bluuebunny/crossref_metadata_2025 huggingface dataset:
Pegylated hemoglobins mechanisms to avoid vasoconstriction and maintain perfusion
Authors: CABRALES PEDRO , FRIEDMAN JOEL M.
Published: February 2008

Despite the advances in blood substitutes, the development of materials that are effective in maintaining blood volume and oxygen delivery remains the priority for emergency care and trauma. Vasoactivity, i.e. vasoconstriction, presumably caused by nitric oxide (NO) scavenging has been defined as the principal problem associated with acellular hemoglobin (Hb) with low hydrodynamic radius. Conversely, Hb‐based materials with very large hydrodynamic radius, achieved by surface decoration of the Hb tetramer with water‐trapping polymers such as polyethylene glycol (PEG) conjugation, have been found vasoinactive in spite of being effective NO scavengers. This article explores possible mechanisms for why PEGylated Hbs not only are not vasoconstrictive but also are actually facilitators for maintaining high perfusion levels in the microcirculation. The most promising mechanisms are based on relatively recent observations and models; they indicate that Hb can actively regulate availability of ‘bioactive’ NO forms. This regulation can occur via: (i) NO transport by Hb in an allosterically controlled reversible chemical reaction with the Cys beta 93 (S‐NO‐Hb); and (ii) production of bioactive forms of NO through nitrite reductase activity of deoxyHb. The principal issues associated with these proposed mechanisms are: (i) how these reactions generate bio‐available NO and (ii) how the generated NO is delivered to the site of action without being either degraded or sequestered. We present a promising hypothesis and preliminary supporting data that PEGylated Hbs through a nitrite‐mediated reaction are especially effective in generating nitrosothiols, creating a transportable source of bioactive NO.
Ultimate Strength and Ductility Characteristics of Intermittently Welded Stiffened Plates Under In-Plane Axial Compression
Authors: Khedmati Mohammad Reza , Rastani Mehran
Published: February 2008

The ultimate strength and ductility characteristics of the intermittently welded stiffened plates under the action of in-plane axial compression are investigated in this paper. A series of detailed numerical analyses of longitudinally stiffened steel plates subjected to in-plane compressive load is performed using the ADINA commercial finite element code. Complete equilibrium paths are traced up to collapse for a nonlinear elastic-plastic response of stiffened plates. Analyzed stiffened plates are imperfect and their aspect ratio, plate slenderness, and column slenderness are changed in a systematic manner. Different types of stiffener are chosen for stiffened plate models. Three different stiffener-to-plate welding procedures are considered: continuous, chain intermittent, and staggered intermittent fillet welding.
Dynamic Stability of a Rotor Filled or Partially Filled With Liquid
Authors: Zhang Wen , Tang Jiong , Tao Mingde
Published: February 2008

The dynamic stability of a high-spinning liquid-filled rotor with both internal and external damping effects involved in is investigated in this paper. First, in the case of the rotor subjected to a transverse harmonic motion, the dynamic pressure of the liquid acting on the rotor is extracted through a planar flow analysis. Then the equation of perturbed motion for the liquid-filled rotor is derived. The analytical stability criteria as well as the stability boundaries are given. The results are extensions of those given by previous literature.
Local Stability of Gyroscopic Systems Near Vanishing Eigenvalues
Authors: Renshaw A. A. , Mote C. D.
Published: February 2008

Vanishing eigenvalues of a gyroscopic system are always repeated and, as a result of this degeneracy, their eigenfunctions represent a combination of constant displacements with zero velocity and the displacements derived from constant, nonzero velocity. In a second-order formulation of the equations of motion, the assumption of harmonic vibration is not sufficiently general to represent this motion as the displacements derived from constant, nonzero velocity are not included. In a first order formulation, however, the assumption of harmonic vibration is sufficient. Solvability criteria are required to determine the complete form of such eigenfunctions and in particular whether or not their velocities are identically zero. A conjecture for gyroscopic systems is proposed that predicts whether the eigenvalue locus is imaginary or complex in the neighborhood of a vanishing eigenvalue. If the velocities of all eigenfunctions with vanishing eigenvalues are identically zero, the eigenvalues are imaginary; if any eigenfunction exists whose eigenvalue is zero but whose velocity is nonzero, the corresponding eigenvalue locus is complex. The conjecture is shown to be true for many commonly studied gyroscopic systems; no counter examples have yet been found. The conjecture can be used to predict divergence instability in many cases without extensive computation.
Asymptotic Theory of Broadband Rotor Thrust, Part II: Analysis of the Right Frequency Shift of the Maximum Response
Authors: Martinez R.
Published: February 2008

One of the more intriguing features observed in rigorously computed frequency spectra of the random thrust on a turbulence-ingesting rotor is a shift of the broad peaks, or “haystacks,” to frequencies slightly higher than blade passage and harmonics. This paper applies the final results of an earlier Part I article to uncover the rotor and flow parameters responsible for that shift. The new work is analytical and asymptotic rather than numerical. It relies on the sole requirement that the rotor have a reasonably high number of blades. The theory shows that the statistical mechanism that causes the shift is fundamentally antitonal, and that it therefore has no corresponding counterpart in deterministic systems of blade/flow interaction.
Rough Balanced Collisions
Authors: Batlle J. A.
Published: February 2008

In multibody systems, balanced collisions—in which the sliding velocity would not change if friction was negligible—are a generalization of central collisions. For them Newton’s and Poisson’s rules are energetically consistent, but even though they are applied an “all linear solution” does not exist if the sliding varies its direction and does not stop. The properties of these collisions are reviewed, the hodographs of the sliding velocity are calculated and used to develop a systematic method to integrate the equations of motion that relies on a single integration from which the remaining unknowns are calculated by means of algebric expressions.
The Effect of Water on Thermal Stresses in Polymer Composites
Authors: Sullivan R. M.
Published: February 2008

The fundamentals of the thermodynamic theory of mixtures and continuum thermo-chemistry are reviewed for a mixture of water and polymer. A specific mixture which is mechanically elastic, where the strain states remain infinitesimal and where water concentration gradients are possible is considered. An expression for the partial pressure of water in the mixture is obtained from Gibbs relation based on certain assumptions regarding the thermodynamic state of the water in the mixture. Along with a simple diffusion equation, this partial pressure expression may be used to simulate the thermostructural behavior of polymer composite materials due to water in the free volumes of the polymer. These equations are applied to a specific polymer composite material during isothermal heating conditions. The thermal stresses obtained by the application of the theory are compared to measured results to verify the accuracy of the approach.
Some Phenomena of Cracks Perpendicular to an Interface Between Dissimilar Orthotropic Materials
Authors: Sung J. C. , Liou J. Y. , Lin Y. Y.
Published: February 2008

The problem of two aligned orthotropic materials bonded perfectly along the interface with cracks embedded in either one or both of the materials while their directions being perpendicular to the interface is considered. A system of singular integral equations for general anisotropic materials is derived. Employing four effective material parameters proposed by Krenk and introducing four generalized Dundurs’ constants, the kernel functions appearing in the integrals are converted into real forms for the present problem which are keys to the present study. The kernel functions for isotropic dissimilar materials can be deduced from the present results directly, no any limiting process is needed. These kernel functions are then employed to investigate the singular behaviors for stresses at the point on the interface. Characteristic equation which determines the power of singularity for stresses is given in real forms for the case of cracks that are going through the interface. Studies of the characteristic equation reveal that the singular nature for the stresses could vanish for some material combinations and the singular nature for the stresses is found to be independent of the replacement of the material parameter Δ by Δ-1. The kernel functions developed are further used to explore analytically some interesting phenomena for the stress intensity factors, which are discussed in detail in the present context. Some numerical results for the stress intensity factors for a typical dissimilar materials are also given.
A Torsional Contact Problem for an Indented Half-Space
Authors: Pak R. Y. S. , Abedzadeh F.
Published: February 2008

This paper is concerned with the torsion of a rigid disk bonded to the bottom of a cylindrical indentation on an elastic half-space. By virtue of Fourier sine and cosine transforms, the mixed boundary value problem in classical elastostatics is shown to be reducible to a pair of integral equations, of which one possesses a generalized Cauchy singular kernel. With the aid of the theory of analytic functions, the inherent fractional-order singularity in the contact problem is rendered explicit. Illustrative results on the torsional stiffness of the base of the indentation and the corresponding contact stress distribution are presented for engineering applications.
A Micromechanical Model for the Fiber Bridging of Macro-Cracks in Composite Plates
Authors: Kardomateas G. A. , Carlson R. L.
Published: February 2008

Recent experimental studies on the propagation of transverse cracks in composites have shown that fiber bridging is frequently present, and can be considered as the cause of increased toughness. This paper presents a model that is capable of quantifying this effect and explaining the decrease in the crack growth rate in either a monotonic or a cyclic load profile. Both Modes I and II are considered. The model is based on the elastic loading of a fiber located on the macro-crack face close to the tip and under dominantly plane strain conditions. Two fundamental cases of fiber bridging configurations are distinguished, namely when the fiber-matrix interface is intact and when the fiber-matrix interface has partially failed. Following the single fiber analysis, the model is extended to the case of multiple fibers bridging the faces of the macro-crack. The analysis is for a generally anisotropic material and the fiber lines are at arbitrary angles. Results are presented for the case of an orthotropic material with unidirectional fibers perpendicular to the crack faces. Specifically, the reduction in the stress intensity factor (relative to the nominal value) is investigated for the glass fibers in a glass/epoxy composite system. The effects of fiber debonding and pullout with friction as well as fiber breaking are accounted for in the analysis, and results with respect to a parameter representing the fiber-matrix interface friction are presented. Results are also presented regarding the partial or full fracture of the fiber bridging zone. The model can also be used to analyze the phenomenon of fiber nesting, which is similar to fiber bridging, and occurs with growing delaminations.
Analysis of High-Speed Rolling With Inertia and Rate Effects
Authors: Iddan D. , Tirosh J.
Published: February 2008

Limit-analysis procedures for time-dependent materials are utilized for assessing some essential technological parameters in high-speed strip rolling (i.e., the torque, the separation force, the minimal friction required to avoid skidding, maximum allowable speed, etc.). The formulations are quite wide in scope (e.g. they include the inertia of the plastic flow beside the material rate effect) but lack, in general, the rigor of the true bound by reasons to be discussed. The solutions are, by default, considered as “approximate bounds” unless stated differently. Due emphasis is given to the development of a lower bound, infrequently employed in metalworking analysis. It yields relevant information about the process which appears entirely consistent with an independent upper bound solution. In particular, the rate effects are shown (in both solutions) to be characterized by the intensity of two dimensionless groups, known universally as Bingham No. and Euler No. Normally they cannot be ignored at high speeds currently attainable in modern industry, above, say, u0 = 50 [m/s]. For slow speeds, the above solutions constitute rigorous upper and lower bounds. The relative close proximity of the two bounds to experimental data (with copper, aluminum, and steel) and their excellent agreement with the rigid-plastic finite element solution, demonstrate the utility of having these dual bounds simultaneously. A seemingly useful by-product from the analysis is the ability to predict the onset of skidding at very high speeds. For this sake, an expression is offered for determining the maximum allowable rolling speeds (at the incipient of skidding) in conjunction with the requirement for a certain minimum interfacial friction.
Nonlinear Dynamics of a Rigid Block on a Rigid Base
Authors: Iyengar R. N. , Roy D.
Published: February 2008

The planar rocking of a prismatic rectangular rigid block about either of its corners is considered. The problem of homoclinic intersections of the stable and unstable manifolds of the perturbed separatrix is addressed to and the corresponding Melnikov functions are derived. Inclusion of the vertical forcing in the Hamiltonian permits the construction of a three-dimensional separatrix. The corresponding modified Melnikov function of Wiggins for homoclinic intersections is derived. Further, the 1-period symmetric orbits are predicted analytically using the method of averaging and compared with the simulation results. The stability boundary for such orbits is also established.
Elastic Force on a Point Defect in or Near a Surface Layer
Authors: Yua H. , Sanday S. C. , Bacon D. J.
Published: February 2008

The elastic force on a point defect within or near a surface layer is determined by the image method. There is no stable equilibrium position for the point defect in the surface layer, it is attracted either to the free surface or to the interface. When the point defect is in the substrate it is attracted to the interface when the surface layer is softer than the substrate and to an equilibrium position in the substrate when the surface layer is stiffer than the substrate, the equilibrium position being a function of the elastic constants and the layer thickness.
A Pressure Projection Method for Nearly Incompressible Rubber Hyperelasticity, Part II: Applications
Authors: Chen Jiun-Shyan , Wu Cheng-Tang , Pan Chunhui
Published: February 2008

In the first part of this paper a pressure projection method was presented for the nonlinear analysis of structures made of nearly incompressible hyperelastic materials. The main focus of the second part of the paper is to demonstrate the performance of the present method and to address some of the issues related to the analysis of engineering elastomers including the proper selection of strain energy density functions. The numerical procedures and the implementation to nonlinear finite element programs are presented. Mooney-Rivlin, Cubic, and Modified Cubic strain energy density functions are used in the numerical examples. Several classical finite elasticity problems as well as some practical engineering elastomer problems are analyzed. The need to account for the slight compressibility of rubber (finite bulk modulus) in the finite element formulation is demonstrated in the study of apparent Young’s modulus of bonded thin rubber units. The combined shear-bending deformation that commonly exists in rubber mounting systems is also analyzed and discussed.
Thermally Induced Instability of Laminated Beams and Plates
Authors: Tylikowski A. , Hetnarski R. B.
Published: February 2008

A theoretical investigation of dynamic stability for linear elastic structures due to non-uniform, time and space-dependent stochastic temperature fields is presented. The study is based on the reformulation of stochastic stability problems as a stability of Itoˆ type equations in some appropriate Hilbert space and is adopted for stability problems of structures with time and space-dependent stochastic coefficients. Uniform stochastic stability criteria of the structure equilibrium are derived using the Liapunov direct method. The energy-like functional and the generalized ltoˆ lemma are used to derive the sufficient stability conditions of the equilibrium state. A symmetrically laminated crossply plate subjected to the wide-band Gaussian temperature distribution and a laminated beam subjected to local short-time heatings are analysed in detail.
Vibration and Coupling Phenomena in Asymmetric Disk-Spindle Systems
Authors: Parker R. G. , Mote C. J.
Published: February 2008

This paper analytically treats the free vibration of coupled, asymmetric disk-spindle systems in which both the disk and spindle are continuous and flexible. The disk and spindle are coupled by a rigid clamping collar. The asymmetries derive from geometric shape imperfections and nonuniform clamping stiffness at the disk boundaries. They appear as small perturbations in the disk boundary conditions. The coupled system eigenvalue problem is cast in terms of “extended” eigenfunctions that are vectors of the disk, spindle, and clamp displacements. With this formulation, the eigenvalue problem is self-adjoint and the eigenfunctions are orthogonal. The conciseness and clarity of this formulation are exploited in an eigensolution perturbation analysis. The amplitude of the disk boundary condition asymmetry is the perturbation parameter. Exact eigensolution perturbations are derived through second order. For general boundary asymmetry distributions, simple rules emerge showing how asymmetry couples the eigenfunctions of the axisymmetric system and how the degenerate pairs of axisymmetric system eigenvalues split into distinct eigenvalues. Additionally, properties of the formulation are ideal for use in modal analyses, Ritz-Galerkin discretizations, and extensions to gyroscopic or nonlinear analyses.
Curvilinear Coordinates and Physical Components: An Application to the Problem of Viscous Flow and Heat Transfer in Smoothly Curved Ducts
Authors: Bolinder C. J.
Published: February 2008

Expressions are derived for the gradient, divergence, Laplacian, curl, and material time derivative in terms of general curvilinear coordinates using physical components of all vector quantities. The results are conveniently expressed in terms of two new coefficients, involving physical and reciprocal base vectors. An application to the problem of viscous flow and heat transfer in arbitrarily smoothly curved ducts is presented. In particular, helical ducts are considered.
An Approximate Method for the Drags of Two-Dimensional Obstacles at Low Reynolds Numbers
Authors: Yano Hideo , Hirata Katsuya , Komori Masanori
Published: February 2008

We propose a new simple method of computing the drag coefficients of two-dimensional obstacles symmetrical to the main-flow axis at Reynolds numbers less than 100. The governing equations employed in this method are the modified Oseen’s linearized equation of motion and continuity equation, and the computation is based on a discrete singularity method. As examples, simple obstacles such as circular cylinders, rectangular prisms, and symmetrical Zhukovskii aerofoils are considered. And it was confirmed that the computed drags agree well with experimental values. Besides optimum shapes of these geometries, which minimize the drag coefficients, are also determined at each Reynolds number.
Slaving the In-Plane Motions of a Nonlinear Plate to Its Flexural Motions: An Invariant Manifold Approach
Authors: Georgiou I. T. , Schwartz I. B.
Published: February 2008

We show that the in-plane motions of a nonlinear isotropic plate can be decoupled from its transverse motions. We demonstrate this decoupling by showing analytically and numerically the existence of a global nonlinear invariant manifold in the phase space of three nonlinearly coupled fundamental oscillators describing the amplitudes of the coupled fundamental modes. The invariant manifold carries a continuum of slow periodic motions. In particular, for any motion on the slow invariant manifold, the transverse oscillator executes a periodic motion and it slaves the in-plane oscillators into periodic motions of half its period. Furthermore, as the energy level of a motion on the slow manifold increases, the frequency of the largest harmonic of the in-plane motion approaches the in-plane natural frequencies.
Equilibrium of a Radially Symmetric Inhomogeneous Plate Under Tension and Load
Authors: Pineda A. R. , Root R. G.
Published: February 2008

This paper studies a mathematical model for small deflections of a radially symmetric strongly inhomogeneous elastic plate under a normal load and tension in the center plane. The type of inhomogeneity studied occurs in injection molded plastics. The model consists of a Dirichlet boundary value problem for a linear fourth-order ordinary differential equation. A general expression is derived for physically reasonable solutions under relatively broad restrictions on the inhomogeneity and load. The solutions are analyzed and interpreted in terms of their physical significance.
Left Eigenvectors: Extraction From Measurements and Physical Interpretation
Authors: Bucher I. , Braun S. G.
Published: February 2008

In this paper the extraction of left eigenvectors from measured frequency response functions is presented and discussed. It is shown that contrary to the extraction of right eigenvectors from measured response data, the extraction of left eigenvectors is inherently ill-posed when the same measured information is being used. The ill-posedness can result in a spatially oscillating additive component (short wavelength) appearing in the identified left eigenvectors, a property which is not described in existing literature on structural dynamics. Some well-known regularization methods are hence used to reduce the inaccuracies appearing in the extracted left eigenvectors. It is also shown that a further improvement in the accuracy of the solution can be achieved by making use of an approximation of the mass distribution combined with regularization. Throughout this paper, an attempt is made to provide a physical insight to the various aspects related to the left eigenvectors and their extraction. This includes (a) the interpretation of left eigenvectors as internal force distributions; (b) the inherent reason for the ill-conditioning, and (c) the spatial filtering of short wavelength achieved by regularization, yielding an improved estimate of the left eigenvectors.
Finite Element Analysis of Wrinkling Membranes
Authors: Kang Seokwoo , Im Seyoung
Published: February 2008

A new iterative scheme is proposed for finite element analysis of wrinkling or tension structures. The scheme is based upon the observation that there exists an invariant relationship, due to the uniaxial tensile stress state of wrinkling, between some of the strain components referred to the local frame aligned with wrinkling in a region where wrinkling occurs. This enables us to update the stress state and the internal forces correctly taking into account the existence of wrinkling. The finite element implementation of the scheme is straightforward and simple, and only minor modifications of the existing total Lagrangian finite element codes for membranes are needed. The validity of the scheme is demonstrated via numerical examples for the torsion of a membrane and the quasi-static inflation of an automotive airbag, both made of isotropic or anisotropic elastic membranes. The examples suggest that the present iterative scheme has a good convergence characteristic even for a large loading step.
Wave Propagation in Poroelastic Media Saturated by Two Fluids
Authors: Tuncay K. , Corapcioglu M. Y.
Published: February 2008

A theory of wave propagation in isotropic poroelastic media saturated by two immiscible Newtonian fluids is presented. The macroscopic constitutive relations, and mass and momentum balance equations are obtained by volume averaging the microscale balance and constitutive equations and assuming small deformations. Momentum transfer terms are expressed in terms of intrinsic and relative permeabilities assuming the validity of Darcy’s law. The coefficients of macroscopic constitutive relations are expressed in terms of measurable quantities in a novel way. The theory demonstrates the existence of three compressional and one rotational wave. The third compressional wave is associated with the pressure difference between the fluid phase and dependent on the slope of the capillary pressure-saturation relation.
Asymptotics of Flexural Waves in Isotropic Elastic Plates
Authors: Losin N. A.
Published: February 2008

The long and short-wave asymptotics of order O(k6h6) for the flexural vibrations of an infinite, isotropic, elastic plate are studied. The differential equation for the flexural motion is derived from the system of three-dimensional dynamic equations of linear elasticity. All coefficients of the differential operator are presented as explicit functions of the material parameter γ = cs2/cL2, the ratio of the velocities squared of the flexural (shear) and extensional (longitudinal) waves. Relatively simple frequency and velocity dispersion equations for the flexural waves are deduced in analytical form from the three-dimensional analog of Rayleigh-Lamb frequency equation for plates. The explicit formulas for the group velocity are also presented. Variations of the velocity and frequency spectrums depending on Poisson’s ratio are illustrated graphically. The results are discussed and compared to those obtained and summarized by R. D. Mindlin (1951, 1960), Tolstoy and Usdin (1953, 1957), and Achenbach (1973).
A Comprehensive Energy Formulation for General Nonlinear Material Continua
Authors: Carini A. , De Donato O.
Published: February 2008

By specialization to the continuum problem of a general formulation of the initial/boundary value problem for every nonpotential operator (Tonti, 1984) and by virtue of a suitable choice of the “integrating operator,” a comprehensive energy formulation is established. Referring to the small strain and displacement case in the presence of any inelastic generally nonlinear constitutive law, provided that it is differentiable, this formulation allows us to derive extensions of well-known principles of elasticity (Hu-Washizu, Hellinger-Reissner, total potential energy, and complementary energy). An illustrative example is given. Peculiar properties of the formulation are the energy characterization of the functional and the use of Green functions of the same problem in the elastic range for every inelastic, generally nonlinear material considered.
Criticality of Damping in Multi-Degree-of-Freedom Systems
Authors: Bhaskar A.
Published: February 2008

The concept of criticality in multi-degree-of-freedom systems is discussed. Sufficient conditions for overdamping, critical damping, and underdamping are derived in terms of the matrices appearing in the modal coordinates. It is noted that results available in the literature for the case of overdamping and mixed damping are erroneous. This has been pointed out by Bhaskar (1991, 1992) for the cases of overdamping and mixed damping, and by Barkwell et al. (1992) for the case of overdamping. The error in the proof of the conditions for overdamping is brought out. A sufficient condition for overdamping is presented. Results obtained for the symmetric systems are then generalized to the symmetrizable systems. Theorems on eigenvalue bounds are applied to establish criticality.
Singularities at the Tip of a Crack Terminating Normally at an Interface Between Two Orthotropic Media
Authors: Sung J. C. , Liou J. Y.
Published: February 2008

The order of stress singularities at the tip of a crack terminating normally at an interface between two orthotropic media is analyzed. Characteristic equation in complex form for the power of singularity s, where 0 < Re{s} < 1, is first set up for two general anisotropic materials. Attention is then focused on the problem that is composed by two orthotropic media where one of them (say, material #2 ) the material principal axes are aligned while the other one (say, material #1) the principal axes can have an angle γ relative to the interface. For such a problem, a real form of the characteristic equation is obtained. The roots are functions of γ in general. Two real roots exist for most values of γ; however, there are possible ranges of γ that the complex roots will occur. The roots s are found to be independent of γ when material #1 has the property that δ(1) = 1. When γ = 0, two roots are always real. Furthermore, each of these two roots is associated with symmetric or antisymmetric mode and they become equal when Δ = 1. Many other features of the effects of the material parameters on the behaviors of the roots s are further investigated in the present work, where the six generalized Dundurs’ constants, expressed in terms of Krenk’s parameters, play an important role in the analysis.
An Efficient Calculation of the Load and Coefficient of Restitution of Impact Between Two Elastic Bodies With a Liquid Lubricant
Authors: Chang L.
Published: February 2008

This paper complements several previous papers on modeling of the impact between two elastic bodies with a liquid lubricant. The main feature of the work is the efficient incorporation of various engineering aspects of the impact process making use of approximations consistent with the physical insights of the problem. The model can very efficiently calculate the impact load and the coefficient of restitution with reasonable accuracy for a wide range of the problem domain. The modeling concepts and methodology may be useful in future research on interdisciplinary analyses of the dynamics of mechanical systems in which the interactions are strong between vibrations of the components and impacts in the lubricated kinematic pairs.
Instability of Laminar Natural Convection Boundary Layer Flow on a Vertical Porous Flat Plate
Authors: Watanabe T. , Taniguchi H. , Pop I.
Published: February 2008

The effects of uniform suction and injection on the linear stability theory of laminar natural convection boundary layer flow along a vertical porous flat plate which is maintained at a constant temperature are studied. The nonsimilar boundary layer equations for the basic steady flow have been solved numerically employing a very efficient finite difference scheme in combination with an iterative method for solving the resulting ordinary differential equations. The temporal neutral stability theory for wavelike disturbances of Tollmien-Schlichting type are then presented for the velocity and temperature functions. The corresponding eigenvalue problem for the disturbance amplitude functions is also solved numerically using a very accurate method. Results are presented graphically for both the basic and disturbance velocity and temperature profiles for some values of the modified local Grashof number G and suction or injection parameter X. The Prandtl number Pr is taken to be 0.73 (air) throughout this paper. The results show clearly the important role that suction or injection parameter X may have on the basic and disturbance flow characteristics in this problem.
Analysis of a Nonlinear System Exhibiting Chaotic, Noisy Chaotic, and Random Behaviors
Authors: Lin H. , Yim S. C. S.
Published: February 2008

This study presents a stochastic approach for the analysis of nonchaotic, chaotic, random and nonchaotic, random and chaotic, and random dynamics of a nonlinear system. The analysis utilizes a Markov process approximation, direct numerical simulations, and a generalized stochastic Melnikov process. The Fokker-Planck equation along with a path integral solution procedure are developed and implemented to illustrate the evolution of probability density functions. Numerical integration is employed to simulate the noise effects on nonlinear responses. In regard to the presence of additive ideal white noise, the generalized stochastic Melnikov process is developed to identify the boundary for noisy chaos. A mathematical representation encompassing all possible dynamical responses is provided. Numerical results indicate that noisy chaos is a possible intermediate state between deterministic and random dynamics. A global picture of the system behavior is demonstrated via the transition of probability density function over its entire evolution. It is observed that the presence of external noise has significant effects over the transition between different response states and between co-existing attractors.
Transient Solutions of the Ring-Spinning Balloon Equations
Authors: Stump D. M. , Fraser W. B.
Published: February 2008

In the textile yarn manufacturing process of ring spinning, a loop of yarn rotates rapidly about a fixed axis. The surface generated by the rotating yarn loop is called a balloon. The solutions of the time-independent, nonlinear, yarn-balloon equations have been extensively investigated for a reference frame that rotates with constant angular velocity and are termed quasi-stationary solutions. A linear perturbation stability analysis of these solutions has shown that while single-loop balloons are stable, multiple-loop balloons are typically unstable. In this paper a numerical method for the calculation of transient solutions of the nonlinear time-dependent PDEs is developed, and the stability of representative quasi-stationary balloons subjected to a model velocity impulse is studied. The results of the linearized analysis are confirmed: Single-loop balloons remain stable while multiple-loop balloons typically collapse within only a few spindle revolutions.
Flow Past a Flat Plate With a Vortex/Sink Combination
Authors: Mourtos N. J. , Brooks M.
Published: February 2008

This paper presents a potential flow model for the leading edge vortex over a two-dimensional flat plate at an angle of attack. The paper is an extension of a model by Saffman and Sheffield (1977). A sink has been added in this model in an effort to satisfy the Kutta condition at both the leading edge and the trailing edge of the plate. The introduction of the sink was inspired by the fact that most steady vortices in nature appear in combination with a flow feature which can be interpreted as a sink at their cores when the flow is analyzed in a two-dimensional observation plane. As in the Saffman and Sheffield model, the presence of a vortex results in increased lift; however, in the current model a unique vortex/sink position is found at each angle of attack. A comparison has also been made between the lift and the drag of this model and the corresponding results for two classical solutions of flow over a flat plate: (a) the fully attached flow with the Kutta condition satisfied at the trailing edge only and (b) the Helmholtz solution of fully separated flow.
Elastic Fields in a Polygon-Shaped Inclusion With Uniform Eigenstrains
Authors: Nozaki H. , Taya M.
Published: February 2008

In this paper the elastic fields in an arbitrary, convex polygon-shaped inclusion with uniform eigenstrains are investigated under the condition of plane strain. Closed-form solutions are obtained for the elastic fields in a polygon-shaped inclusion. The applications to the evaluation of the effective elastic properties of composite materials with polygon-shaped reinforcements are also investigated for both dilute and dense systems. Numerical examples are presented for the strain field, strain energy, and stiffness of the composites with polygon shaped fibers. The results are also compared with some existing solutions.
Asymptotic Distribution of Eigenvalues of a Constrained Translating String
Authors: Zhu W. D. , Mote C. D. , Guo B. Z.
Published: February 2008

A new spectral analysis for the asymptotic locations of eigenvalues of a constrained translating string is presented. The constraint modeled by a spring-mass-dashpot is located at any position along the string. Asymptotic solutions for the eigenvalues are determined from the characteristic equation of the coupled system of constraint and string for all constraint parameters. Damping in the constraint dissipates vibration energy in all modes whenever its dimensionless location along the string is an irrational number. It is shown that although all eigenvalues have strictly negative real parts, an infinite number of them approach the imaginary axis. The analytical predictions for the distribution of eigenvalues are validated by numerical analyses.
The Hamilton-Jacobi Equation Applied to Continuum
Authors: Leech C. M.
Published: February 2008

The Hamilton-Jacobi partial differential equation is established for continuum systems; to do this a new concept in material distributions is introduced. The Lagrangian and Hamiltonian are developed, so that the Hamilton-Jacobi equation can be formulated and the principal function defined. Finally the principal function is constructed for the dynamics of a one-dimensional linear elastic bar; the solution for its’ vibrations is then established following the differentiation of the principal function.
Vibrations of Ballooning Elastic Strings
Authors: Zhu F. , Sharma R. , Rahn C. D.
Published: February 2008

This paper investigates the nonlinear dynamic response of a linearly elastic string fixed at one boundary and undergoing constant speed circular motion at the other boundary. The response divides into nonlinear steady-state ballooning that is fixed relative to a rotating coordinate system and linearized vibration about the steady state. Single-loop balloons have high tension and purely imaginary eigenvalues. The single-loop vibration frequencies generally decrease with increasing balloon length. Highly extensible strings whirl in first and higher modes with forward whirling modes having lower frequencies. Axially stiff strings exhibit whirling only in higher modes. If the nondimensional string stiffness is larger than 1000, then the inextensible steady-state solutions and the lowest six vibration frequencies match the extensible results to within three percent. One-and-a-half loop balloons are divergently unstable. Long and/or sufficiently extensible strings form low-tension double-loop balloons. Inextensible double balloons are coupled mode flutter unstable. The steady-state balloons, steady-state eyelet tension, and balloon stability are experimentally verified.
The Reissner-Sagoci Problem for the Transversely Isotropic Half-Space
Authors: Hanson M. T. , Puja I. W.
Published: February 2008

This paper evaluates the elastic field in a transversely isotropic half-space caused by a circular flat bonded punch under torsion loading. The elastic field is found by integrating the point force potential functions. For the case of isotropy the present results agree with previous analysis.
On the Transient Response of a Spinning Disk Under a Space-Fixed Load
Authors: Chen Jen-San , Hsu C.-M.
Published: February 2008

The titled problem is studied analytically by an eigenfunction expansion method. In the early stage following the excitation, symmetric deformation is observed when the rotation speed is around the first critical speed. At a rotation speed ten times higher than the first critical speed, at which the convective velocity of the media is comparable to the wave propagation speed, asymmetric deformation becomes apparent.
Micromechanical Modeling of Creep Behavior in Particle-Reinforced Silicone-Rubber Composites
Authors: Chen Chao-Hsun , Cheng Chaing-Ho
Published: February 2008

A micromechanically based composite model is proposed to study the viscoelastic behavior of solid-filled rubber composites. A nonlinear So-Chen’s (1991) mechanical model which describes the viscoelastic behavior of the rubber matrix is proposed to relate volume-average deformation and stress within the two-phase composite inclusion to the remote (macroscopic) fields. The influence of the volume fractions of inclusions on the overall creep strain of a rubber-matrix composite is investigated at the level of dilute concentration. The creep rate of the rubber matrix, which depends nonlinearly on the creep strain and the primary creep and secondary creep resulting from the viscous flow of creep deformation, is also considered in addition to the usual steady-state, or secondary, creep. The method developed for the calculation of the incremental process is based upon Eshelby’s (1957) equivalence principle of an inhomogeneity-transformation problem and Mori-Tanaka’s (1973) idea of mean-field stress. In order to examine the applicability of the model as well as the nonlinear stretch parameter, a series of experiments on solid-filled silicone rubbers has been carried out, which included constant rate of tensile tests and creep tests. It is demonstrated that this simple, albeit approximate micromechanical modeling is capable of predicting the volume fraction dependence of the time dependent creep, with characteristic consistency with the known elastic behavior.
Thermal Analysis of a Round Roll
Authors: Qualls W. R. , Good J. K.
Published: February 2008

A method for calculating the internal stress distribution in a wound roll subjected to a homogeneous temperature change is presented. The nonlinear constitutive behavior apparent in the stack-wise direction of the roll is represented by a function dependent upon pressure that is incrementally updated during the analysis. In addition to the mechanics of the model, procedures for measuring the circumferential and radial coefficients of thermal expansion are described. Particular examples are presented that show, by comparison with experimental data, the model described herein accurately predicts interlayer pressures in a wound pack. In addition, the marked effect of the core expansion coefficient on the stress distribution is shown and this example illustrates the potential for optimizing the selection of core materials such that the effects of environmental changes on roll structure are minimized.
On the Eigenvalues and Critical Speed Stability of Gyroscopic Continua
Authors: Parker R. G.
Published: February 2008

In order to provide analytical eigenvalue estimates for general continuous gyroscopic systems, this paper presents a perturbation analysis to determine approximate eigenvalue loci and stability conclusions in the vicinity of critical speeds and zero speed. The perturbation analysis relies on a formulation of the general continuous gyroscopic system eigenvalue problem in terms of matrix differential operators and vector eigenfunctions. The eigenvalue λ appears only as λ2 in the formulation, and the smoothness of λ2 at the critical speeds and zero speed is the essential feature. First-order eigenvalue perturbations are determined at the critical speeds and zero speed. The derived eigenvalue perturbations are simple expressions in terms of the original mass, gyroscopic, and stiffness operators and the critical-speed/zero-speed eigenfunctions. Prediction of whether an eigenvalue passes to or from a region of divergence instability at the critical speed is determined by the sign of the eigenvalue perturbation. Additionally, eigenvalue perturbation at the critical speeds and zero speed yields approximations for the eigenvalue loci over a range of speeds. The results are limited to systems having one independent eigenfunction associated with each critical speed and each stationary system eigenvalue. Examples are presented for an axially moving tensioned beam, an axially moving string on an elastic foundation, and a rotating rigid body. The eigenvalue perturbations agree identically with exact solutions for the moving string and rotating rigid body.
Dynamical Friction Behavior in a Forced Oscillator With a Compliant Contact
Authors: Liang J.-W. , Feeny B. F.
Published: February 2008

Contact compliance, which may arise from elastic deformation near the contact point or in the surrounding structure, affects the dynamical friction behaviors in mechanical oscillators. An idealized model consisting of a mass sliding harmonically on a mass-less compliant contact produces hysteresis in friction-velocity plots. Dynamical friction features, depending on the contact stiffness, friction level, and the frequency and amplitude of oscillation, are predicted and quantified. Contact compliance can also lead to oscillations at the transition from slip to stick. Experiments and simulations verify the model and tie together phenomena of both continuous sliding and stick-slip.
Asymmetric Shielding Mechanisms in the Mixed-Mode Fracture of a Glass/Epoxy Interface
Authors: Swadener J. G. , Liechti K. M.
Published: February 2008

An asymmetric increase in the apparent values of the interfacial fracture toughness with increasing mode II component of loading has been observed by several investigators. In this study, cracks were grown in a steady-state manner along the glass/epoxy interface in sandwich specimens in order to determine the mechanisms responsible for the shielding effect. Finite element analysis using a hydrostatic stress and strain rate dependent plasticity model for the epoxy and a cohesive zone model for the interface shows that plastic dissipation in the epoxy accounts for the asymmetric shielding seen in these experiments which cover a wide range of mode mix. Numerical predictions of normal crack-opening displacements yielded results that were consistent with measured values which were made as close as 0.3 μm from the crack tip.
Stress Concentration in an Elastic Cosserat Plate Undergoing Extensional Deformations
Authors: Krishnaswamy Shankar , Jin Z.-H. , Batra R. C.
Published: February 2008

We formulate and solve the boundary value problem of a linearly elastic, infinite Cosserat plate which contains a circular hole and which is loaded in tension at infinity. The effect of hole radius, plate thickness, and material parameters on the stress concentration at the hole is discussed. We also discuss the stress concentration when the plate is subjected to pure shear.
The Jamb (Self-Locking) Process in Three-Dimensional Collisions
Authors: Batlle J. A. , Cardona S.
Published: February 2008

For collisions that can be described by means of Routh’s incremental model, the jamb or self-locking process, which is characterized by a negative slope of the plot of the normal (separating) velocity vn as a function of the normal impulse Pn, is far more complicated in three dimensions than in planar collisions because its occurrence depends not only on the friction coefficient μ, but also on the direction of sliding σ, which is variable. A thorough study of the jamb process as it occurs in Routh’s model is presented. For a given collision configuration the system behavior concerning jamb can be fully characterized in the plane of vectors μσ, where four jamb-related domains are defined. Jamb is investigated in the plane of the sliding velocity—where it occurs in an angular sector—and in the vn(Pn) plots. When jamb starts during expansion, vn>O, a second compression-expansion phase can take place in some cases, and then the usual energetical restitution coefficient ew may be ill-defined. A new formulation for the energy dissipated by the normal force is presented that can be consistently applied in all cases. The new concepts and procedures are illustrated by means of an application example.