bluuebunny/crossref_metadata_2025 huggingface dataset:
Equilibrium Path Bifurcation Due to Strain-Softening Localization in Ellipsoidal Region
Authors: Bazˇant Z. P.
Published: April 2008

A preceding study of the loss of stability of a homogeneous strain state in infinite homogeneous solid due to localization of strain into an ellipsoidal region is complemented by determining the condition of bifurcation of equilibrium path due to ellipsoidal localization mode. The bifurcation occurs when the tangential moduli matrix becomes singular, which coincides with Hill’s classical bifurcation condition for localization into an infinite layer. The bifurcation is normally of Shanley type, occurring in absence of neutral equilibrium while the controlled displacements at infinity increase. During the loading process with displacement increase controlled at infinity, this type of bifurcation precedes the loss of stability of equilibrium due to an ellipsoidal localization mode, except when the tangential moduli change suddenly (which happens, e.g., when the slope of the stress-strain diagram is discontinuous, or when temperature is increased).
Incident Wave and Dislocation Acceleration Effects in Dislocation Emission From Cracks
Authors: Brock L. M. , Wu J.-S.
Published: April 2008

Some previous transient analyses of dislocation emission from dynamically loaded cracks have treated glide at constant speeds, and have invoked an emissions criterion that allows the dislocation force to exceed the yield stress level during glide. In the context of nonstrain-hardening plasticity, this analysis requires that the force remain at the yield stress level. For an exact solution to the problem of screw dislocation emission from a crack subjected to plane SH-wave diffraction, the result is an equation of motion for the dislocation, which can be integrated exactly. The dislocation is found to accelerate during glide to a high but subcritical speed, before decelerating to its arrest position. A general incident SH-wave is considered, but is then specialized to the cases of a step-stress and a sinusoidal wave. Calculations on the basis of material and wave parameters show that purely brittle fracture can be difficult to achieve, and that wavelength/frequency cutoffs exist, beyond which emission cannot occur.
Strain-Induced Elastic Anisotropy Measured With Ultrasonic Waves
Authors: Sasaki Kazuyuki , Iwashimizu Yukio , Kobori Osami
Published: April 2008

Measurements on ultrasonic velocities were performed to define elastic anisotropy produced in steel by plastic compressive deformation. Cylindrical blocks cut from a SS41 steel bar were compressed plastically along the bar axis, and then used to make specimens available for different propagation directions. Velocity variations with plastic strain were shown linear in the strain range from 0.09 to 0.22, and, the strain-induced transverse isotropy of slight degree was determined by analyzing their direction dependences.
Relationship Between the Elastic Buckling of Square Tubes and Rectangular Plates
Authors: Li S. , Reid S. R.
Published: April 2008

The buckling behavior of axially compressed square tubes is investigated by introducing realistic edge conditions for the panels which correspond to symmetry or antisymmetry in the modes of deformation of the tube cross-section with regard to the diagonals of the section. The results show a number of differences between the buckling behavior of square tubes and of simply-supported plates. This vanishes only for very thin tubes and plates. The comparison between the buckling mode for thinner and thicker tubes suggests an explanation for the existence of compact and noncompact crushing modes in the subsequent crushing of tubes.
Buckling and Post-Buckling Behavior of Elliptical Plates: Part I—Analysis
Authors: Chai Herzl
Published: April 2008

A polynomial series expansion for displacements is used in conjunction with the Rayleigh-Ritz energy method to produce buckling and post-buckling stress solutions for an elliptically-shaped surface layer that has been delaminated from the main load-bearing body. Plate deformations are induced by a combined in-plane displacement field applied to the plate boundary and normal pressure. Convergence of the plate solution is assessed by systematically increasing the number of displacement terms in the series expansion. The convergence of membrane and bending stresses at the plate boundary was generally slow and nonuniform. The degrees-of-freedom necessary for a satisfactory solution typically increase with increasing complexity or magnitude of the plate deformations. By employing as many as 77 displacement terms, practically exact stress solutions are obtained for a wide variety of basic delamination plate problems. The proposed solution procedure is highly efficient and economical, and it may be easily extended to other plate geometries or loading conditions.
Free Vibration and Tension Buckling of Circular Plates With Diametral Point Forces
Authors: Ayoub E. F. , Leissa A. W.
Published: April 2008

This paper presents the first known results for the free vibrations of a circular plate subjected to a pair of static, concentrated forces acting on the boundary at opposite ends of a diameter. The closed-form exact solution of the plane elasticity problem is used to provide the in-plane stress distribution for the vibration problem. A proper procedure using the Ritz method is developed for solving the latter problem for clamped, simply supported, or free boundary conditions. Numerical results are given for the vibration frequencies of a simply supported circular plate, which separate into four symmetry classes of mode shapes. Compressive buckling loads for each symmetry class are determined as a special case as the frequencies decrease to zero with increasing compressive force. Tracking the frequency versus loading data with increasing tensile forces shows that buckling due to tensile force can also occur, and the critical value of the force is found.
The Various Approximations of the Bimetallic Thermostatic Strip
Authors: Pionke Christopher D. , Wempner Gerald
Published: April 2008

A thin strip, formed by bonding two dissimilar materials, constitutes a simple thermostatic element. If edge effects are neglected, then the strip is reduced to a uniform beam, or plate, with two degrees-of-freedom. The flexure occurs only because of the bond and interfacial shear which is also accompanied by transverse normal stress. These latter stresses are very localized at the end and edges. Here, the elementary approximations, and refinements via finite elements, are presented and compared. Deflections are given with reasonable accuracy by the simple approximations, but the severe interfacial stresses are revealed only by the refinements.
Thermoelastic Problems of Reinforced Rectangular Panels
Authors: Birman Victor
Published: April 2008

The static response of isotropic reinforced panels in nonuniform thermal fields is discussed. The effects of temperature on material properties are included into consideration. The governing equations formulated in the Note allow the solution both by energy methods and using equilibrium equations. The theory is applied to estimation of the effect of a uniform temperature on stability of compressed reinforced panels and to the problem of thermal bending of unstiffened plates.
Nonaxisymmetric Annular Punch Problem
Authors: Fabrikant V. I.
Published: April 2008

A general formulation is given for the first time to the title problem. The method is based on the new results in potential theory obtained by the author earlier. The problem is reduced to a two-dimensional integral equation with an elementary kernel. Several specific examples are considered.
Reflection and Transmission of a Plane Wave by an Array of Cavities in the Interface of Two Solids
Authors: Xu Yonglin
Published: April 2008

The reflection and transmission of a plane wave by a distribution of cavities in the interface of two solids of different mechanical properties are investigated. For the calculation of the reflection and transmission coefficients by a distribution of cavities, six auxiliary wave states are used in conjunction with the reciprocal identity. Specific results are presented for scattering by a doubly periodic array of cavities in the interface of solids of different elastic moduli and mass densities. For a typical cell, the boundary integral equations for scattering by a cavity at the interface of two solids are derived on the basis of continuity of displacements and tractions across the interface and by taking advantage of the geometrical periodicity. Solutions to the system of singular integral equations have been obtained by the boundary element method. Numerical results are presented as functions of the frequency for two angles of incidence.
Overdamped and Gyroscopic Vibrating Systems
Authors: Barkwell Lawrence , Lancaster Peter
Published: April 2008

Some linear vibrating systems give rise to differential equations of the form Ix¨(t) + Bx˙(t) + Cx(t) = 0, where B and C are square matrices. Stability criteria involving only the matrix coefficients I, B, C, and a single parameter are obtained for some special cases. Thus, if B* = B> 0, C* = C>0 and B>kI + k−1C, then the system will be overdamped (and hence stable). Gyroscopic systems also have the above form where B is real and skew symmetric. The case where C>0 is well understood and for the case −C>0 we show the condition Babs>kI−k−1C for some k>0 will ensure stability. In fact, this condition can be generalized to systems with B* = B, C>0.
Symmetry Reduction of Reynolds Equation and Applications to Film Lubrication
Authors: Abell M. L. , Ames W. F.
Published: April 2008

A symmetry reduction using a one-parameter spiral group is performed on a Reynolds equation in order to analyze this equation arising in the study of film lubrication. Approximate solutions are found for the time-independent case-both numerically and by the method of perturbation. Solutions to the time-dependent equation are found by using the invariance in the time and angular variables only. These solutions, called semi-invariant solutions, are determined through separation of variables.
A General Solution for the Pressurized Elastoplastic Tube
Authors: Durban David , Kubi Michael
Published: April 2008

The problem of a thick-walled cylindrical tube subjected to internal pressure is investigated within the framework of continuum plasticity. Material behavior is modeled by a finite strain elastoplastic flow theory based on the Tresca yield function. The deformation pattern is restricted by the plane-strain condition but arbitrary hardening and elastic compressibility are accounted for. A general solution is given in terms of quadratures. The analysis also includes treatment of a second plastic phase, characterized by corner relations, that may develop at the inner boundary. It is shown that the interface between the two plastic regions moves initially outwards and then, beyond a certain strain level, it moves back inwards. Some useful and simple results are given for thin-walled tubes of hardening materials and for thick-walled elastic/perfectly plastic tubes.
On the Numerical Evaluation of the Unforced Response of a Duffing Oscillator
Authors: Hahn G. D. , Carney J. F. , Ray Malcolm H.
Published: April 2008

A recent study suggested that the use of numerical integration methods would generally lead to the erroneous prediction of chaotic behavior for an unforced Duffing’s oscillator. It is shown herein that appropriate implementations of such methods lead to accurate, nonchaotic computations of the associated response.
On Transverse Vibrations of a Rotating Disk of Uniform Strength
Authors: Gu¨ven Ugˇur
Published: April 2008

Transverse, axisymmetric vibrations of a rotating disk of uniform strength is studied. Closed-form solution for the equation of transverse motion is obtained in terms of confluent hypergeometric functions.
The Optimal Mode and an Approximate Expression of Final Displacement in Dynamic Plastic Response of Structures
Authors: Huang Zhu-ping , Sun Li-zhi
Published: April 2008

The paper is concerned with the dynamic response of impulsively loaded rigid-perfectly plastic structures. By combining the mode approximation technique with the upper and the lower bound theorems, we have derived a set of sequential inequalities on the final displacement of the structure. This can be applied to give a reasonable explanation for the criterion of choosing an optimal mode proposed by Symonds (1980). In addition, an approximate expression of the final displacement of the structure is suggested in cases where the “mode approximation” apparently works poorly. Finally, the suggested expression is also illustrated by examples.
Bonded Bi-material Half-Planes With Semi-elliptical Notch Under Tension Along the Interface
Authors: Hasebe Norio , Okumura Mikiya , Nakamura Takuji
Published: April 2008

A problem of two bonded, dissimilar half-planes containing an elliptical hole on the interface is solved. The external load is uniform tension parallel to the interface. A rational mapping function and complex stress functions are used and an analytical solution is obtained. Stress distributions are shown. Stress concentration factors are also obtained for arbitrary lengths of debonding and for several material constants. In addition, an approximate expression of the stress concentration factor is given for elliptical holes and the accuracy is investigated.
Influence of Cracking Direction on Interfacial Fracture in Bicrystals With Symmetric Tilt Boundary
Authors: Mohan R. , Ortiz M. , Shih C. F.
Published: April 2008

Recent experiments by Wang (1990) on copper bicrystals with a [110] symmetric tilt of 38.9 degrees have shown that the mode of fracture of these bicrystals, i.e., whether fracture is of a ductile or brittle nature, depends on the direction of cracking. An analysis of this effect within the framework of continuum crystal plasticity is presented. The formulation accounts for finite deformations and finite lattice rotations, as well as for the full three-dimensional collection of slip systems in FCC crystals. Our results indicate that, whereas the level of stress ahead of the crack tip is similar for the ductile and brittle cracking directions, the sizes of the plastic regions differ significantly in the two cases.
Impact Response of a Single Edge Crack in an Orthotropic Strip
Authors: Shindo Yasuhide , Higaki Hiroaki , Nozaki Hideaki
Published: April 2008

The elastodynamic response of a single edge crack in an orthotropic strip under normal impact is considered in this study. The edge crack is oriented in a direction normal to the edge of the strip. Laplace and Fourier transforms are used to reduce the transient problem to the solution of a pair of dual integral equations in the Laplace transform plane. The solution to the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. A numerical Laplace inversion routine is used to recover the time dependence of the solution. Numerical values on the dynamic stress intensity factor for several fiber-reinforced composite materials are obtained, and the results are graphed to display the influence of the material orthotropy.
Dynamic Crack Propagation Analysis by Moving Singular Boundary Elements
Authors: Gallego Rafael , Dominguez Jose´
Published: April 2008

An efficient boundary element procedure for the dynamic analysis of crack propagation in unbounded and arbitrary shape finite bodies is presented. The procedure is based on the direct time domain formulation of the boundary element method. A moving singular element and a remeshing technique have been developed to model the asymptotic solution of the stresses near the propagating crack tip. These ideas are easily implemented for a boundary discretization as opposed to similar procedures previously developed in a finite element context. The method is applied to problems of dynamic crack propagation in finite and infinite elastic domains. The obtained numerical results are compared with infinite domain analytical solutions and with available numerical solutions for finite domains.
The Equations of Motion for the Torsional and Bending Vibrations of a Stranded Cable
Authors: White Warren N. , Venkatasubramanian Srinivasan , Lynch P. Michael , Huang Chi-Lung D.
Published: April 2008

Equations of motion of a thin, stranded elastic cable with an eccentric, attached mass and subject to aerodynamic loading are derived using Hamilton’s principle. Coupling between the translational and rotational degrees of freedom owing to inertia, elasticity, and stranded geometry are considered. By invoking simplifying assumptions, the equations of motion are reduced to those obtained previously by other researchers.
Effects of Load Parameters on the Natural Frequencies and Stability of a Flexible Spinning Disk With a Stationary Load System
Authors: Chen Jen-San , Bogy D. B.
Published: April 2008

The orthogonality properties among the eigenfunctions for a gyroscopic system are derived for a stiffness operator that is not positive definite. The derivatives of the eigenvalues with respect to certain parameters in the system are then obtained. The results are applied to a spinning disk in contact with a stationary load system, which contains such parameters as friction force, transverse mass, damping, stiffness, and the analogous pitching elements, to predict the effects of these parameters and the stiffening of the disk due to the centrifugal force on the natural frequencies and stability of the spinning disk. The results obtained provide a theoretical understanding for previously reported observations based on numerical solutions.
Elementary Solutions and Process Sensitivities for Plane-Strain Sheet-Metal Forming
Authors: Wenner M. L.
Published: April 2008

Solutions to simple, plane-strain sheet-metal forming problems are developed using an exact solution to the membrane equilibrium equations and apre-integrated version of the plasticity equations. This approach allows the numerical errors to be driven to very low levels in an economical manner. Both stretch and draw conditions are considered, and solutions are presented for several problems which have been proposed as benchmarks for sheet-metal forming computer programs. The simplicity of this approach allows us to calculate formulas for the sensitivity of the solutions to process parameters. It is demonstrated that draw problems can exhibit very strong dependencies on parameters, especially drawbead restraint force.
Stress Concentration at a Nearly Circular Hole With Uncertain Irregularities
Authors: Givoli Dan , Elishakoff Isaac
Published: April 2008

We study the stress concentration on the boundary of an uncertain nearly circular hole in an infinite elastic plane under uniform radial tension at infinity. The uncertainty in the deviation of the hole profile from an ideal circle is modeled deterministically. The shape of the hole boundary in polar coordinates is assumed to have the form r = R + εh(θ), where R is the radius of the unperturbed circle and ε is a small parameter. First, we find an asymptotic solution for the stress concentration factor around the hole for any profile h(θ). Then we consider a certain set of bounded profiles, and we find the specific profile that yields the maximum stress concentration factor. This may provide the designer with a useful “worst case” information regarding the influence of the uncertainty of the hole shape on the uncertainty of the resulting stress concentration factor.
Shear Constitutive Relations for Laminated Anisotropic Shells and Plates: Part I—Methodology
Authors: Dong S. B. , Chun C. K.
Published: April 2008

Shear constitutive relations of a first-order shear deformation theory for laminated anisotropic shells and plates are formulated following Mindlin’s procedure for homogeneous isotropic plates. Because thickness-shear motions for laminated anisotropic thickness profiles may not be polarized in planes normal to the reference surface, the concept of generalized principal shear planes is needed. These planes are established by least-squares minimization of the out-of-plane motions of infinitely long thickness-shear waves based on an elasticity analysis of the profile. Typical shear rigidities for a variety of laminated composite and sandwich profiles are given. In a companion paper, the efficacy of this form of shear constitutive relations in predicting the response of a class of laminated composite and sandwich cylindrical shells is demonstrated.
Mathematical Structure of Modal Interactions in a Spinning Disk-Stationary Load System
Authors: Chen Jen-San , Bogy D. B.
Published: April 2008

In a previous paper (Chen and Bogy, 1992) we studied the effects of various load parameters, such as friction force, transverse mass, damping, stiffness and the analogous pitching parameters, of a stationary load system in contact with the spinning disk on the natural frequencies and stability of the system when the original eigenvalues of interest are well separated. This paper is a follow-up investigation to deal with the situations in which two eigenvalues of the freely spinning disk are almost equal (degenerate) and strong modal interactions occur when the load parameters are introduced. After comparing an eigenfunction expansion with the finite element numerical results, we find that for each of the transverse and pitching load parameters, a properly chosen two-mode approximation can exhibit all the important features of the eigenvalue changes. Based on this two-mode approximation we study the mathematical structure of the eigenvalues in the neighborhood of degenerate points in the natural frequency-rotation speed plane. In the case of friction force, however, it is found that at least a four-mode approximation is required to reproduce the eigenvalue structure. The observations and analyses presented provide physical insight into the modal interactions induced by various load parameters in a spinning disk-stationary load system.
Free-Surface Oscillations in a Slowly Draining Tank
Authors: Zhou Qiao-Nian , Graebel W. P.
Published: April 2008

The initial behavior of a free surface in a draining (filling) circular tank is analyzed using a linearized model. The withdrawal (injection) of fluid damps (enhances) oscillations which either exist before the withdrawal (filling) or are induced by the withdrawal (injection). The initial growth rate of the drainage-initiated free-surface oscillations strongly depends on the initial behavior of the drain rate function. If the drain is turned on gradually, the drainage-initiated free-surface oscillation is weaker compared to the forced one, so there are no drainage-initiated oscillations. However, if the drain is turned on suddenly, the induced oscillatory motion dominates the forced motion. For periodic drainage, the results show that the strongest resonant oscillation occurs when the drainage frequency w coincides with the first natural frequency of the flow system. All of the nonresonant modes of the oscillations are stable regardless of the initial behavior of the drain rate. If q(t) = sinωt, all of the resonant oscillations are stable. In the case when q(t) = cosωt, the initial jump in the drainage means that the resonance modes can be either unconditionally unstable, unconditionally stable, or conditionally unstable, depending on the various parameters.
Nonlinear Response of Graphite-Epoxy Wide Columns Subject to Eccentric Load
Authors: Griffin O. Hayden , Johnson Eric R. , Sensmeier Mark D.
Published: April 2008

It is shown that including the effects of bend-twist coupling and material nonlinearity on the large displacement flexural response of graphite-epoxy wide columns is necessary to adequately model their response. Results from static tests on [030]T and [(30/0/-30)5]s laminated specimens under eccentric axial compression are compared to a nonlinear analysis. The analysis is based on a Kantrovich expansion of the displacements in the width coordinate and a finite element representation in the axial coordinate. An incremental, updated Lagrangian formulation and element corotational coordinates are employed. Nonlinear elastic material behavior was measured in a separate set of material characterization tests, and these data are used to compute tangent stiffnesses in the updated configuration.
A Geometrically Nonlinear Theory of Elastic Plates
Authors: Hodges Dewey H. , Atilgan Ali R. , Danielson D. A.
Published: April 2008

A set of kinematical and intrinsic equilibrium equations are derived for plates undergoing large deflection and rotation but with small strain. The large rotation is handled by means of the general finite rotation of a frame in which the material points that are originally along a normal line in the undeformedplate undergo only small displacements. The unit vector fixed in this frame, which coincides with the normal when the plate is undeformed, is not in general normal to the deformed plate average surface because of transverse shear. The arbitrarily large displacement and rotation of this frame, which vary over the surface of the plate, are termed global deformation; the small relative displacement is termed warping. It is shown that rotation of the frame about the normal is not zero and that it can be expressed in terms of other global deformation variables. Exact intrinsic virtual strain-displacement relations are derived; based on a reduced two-dimensional strain energy function from which the warping has been systematically eliminated, a set of intrinsic equilibrium equations follow. It is shown that only five equilibrium equations can be derived in this manner, because the component of virtual rotation about the normal is not independent. These equilibrium equations contain terms which cannot be obtained without the use of a finite rotation vector which contains three nonzero components. These extra terms correspond to the difference of in-plane shear stress resultants in other theories; this difference is a reactive quantity in the present theory.
On the Conditions to Prevent Plastic Shakedown of Structures: Part I—Theory
Authors: Polizzotto Castrenze
Published: April 2008

For a structure of elastic perfectly plastic material subjected to a given cyclic (mechanical and/or kinematical) load and to a steady (mechanical) load, the conditions are established in which plastic shakedown cannot occur whatever the steady load, and thus the structure is safe against the alternating plasticity collapse. Static and kinematic theorems, analogous to those of classical shakedown theory, are presented.
Elastic-Plastic Tip Field for a Stationary Crack in a Reinforced Thin Sheet
Authors: Sta˚hle P.
Published: April 2008

A class of plane stress problems for incompressible materials is studied. The class concerns problems for unidirectionally reinforced thin sheets under quasi-static loading conditions.
Initiation of an Interface Crack Under Mixed-Mode Loading
Authors: Foltyn P. A. , Ravi-Chandar K.
Published: April 2008

The compact tension shear specimen is proposed as a simple experimental configuration suitable for the determination of the variation of the interfacial fracture toughness as a function of the loading mixity. The suitability of this specimen is demonstrated on a model system of diffusion bonded PMMA.
On the Approximation of a Deflection Curve by Force Actuators
Authors: Natarajan K. , Dumont G. A. , Davies M. S.
Published: April 2008

In this paper we discuss a method of approximating a deflection curve of a simple beam by means of a given number of equispaced force actuators subject to constraints on the bending moment. The deflection curve is assumed to be specified at a number of equi-spaced points greater than the number of actuators. The method developed minimizes the approximation error in an integral squared sense. The method is applied to an example of approximation of a deflection curve of the slice lip on a paper machine headboxfor the control of basis weight of paper.
Further Results on Iterative Approaches to the Determination of the Response of Nonclassically Damped Systems
Authors: Udwadia Firdaus E.
Published: April 2008

Iterative schemes for obtaining the response of nonclassically damped dynamic systems have been shown to converge when the damping matrix possesses certain specific characteristics. This paper extends those previous results which pertain to symmetric, positive-definite damping matrices. The paper considers a more general decomposition of the damping matrix, and extends the applicability of these iterative methods to all positive definite, symmetric damping matrices. This decomposition is governed by a parameter α. Conditions on α under which convergence is guaranteed are provided. Estimates of a which yield the fastest asymptotic convergence as well as estimates of the value of this asymptotic rate of convergence are also provided.
On the Dundurs Correspondence Between Cavities and Rigid Inclusions
Authors: Markenscoff X.
Published: April 2008

In plane elasticity the solutions of the stress field of rigid inclusion problems yield the solutions of cavity problems loaded by uniform shear tractions σ = 2μ (Ω − ω0) |κ = −1 where Ω is the rotation of the inclusion and ω0 the rotation of the material (evaluated at κ = −1, κ being the Kolosov constant). It is proved that if the limit of the stress field for the inclusion problem exists at κ = −1, then it corresponds to a constant rotation field.
Buckling and Post-buckling Characteristics of Pressure-Loaded Cylinders
Authors: Yamada Seishi , Croll J. G. A.
Published: April 2008

Nonlinear Ritz analysis is used to investigate the elastic buckling behavior of pressure loaded cylinders. Careful analysis of the energy changes during the buckling process allows definition of a reduced stiffness theoretical model. This reduced stiffness model provides a convenient means for estimating lower bounds to the imperfection sensitive elastic buckling behavior.
Energy Considerations in the Flow Enhancement of Viscoelastic Liquids
Authors: Siginer A. , Valenzuela-Rendo´n A.
Published: April 2008

Flow enhancement effects due to different waveforms in the tube flow of rheologically complex fluids driven by a pulsating pressure gradient are investigated. It is found that the squarer the waveform the larger the enhancement. In each case the enhancement is strongly dependent on the viscosity function, but the elastic properties also play an important role. We determine that considerable energy savings may be obtained in the transport of viscoelastic liquids if an oscillatory gradient is superposed on a mean gradient. The closer the oscillation to the square wave the larger the energy savings.
Kinetic Energy and Complementary Kinetic Energy in Gyrodynamics
Authors: Rimrott F. P. J. , Szczygielski W. M. , Tabarrok B.
Published: April 2008

The concepts of kinetic energy and complementary kinetic energy permit to distinguish between two different formulations of what happens to be the same quantity in Newtonian mechanics. These formulations turn out to play a significant role in gyrodynamics in that they can be used very effectively to establish fundamental equations. It is relatively straightforward to establish a complementary kinetic energy expression. The establishment of the kinetic energy expression is, in spite of its unambiguous definition, more complicated, and a way is presented how to obtain it without too much difficulty. Equations are presented for the more common angle systems, i.e., for Euler angles of the first kind, Cardan angles of the first kind, both because of their fundamental importance, and Cardan angles of the fifth kind because of its prevalence in aeronautics.
The Axisymmetric Crack Problem in a Nonhomogeneous Medium
Authors: Ozturk M. , Erdogan F.
Published: April 2008

In this paper, the axisymmetric crack problem for a nonhomogeneous medium is considered. It is assumed that the shear modulus is a function of z approximated by μ = μ0eαz. This is a simple simulation of materials and interfacial zones with intentionally or naturally graded properties. The problem is a mixed-mode problem and is formualated in terms of a pair of singular integral equations. With fracture mechanics applications in mind, the main results given are the stress intensity factors as a function of the nonhomogeneity parameter a for various loading conditions. Also given are some sample results showing the crack opening displacements.
Vibration of Elastic Structures With Cracks
Authors: Shen I. Y.
Published: April 2008

An analytical algorithm is proposed to represent eigensolutions [λm2, ψm(r)]m=1∞ of an imperfect structure C containing cracks in terms of crack configuration σc and eigensolutions [ωn2, φn(r)]n=1∞ of a perfect structured without P the cracks. To illustrate this algorithm on mechanical systems governed by the two-dimensional Helmholtz operator, the Green’s identity and Green’sfunction of P are used to represent ψm(r) in terms of an infinite series of φn(r). Substitution of the ψn(r) representation into the Kamke quotient of C and stationarity of the quotient result in a matrix Fredholm integral equation. The eigensolutions of the Fredholm integral equation then predict λm2 and ψm(r) of C. Finally, eigensolutions of two rectangular elastic solids under antiplane strain vibration, one with a boundary crack and the other with an oblique internal crack, are calculated numerically.
Natural Frequencies and Stability of a Flexible Spinning Disk-Stationary Load System With Rigid-Body Tilting
Authors: Chen Jen-San , Bogy D. B.
Published: April 2008

The effects of rigid-body tilting on the natural frequencies and stability of the head-disk interface of a flexible spinning disk are studied both by analysis and numerical computation. Another problem of a stationary flexible disk with rigid body tilting subject to a rotating load system is also studied. In the conventional case without rigid-body tilting, these two problems are mathematically identical except for the additional membrane stress terms arising from the centrifugal force. When the rigid-body tilting is included, however, these two problems differ not only by the centrifugal effect, but also by additional terms which arise from the gyrodynamic effect. After properly defining the inner product between two state vectors, the set of equations of motion is proven to fall into the category of gyrosopic systems. Then the derivatives of the eigenvalues of the coupled system are obtained to provide a better understanding of the numerical results.
Exact Analytical Solutions for the Vibrations of Sectorial Plates With Simply-Supported Radial Edges
Authors: Huang C. S. , Leissa A. W. , McGee O. G.
Published: April 2008

The first known exact analytical solutions are derived for the free vibrations of sectorial thin plates having their radial edges simply supported, with arbitrary conditions along their circular edges. This requires satisfying: (1) the differential equation of motion, (2) boundary conditions along the radial and circular edges, and (3) proper regularity conditions at the vertex of the radial edges. The solution to the differential equation involves ordinary and modified Bessel functions of the first and second kinds, of non-integer order, and four constants of integration. Utilizing a careful limiting process, the regularity conditions are invoked to develop two equations of constraint among the four constants for sector angles exceeding 180 deg (re-entrant corners). Moment singularities for re-entrant corners are shown to be the same as the ones determined by Williams (1952) for statically loaded sectorial plates. Frequency determinants and equations are generated for circular boundaries which are clamped, simply-supported, or free. Nondimensional frequency parameters are presented for all three types of configurations for sector angles of 195, 210, 270, 330, and 360 deg (i.e., re-entrant corners).
Stability of Conventional Controller Design for Flexible Manipulators
Authors: Tang L. , Skaar S. B.
Published: April 2008

The paper investigates the independent joint control of flexible manipulators which are acted upon by gravity. Both finite-dimensional coordinates, and infinite-dimensional, spatially varying, distributed coordinates are used to describe the deformation of the flexible links. The effects of the flexibility on the closed-loop system behavior in the presence of both derivative and integral feedback control are studied both in the Laplace transform domain using the linearized model of the original nonlinear system and in the time domain using the original nonlinear model. The use of infinite-dimensional coordinates is shown to be especially effective in obtaining the frequency domain characteristics of the linearized model because the exact frequency content of the linearized system may be extracted without involving the difficult order reduction problem. The problem of convergence onto an incorrect solution which is associated with using the eigenvectors of a clamped-free beam as the comparison functions in approximating the motion of the flexible arm is demonstrated and various factors affecting the performance of the flexible manipulator, such as control gains and material damping, are studied.
A Hardening Rule Between Stress Resultants and Generalized Plastic Strains for Thin Plates of Power-Law Hardening Materials
Authors: Chou C. H. , Pan J. , Tang S. C.
Published: April 2008

For power-law hardening materials, a stress resultant constitutive law of incremental plasticity nature for thin plates is constructed. The yield function in the stress resultant space is approximated in quadratic form and an equivalent stress resultant is defined. One of two parameters in the yield function is analytically determined based on the concept of complementary potential surface. The other is determined by the least square method to fit the complementary potential surface of Chou et al., (1991). In analogy to the work of Hill (1979), the equivalent work-conjugate generalized plastic strain rate is derived. Finally, the hardening rule between the equivalent stress resultant and generalized plastic strain is obtained based on the results of Chou et al. (1991) for power-law materials under proportional straining conditions.
Green’s Functions for Generalized Plane Problems of Anisotropic Bodies With a Hole or a Rigid Inclusion
Authors: Wang Yung-Ming , Tarn Jiann-Quo
Published: April 2008

Green’s function solutions are presented for the generalized plane problems of a point force and an edge dislocation located in the general anisotropic elastic medium with a hole or with a rigid inclusion. The Lekhnitskii’s complex potential approach is used and a general expression of the solutions is obtained. Particular attention is paid to the determination of appropriate mapping functions that map the exterior of the hole or the inclusion onto the exterior of a unit circle. The conditions under which the conformal mapping is possible are explored. Examples using the Green’s functions for the solution of notch problem are given.
Fluid Flow and Heat Transfer in the Crescent-Shaped Lumen Catheter
Authors: Ebadian M. A. , Zhang H. Y.
Published: April 2008

This paper presents a numerical investigation of fluid flow, frequency response in the fully developed region, and convective heat transfer in the entrance region of the crescent-shaped lumen catheter. The catheter is commonly used in the biomedical field to clinically diagnose heart disease and also to treat vessel blockage in surgery. The catheter is subjected to a constant wall temperature. The solution to discretization of the momentum and energy equations is obtained by using the numerically generated boundary fitted coordinate system. According to this method, the complex domain in the physical plane is transformed into a regular square domain in the computational plane. The control volume-based finite difference method is then used to discretize the transformed governing equations. Results for the thermal entry region flow, frequency response, and heat transfer are presented in graphical form. The representative curves illustrating variations of the flow rate, frequency response, damping coefficient, bulk temperature, and the Nusselt numbers with pertinent parameters in the entire thermal entry region are plotted. The optimized catheter design for diagnostic use in the medical industry is also presented graphically.
Stress Field due to a Dislocation on the Interface Between Two Quarter Planes
Authors: Kelly P. , Hills D. A. , Nowell D.
Published: April 2008

Solutions are found for the state of stress obtaining along the interface between two bonded quarter planes, induced by an edge dislocation located at an arbitrary point on the interface. Explicit asymptotic expressions are given for the stress at points close to the free surfaces.
A Doubly Periodic Rectangular Array of Fiber-Matrix Interfacial Cracks Under Longitudinal Shearing
Authors: Teng Hong , Agah-Tehrani A.
Published: April 2008

The antiplane strain problem of a unidirectional fiber composite consisting of a doubly periodic rectangular array of fibers containing interfacial cracks in an infinite matrix is considered. The interfacial cracks are assumed to exhibit the same periodicity as the fibers. The periodicity of the geometry allows the use of a unit cell in the formulation of the problem. The governing weakly singular integral equation of the mixed boundary value problem permits an explicit solution which contains a set of unknown constants. The unknown constants are then determined by satisfying the boundary conditions on the external surfaces of the unit cell through the method of least squares. The stress intensity factor is calculated for various crack lengths, fiber volume fractions, and fiber spacings. Unlike the plane strain or plane stress deformation, the oscillations in stress and displacement around the interface crack tip are absent in the current antiplane strain problem.
Transient Wave Propagation Methods for Determining the Viscoelastic Properties of Solids
Authors: Blanc R. H.
Published: April 2008

The following two solutions are proposed for deducing the viscoelastic properties of a solid from the change in the shape of a one-dimensional transient mechanical wave as it propagates through the medium: (i) The general solution:—the phase velocity and the attenuation coefficient are expressed in terms of the Fourier transforms of the pulse after two distances of travel, and (ii) A filter method. An experimental set-up is described. The results, which are obtained with no heating of the material, come within the audiofrequency range. This method fills a gap between the existing vibratory and ultrasonic methods.
Nonlinear Adaptive Engine Speed Control Using an Instrumental Variables Approach and a Truncated Volterra Series
Authors: Anders Jonathan W. , Franchek Matthew A.
Published: April 2008

An instrumental variable approach to nonlinear model-based adaptive control of engine speed is investigated and implemented on a spark ignition internal combustion engine. A four-step version of the instrumental variable parameter estimation algorithm is used to identify a bias-free and noise tolerant model of the engine dynamics between the by-pass air valve voltage and engine speed. The parametric model representing the engine dynamics is a truncated Volterra series with a time delay. Model-based adaptive control is accomplished through a partitioned inversion of the engine model which is minimum phase and OL stable. The desired closed loop throttle response and disturbance rejection dynamics are introduced via a two-degree-of-freedom feedback control structure. Performance of the nonlinear model-based adaptive control algorithm is verified experimentally.
In SI Engines: Prediction of Ring Crevice Hydrocarbons Depending on Some Engine Parameters
Authors: Yildirim A. Murat , Ozatay Evren , Gul Zafer
Published: April 2008

This paper represents results of a theoretical work devoted to diffusion and removal of ring crevice HC’s. The model consists of three major sub models: a model for prediction of time-varying composition of combustion gases, a model for the ring crevice HC’s during late expansion and exhaust stroke and the last one for a simple phenomenological approach to calculate temperature variation. Flow field and HC concentrations are determined by solution of governing equations. Oil film HC’s and post flame oxidation are excluded, as for the last, solution procedure enhances the period after which in cylinder oxidation ceases. A 60 × 60 variable mesh flow field is adapted for finite volume solution procedure. Results are presented at the extended limited counterparts allowed, due to the lack of common parameters adapted in different studies amongst plenty of them.
A New Method for the Identification of Coulomb and Viscous Friction
Authors: Liu Lilan , Liu Hongzhao , Wu Ziying , Yuan Daning
Published: April 2008

In this paper, a new method for simultaneously estimating Coulomb and viscous friction parameters from the free vibration of a damped oscillator is put forward. In the method, the nonlinear vibration equation with Coulomb and viscous friction is transformed into a linear procedure with equivalent viscous damping which is a function of velocity. The proposed method works well with both the displacement and velocity response data, while the case of zero velocity is not considered. From the displacement decaying curve, the equivalent viscous damping ratios are obtained by means of the local exponential fitting method, and different velocities corresponding to the equivalent viscous damping ratios are also obtained from the velocity decaying curve. Then, according to the relationship between the equivalent viscous damping ratio and the velocity, the Coulomb friction and the viscous damping are achieved using the least square method. The validity and accuracy of the proposed method are demonstrated through good simulation results.
The Dynamic Study of a Frontal-Sinusoidal Transmissions With Balls
Authors: Bara Mircea
Published: April 2008

The first part of the paper are analyzed the components of the torque of the forces of inertia that act upon the frame of the frontal–sinusoidal transmission with balls. Analyzing at turn the expressions of the main vector and of the momentum of the forces of inertia one realizes that these are null, which shows that the transmission is balanced. In the second part they determine the way in which the geometrical parameters of the running channels of the balls influence the energy dissipation in the frontal sinusoidal transmission with balls.
Variable Thermal Conductivity Heat Transfer With Symbolic Algebra
Authors: Aziz A.
Published: April 2008

This paper deals with the analysis of heat transfer in media with variable thermal conductivity. The tool employed is the symbolic algebra package Maple. The specific problems considered are (1) steady conduction in a heat generating plane wall with thermal conductivity increasing as the square of the coordinate, (2) steady conduction in a circular rod with axially varying thermal conductivity exposed to a cross flow stream, (3) steady conduction in a hollow cylindrical shell with simultaneous coordinate and temperature dependent thermal conductivity, (4) steady conduction in a two-layered hollow cylindrical shell with the thermal conductivity of the inner shell varying linearly with the radial coordinate and the thermal conductivity of the outer shell varying linearly with temperature, (5) two-dimensional steady conduction in an orthotropic plate with different thermal conductivities along the two axes, and (6) transient conduction in a plane wall with coordinate dependent thermal conductivity. The paper demonstrates the effectiveness of the software that is capable of producing analytical solutions for problems that are very cumbersome to solve by hand, and at the same incorporates powerful numerical and graphical capabilities for solving problems that are analytically intractable. The paper should not be perceived as a commercial endorsement of Maple.