: July 2009

The paper presents a unified approach to the solution of laminar pipe-flow transients in which the forcing function may depend on the motion itself. The key to the solution procedure is a power series expansion of the local velocity in terms of radial position, involving a single time-dependent coefficient. The method of analysis is applied to the solution of two particular cases of transients, namely flow establishment, without and with inflow, respectively. It is found to yield results that are in excellent agreement with other known analytical solutions and experimental observations.
Buckling and Postbuckling of a Long-Hanging Elastic Column Due to a Bottom Load
Authors: Wang C. Y.
Published: July 2009

A long heavy elastic column is supported at the top end. The bottom end is subjected to a compressive force. The critical buckling loads, related to zeroes of Airy functions, are quite different from the Euler buckling loads. Postbuckling shapes are integrated numerically.
Theoretical and Experimental Investigation of the Nonlinear Torsion and Extension of Initially Twisted Bars
Authors: Rosen A.
Published: July 2009

A set of nonlinear equations that describe the nonlinear deformation of initially twisted bars under the influence of torsional moment and tension force, which act simultaneously, are derived. Special attention is devoted to the case of thin symmetrical cross sections and the equations appropriate to this case are shown. The linear terms of the equations, in the case of thin rectangular cross sections, are compared to solutions of the same problem, obtained by other researchers, who investigated the torsion and extension of helicoidal shells. It is shown that even for thin cross sections having large values of initial twist, the deviations between the two linear solutions are very small. To check the applicability of the theory to nonlinear regions, the theoretical results are compared to experimental results obtained during the course of the present research. The experiments include the torsion and extension of thin steel strips having rectangular cross sections. The agreement between both is very good, which proves the validity of the theory.
Inversion of Creep Response for Retardation Spectra and Dynamic Viscoelastic Functions
Authors: Thigpen L. , Hedstrom G. W. , Bonner B. P.
Published: July 2009

The basic problem addressed here is that of obtaining the unknown retardation time spectrum from experimental creep response curves. The spectrum may be a set of discrete times or it may be a spectrum characterized by a continuous distribution function. The present work employs a general model which assumes that the observed creep compliance is due to the summed effect of an arbitrary distribution of mechanisms. The analysis requires the solution of Fredholm integral equations of the first kind. It is well known that this problem is ill-conditioned so that any numerical scheme will have to involve some smoothing to obtain accurate solutions. The present work employs Butler’s method of constrained regularization which takes advantage of the fact that the solution is positive and uses data-dependent smoothing. This work indicates that the imposition of the positivity constraint makes the computation of the solution much better conditioned. Computations with the method of constrained regularization employing near-optimal smoothing demonstrate its superiority over the method of Schapery for obtaining accurate solutions when the data are very noisy.
Equivalent Linearization for Continuous Dynamical Systems
Authors: Iwan W. D. , Krousgrill C. M.
Published: July 2009

An approximate method is presented for determining the dynamical response of certain continuous nonlinear systems. In the proposed method, the system equation is linearized in the time domain prior to generation of a solution in the spatial domain. The approach is particularly suited to problems with complex boundary conditions which make selection of realistic global, spatial, domain comparison functions difficult. The approach is ideally suited to problems where discretization using finite elements is appropriate. The transverse response of a nonlinear rectangular plate is examined by way of the application of the proposed method.
Rotating Compressible Flow Over an Infinite Disk
Authors: Solan A. , Olek S. , Toren M.
Published: July 2009

The laminar boundary layer in rotating compressible flow over an infinite rotating disk is considered for various ratios of disk-to-infinity rotation rates and temperatures. It is shown that a similarity solution exists for Td/T∞ < (Ωd/Ω∞)2 and linearized solutions near this limit are presented. Numerical solutions for flow and temperature are given for representative values of the parameters, near and far from the limit.
The Effect of Viscosity on the Forced Vibrations of a Fluid-Filled Elastic Shell
Authors: Su T. C.
Published: July 2009

The effect of viscosity on the axisymmetric, forced vibrations of a fluid-filled, elastic, spherical shell is studied analytically. Necessary theory, using boundary layer approximation for the fluid as developed in a previous paper for free vibrations, has been extended to incorporate an external forcing excitation. Shell response, fluid loading, and energy dissipation rate are computed for radial, tangential, and combined force excitations. The essential feature of the modal and the total responses is determined by resonant frequencies and various vibration-absorbing frequencies. Frequency spectra for such frequencies, as well as various response curves, are presented in dimensionless forms to illustrate the characteristics of the solution.
Developments in High-Speed Viscoplastic Flow Through Conical Converging Dies
Authors: Camenschi G. , Cristescu N. , S¸andru N.
Published: July 2009

The problem of high-speed wire drawing is solved based on a global Coulomb friction condition on the die surface. The drawing force is determined as a function of the die angle, friction coefficient, reduction in area, and the Bingham number.
Statistical Cumulative Damage Theory for Fatigue Life Prediction
Authors: Hashin Z.
Published: July 2009

A statistical cumulative damage theory is developed with the purpose of prediction of mean, standard deviation and probability density of fatigue lifetime of randomly variable specimens subjected to the same deterministic cyclic loading program. The theory requires availability of a deterministic cumulative damage theory for ideal nonvariable specimens, called clones. Detailed analysis is given for two-stage cyclic loading based on a previously developed deterministic cumulative damage theory and log-normal distribution of S—N curve lifetimes. Results indicate that the usual interpretation of deterministic cumulative damage theory in terms of means of lifetimes is not valid for significant scatter. Preliminary experimental results for two-stage loading are compared with analytical predictions.
Nonlinear Analysis of a Dynamical System Being Pulled by Cables
Authors: Aranha J. A. P. , Martins C. A.
Published: July 2009

Offshore pipeline must, in certain situation, be pulled by means of cables placed in a barge. An important nonlinear aspect of the wave-induced dynamic motion is the fact that the cable can become loose. This paper analyzes a simplified dynamical model whose steady state is obtained analytically. A feature of this model is that the output steady state frequency changes from ω to ω/2 as the input (wave) frequency ω increases. An order of magnitude analysis shows that this nonlinear effect is of importance for the usual offshore pipeline.
Forced Nonlinear Oscillations of an Autoparametric System—Part 1: Periodic Responses
Authors: Hatwal H. , Mallik A. K. , Ghosh A.
Published: July 2009

Forced oscillations of a two degree-of-freedom autoparametric system are studied with moderately high excitations. The approximate results obtained by the method of harmonic balance are found to be satisfactory by comparing with those obtained by numerical integration. In the primary parametric instability zone, separate regions of stable and unstable harmonic solutions are obtained. In the regions of unstable harmonic solutions, depending on the forcing amplitude and frequency, the solutions may be amplitude modulated or completely nonperiodic. In the latter case the numerical integrations do not converge.
Control of Reflector Vibrations in Large Spaceborne Antennas by Means of Movable Dampers
Authors: Wang P. K. C. , Sarina J. C.
Published: July 2009

A simple approach to the design of feedback controls for damping the vibrations in large spaceborne antennas with flexible dish reflectors is proposed. The feedback controls consist of movable velocity-feedback dampers whose positions are determined by minimizing the rate of change of total vibrational energy at any time. The performance of the proposed feedback controls is studied via computer simulations.
Compression of Fluid-Filled Spherical Shells by Rigid Indenters
Authors: Taber L. A.
Published: July 2009

Two variational solutions were studied for large deflection of a fluid-filled hemispherical shell by a rigid cylindrical indenter. One solution is based on shell theory (including bending and stretching energy) and the other on a membrane model (stretching only). To study the transition from bending to membrane action, calculations are compared to load and fluid pressure data from experiments on water-filled rubber shells of various thicknesses. While bending effects dominate deflection as large as 20 percent of the radius for very thick shells (R/t ≥ 10), the results indicate that membrane stress is significant in thinner shells even when the deflection is small.
A Viscoelastic Correspondence Principle for Plane Membranes Subjected to Lateral Pressure
Authors: Stora˚kers B.
Published: July 2009

The classical Fo¨ppl equations, governing the deflection of plane membranes, constitute the first-order consistent approximation in the case of linear elastic material behavior. It is shown that despite the static and kinematic nonlinearities present, for arbitrary load histories a correspondence principle for viscoelastic material behavior exists if all relevant relaxation moduli are of uniform time dependence. Application of the principle is illustrated by means of a popular material model.
On the Approach to Steady State for Frictional Contact Under Moving Loads
Authors: Dundurs J. , Gautesen A. K.
Published: July 2009

There is a class of problems involving frictional contact for which a steady state of slip is possible under moving loads as, for instance, when a tire is press-fitted on a wheel, and loaded by forces that travel along its circumference and induce localized slip between the tire and the wheel. The steady state slip has been investigated before, but no estimates showing how quickly the steady state is approached are available. The present paper considers for this purpose a problem that can largely be reduced analytically. It involves two half spaces that are pressed together and sheared. The contact interface is locally pried apart by concentrated normal tractions which, after application, start to move. The moving normal forces induce localized separation and slip zones that travel along the interface. The analysis based on integral equations shows that the approach to steady state is relatively slow.
Ultrasonic Wave Scattering by a Subsurface Flaw in Joined Fluid-Solid Half Spaces
Authors: Varadan V. V. , Pillai T. A. K. , Varadan V. K.
Published: July 2009

The scattering of waves by a flaw (cavity or inclusion) that is embedded in an elastic half space at a finite depth below the interface with a fluid half space is studied using the T-matrix approach. Expressions are derived for the scattered fields generated in the fluid and solid half spaces as well as the asymptotic form of the field in the fluid at a large distance from the interface. Numerical results are presented for spherical voids and steel inclusions embedded in epoxy as well as oblate spheroidal voids in a metal for various flaw depths, scattering geometries, and frequency of the incident wave. The results obtained by keeping different orders of multiple scattering between the flaw and the interface are critically discussed.
Evaluation of Finite Element Calculations in a Cracked Cylinder Under Internal Pressure by Speckle Photography
Authors: Kaufmann G. H. , Lopergolo A. M. , Idelsohn S.
Published: July 2009

The usefulness of using the speckle photography technique in fracture mechanics to check numerical calculations is demonstrated for an internally pressurized cylinder with a surface flaw. A pointwise technique was utilized to measure the opening displacements along the crack line and the Mode I stress-intensity factor was determined by extrapolating these results to the crack tip. Finite element calculations were performed to be compared with experimental data and good agreement was obtained.
On the Foundations of Biomechanics
Authors: Fung Y. C.
Published: July 2009

After a brief survey of the present status of the vast field, a more concentrated review is presented on some issues concerning the foundations of biomechanics. The mechanical properties of living tissues, or their mathematical expressions, i.e., the constitutive equations, are discussed in some detail. Future prospects are considered. The expanding domain of biomechanics is surveyed, and new guideposts — the recently published books, are listed.
On Structural Optimization
Authors: Olhoff N. , Taylor J. E.
Published: July 2009

This paper presents a survey of the field of optimal structural design, with the main emphasis laid on fundamental aspects. The basic concepts for structural optimization problems are outlined, and we discuss the mathematical formulation and the characteristic properties and features of such problems for both discrete and continuum structures. A picture of the present status of the field is given, and we present an assessment of areas that are currently of special importance and undergoing rapid development. Furthermore, we identify some types of problems that require particular care in their formulation, and we indicate issues for future research.
Recent Progress in Rheology
Authors: Tanner R. I.
Published: July 2009

Progress in fluid rheology is surveyed, including simple flows useful for stress measurements. The question of how to describe more complex flows is discussed in the light of knowledge of fluid microstructure, and several constitutive relations are exhibited. Finally, the need for numerical solutions to problems is emphasized.
Shell Stability
Authors: Babcock C. D.
Published: July 2009

Recent advances in shell buckling research are reviewed. Five separate subject areas are covered: elastic postbuckling behavior and imperfection sensitivity, plastic buckling, dynamic buckling, experiments and computations. Recent history of the research is presented emphasizing important advances in understanding. Areas of needed research and current trends are pointed out.
Experimental Methods in Applied Mechanics
Authors: Daniel I. M.
Published: July 2009

An overview is presented of recent developments and the current status of several experimental mechanics methods, i.e., strain gages, moire´, photoelasticity, and interferometry. Examples of applications of these methods are given. Progress has been noted in all aspects, including methodology, data acquisition instrumentation, data processing, and range of applications. The trend is to tackle more difficult problems and to take full advantage of technological advances.
Constitutive Relations for Fiber-Reinforced Inelastic Laminated Plates
Authors: Aboudi J. , Benveniste Y.
Published: July 2009

Effective stress-strain relations for inelastic unidirectional composites developed previously are used to derive the gross constitutive behavior of inelastic laminates in which every lamina is fiber-reinforced. The laminated plate is subjected to stretching and bending deformation and the strain field is described by the Love-Kirchhoff hypothesis. The distribution of the resulting stresses across the thickness is necessarily nonlinear and a Legendre expansion formalism is used to determine the stress field. Results are given for cross-ply symmetric laminates under pure cylindrical bending.
Liquid-Metal MHD Open-Channel Flows
Authors: Hays P. R. , Walker J. S.
Published: July 2009

Many metallurgical applications of magnetohydrodynamics (MHD) involve open-channel liquid-metal flows with magnetic fields. This paper treats the three-dimensional, variable-depth flow in a rectangular open channel having an electrically insulating bottom and perfectly conducting sides. A steady, uniform magnetic field is applied perpendicular to the channel bottom. Induced magnetic fields and surface tension effects are neglected, while the applied magnetic field is sufficiently strong that inertial effects are negligible everywhere. Viscous effects are confined to boundary layers adjacent to the bottom, sides, and free surface. Solutions are presented for the inviscid core and the boundary layers. The locations of the free surface above the core and above the boundary layers adjacent to the sides are obtained. The side-layer variables are rescaled into universal profile functions which depend on the coordinates in the channel’s cross section and on a parameter related to the local slopes of the bottom and the free surface. The solutions for the side layers in open channels are compared to the side-layer solutions for certain rectangular closed ducts in order to reveal the effects of the free surface. This comparison leads to a qualitative correspondence principle between open-channel and closed-duct side-layer solutions. The similarities and differences between corresponding open-channel and closed-duct side layers are discussed.
A Multiple-Mode Approach to Large-Amplitude Vibration of Moderately Thick Elliptical Plates
Authors: Sathyamoorthy M. , Prasad M. E.
Published: July 2009

Based on a multiple-mode analysis, solutions to the nonlinear equations of motion are presented for elliptical plates in terms of variations of nonlinear periods with amplitudes of vibration. The governing equations are written in terms of lateral displacement w and stress function F and the effects of transverse shear deformation and rotatory inertia are incorporated into these equations. For the multiple-mode approach considered in this paper, an exact solution to the stress function is determined. Effects of geometric nonlinearity, shear deformation, rotatory inertia, plate geometry, and modal interaction on the vibration behaviors of elliptical plates are investigated in detail.
Friction, Restitution, and Energy Loss in Planar Collisions
Authors: Brach R. M.
Published: July 2009

Both particle and rigid body planar collisions are covered in this paper. For particles, the classical equations for oblique impacts are derived using Newton’s laws along with definitions of the coefficient of restitution and equivalent coefficient of friction. A general expression is obtained for the kinetic energy loss explicity containing the two coefficients. This expression for energy loss as a function of the friction coefficient possesses a maximum. The value of the friction coefficient at the maximum is a limiting value which can be used to determine whether or not sliding exists at separation. The maximum energy loss is independent of the physical mechanism of generation of tangential forces (friction) and serves as an upper bound for two-particle collisions. It is shown that to properly formulate and solve the rigid body problem, a moment must be considered at the common “point” of impact. A moment coefficient of restitution must be defined. This leads to six linear algebraic equations from which the six final velocity components can be calculated. An analytical solution is obtained for the general rigid body problem. In a reduced form, it is used to solve the problem of a single rigid body impacting a rigid barrier. This solution is then applied to a classical textbook problem. As shown for particle impacts, the concepts of limiting friction coefficient and maximum energy loss apply to rigid body impacts.
Thin Airfoil Theory for Planar Inviscid Shear Flow
Authors: Chin W. C.
Published: July 2009

Steady, inviscid, planar and constant density shear flows past thin airfoils have strongly coupled thickness and camber flowfields which can be simply analyzed using some invariant properties of Euler’s equations. In this paper, both the nonlinear vorticity generation term in Poisson’s disturbance stream-function equation and the Bernoulli constant (which varies from streamline to streamline) are explicitly evaluated in terms of the known plane parallel flow far upstream, recognizing that vorticity convects unstretched and unchanged along streamlines; this produces a governing differential equation with an explicitly available right side plus a Bernoulli integral with a true constant fixed throughout the entire flow field. Using these results, the inverse problem, which solves for the shape that induces a prescribed pressure, is formulated as a nonlinear boundary value problem with mixed Dirichlet and Neumann surface conditions; here, trailing edge shape constraints are directly enforced by controlling jumps in the stream-function or its streamwise derivative through the downstream wake (analogies with potential flows past axisymmetric ringwings showing similar source and vortex interactions are also described). For flows with arbitrary profile curvature, we show that the linearized stream-function equation can be put in conservation form, thus leading to new and more general Cauchy-Riemann conditions which extend the notion of the velocity potential; the analysis problem, which determines the flow past a known shape subject to Kutta’s condition, is shown to satisfy a simple boundary value problem for a “super-potential” identical to the irrotational planar formulation except for an axisymmetric-like change to the Cartesian form of Laplace’s equation. For flows with uniformity vorticity, closed-form solutions are given which clearly illustrate the interaction between thickness and camber; also, for arbitrary thin airfoils, a particularly simple expression shows that the lift due to thickness varies directly as the product of vorticity and enclosed area. With more general shears, numerical approaches are especially convenient; these require only simple code changes to existing algorithms, for example, established potential function methods readily available for analysis problems, or “direct stream-function methods” for inverse problems recently developed by this author. Numerical methods and results that cross-check and extend derived analytical solutions are given for both analysis and design problems with vorticity. Also, extensions of the basic theory to three-dimensional constant density and planar compressible shear flows are given.
The Use of Manganin Stress Transducers in Impulsively Loaded Long Rod Experiments
Authors: Rosenberg Z. , Mayseless M. , Partom Y.
Published: July 2009

The purpose of this Brief Note is to demonstrate the feasibility of using commercial manganin stress gauges in dynamic uniaxial stress experiments. This was demonstrated by measuring the stress-time histories inside long aluminum rods that were impacted by rigid wall impactors. The experimental records are compared with a two-dimensional Lagrangian calculation using a recently developed constitutive model (the Phases Model) to describe material behavior.
Large Amplitude Vibrations of Clamped Circular Plate of Variable Thickness
Authors: Chaudhuri S. K.
Published: July 2009

In this paper nonlinear oscillations of a clamped circular plate of linearly varying thickness have been investigated using von Karman equations expressed in terms of displacement components. Numerical results obtained have been compared and discussed.
Thin-Shear-Layer Model in Supercritical Hydraulic Flow
Authors: Andersson H. I. , Ytrehus T.
Published: July 2009

A supercritical, free-surface flow on an adverse incline has been modeled as a “thin-shear-layer” with algebraic eddy-viscosity included to account for turbulent shear stresses. The model has been solved numerically by a finite-difference technique for parabolic systems. Turbulent-viscous and adverse gravity effects are found to interact via the free-surface behavior in a way that leads to breakdown of the steady two-dimensional flow. Computed breakdown positions, velocity, and flow depth developments are compared with experimental and semi-empirical hydraulic results.
Hydrodynamical Entrance Length Effects for Duct Flows With Arbitrary Inlet Velocity Profiles
Authors: Du Plessis J. P. , Kro¨ger D. G.
Published: July 2009

An existing analytical method for predicting the entrance region pressure drop and relating effects in straight ducts of arbitrary cross section is generalized to include the application of arbitrary inlet velocity profiles. The only requirement for the use of the derived theoretical results is the availability of integrable (analytically or numerically) expressions for the inlet and the fully developed velocity profiles for the cross-sectional geometry under consideration. The derived results are applied to the case of the transition of fully developed laminar tube flow to fully developed circular-sectorial flow. The latter may be induced by the introduction of a flow divider into the tube. The numerical results are tabulated and also presented graphically.