bluuebunny/crossref_metadata_2025 huggingface dataset:
Stochastic Averaging of Quasi-Nonintegrable-Hamiltonian Systems
Authors: Zhu W. Q. , Yang Y. Q.
Published: February 2008

A stochastic averaging method is proposed to predict approximately the response of multi-degree-of-freedom quasi-nonintegrable-Hamiltonian systems (nonintegrable Hamiltonian systems with lightly linear and (or) nonlinear dampings and subject to weakly external and (or) parametric excitations of Gaussian white noises). According to the present method, a one-dimensional approximate Fokker-Planck-Kolmogorov equation for the transition probability density of the Hamiltonian can be constructed and the probability density and statistics of the stationary response of the system can be readily obtained. The method is compared with the equivalent nonlinear system method for stochastically excited and dissipated nonintegrable Hamiltonian systems and extended to a more general class of systems. An example is given to illustrate the application and validity of the present method and the consistency of the present method and the equivalent nonlinear system method.
Exact Solutions of Some Shear Dislocation Problems Involving a Stopping Effect
Authors: Lai Gwolong , Robinson A. R.
Published: February 2008

An analytical approach is developed for dealing with the sudden stopping of a shear dislocation that acts over an expanding circular or elliptical region. The analysis begins with the case of circular region. Despite the fact that this problem is not self-similar, it has been possible to express the solution as a superposition of several self-similar problems that have different degrees of homogeneity. The use of a new rotational superposition technique that includes a stretching effect developed by the authors allows the extension to elliptical shear dislocation problems.
The Kink Band Mechanism for the Compressive Failure of Fiber Composite Materials
Authors: Christensen R. M. , DeTeresa S. J.
Published: February 2008

A simple strain-based yield/failure criterion for fiber composite materials is incorporated into a kink band analysis of compressive failure. Under realistic conditions of fiber misalignment the analysis predicts compressive failure at load levels about one–fifth of the ideal value, and with kink band inclinations of about 20 deg. Some parametric variations of the relevant physical variables are given in simple graphical forms, and comparisons are made with newly obtained micrographs of kink bands.
An Orthotropic Viscoelastic Winding Model Including a Nonlinear Radial Stiffness
Authors: Qualls W. R. , Good J. K.
Published: February 2008

A realistic and adaptive viscoelastic model for prediction of transient wound roll stress distributions is presented. The web material is taken to be orthotropic with a nonlinear radial stiffness dependent upon interlayer pressure. Viscoelastic behavior is represented by a generalized Maxwell model for creep written as a convolution integral. Numerical solutions to the resulting integral boundary value problem give both initial and transient stress distributions within the wound roll. The model is successfully compared to the analytical solution for a simple case of isotropy as well as to published works on this topic. In contrasting the solutions, the advantages and adaptability of this formulation will be readily seen.
Equivalent Nonlinear System Method for Stochastically Excited and Dissipated Integrable Hamiltonian Systems
Authors: Zhu W. Q. , Lei Y.
Published: February 2008

An equivalent nonlinear system method is proposed to obtain the approximate probability density for the stationary response of multi-degree-of-freedom integrable Hamiltonian systems with linear and (or) nonlinear dampings and subject to external and (or) parametric excitations of Gaussian white noises. The equivalent nonlinear systems are obtained on the basis of one of the following three criteria: least mean-squared difference in damping forces, dissipation energy balancing, or least mean-squared difference in dissipation energies. Two examples are given to illustrate the application and validity of the method and the differences in the three equivalence criteria. The method is also extended to a more general class of systems which include the stochastically excited and dissipated integrable Hamiltonian systems as special cases.
Experiments on Nonlinear Dynamic Behavior of an Oscillator With Clearance and Periodically Time-Varying Parameters
Authors: Kahraman A. , Blankenship G. W.
Published: February 2008

A number of experiments on a physical system with clearance having combined parametric and external forcing excitation are presented. The data demonstrate several nonlinear phenomena that exist in periodically excited oscillators subject to clearance at a contact interface. Jump discontinuities in forced response curves are shown to exist and subharmonic resonances which are formed by period-n (nT) motions with n ≥ 2 are demonstrated. Long-period subharmonic motions with periods as long as nine times the excitation period are reported. Finally, several cases of measured chaotic motions are also illustrated through time-traces, phase portraits, Fourier spectra, and Poincare plots which form strange attractors.
On the Motion of Lineal Bodies Subject to Linear Damping
Authors: Beatty M. F.
Published: February 2008

Wilms (1995) has considered the plane motion of three lineal rigid bodies subject to linear damping over their length. He shows that these plane single-degree-of-freedom systems are governed by precisely the same fundamental differential equation. It is not unusual that several dynamical systems may be formally characterized by the same differential equation, but the universal differential equation for these systems is unusual because it is exactly the same equation for the three very different systems. It is shown here that these problems belong to a more general class of problems for which the differential equation is exactly the same for every lineal rigid body regardless of its geometry.
On the Use of a Plane-Strain Model to Solve Generalized Plane-Strain Problems
Authors: Hu Shoufeng , Pagano N. J.
Published: February 2008

Many composite problems are generalized plane strain in nature. They are often solved using three-dimensional finite element analyses. We propose a technique to solve these problems with a plane-strain model, which is achieved by introducing some artificial out-of-plane thermal strains in a two-dimensional finite element analysis. These artificial thermal strains are chosen such that an identical stress field is obtained, while the actual strains and displacements can also be determined.
A Volume Integral Equation Technique for Multiple Inclusion and Crack Interaction Problems
Authors: Lee Jungki , Mal Ajit
Published: February 2008

A volume integral equation method is introduced for the solution of elastostatic problems in heterogeneous solids containing interacting multiple inclusions, voids, and cracks. The method is applied to two-dimensional problems involving long parallel cylindrical inclusions and cracks. The influence of interface layers on the interfacial stress field is investigated. The stress intensity factors for microcracks in the presence of interacting inclusions or voids are also calculated for a variety of model geometries. The accuracy and efficiency of the method are examined through comparison with results obtained from analytical and boundary integral methods.
Seismic Waves in a Laterally Inhomogeneous Layered Medium, Part II: Analysis
Authors: Zhang Ruichong , Zhang Liyang , Shinozuka Masanobu
Published: February 2008

Seismic wave scattering representation for the layered half-space with lateral inhomogeneities subjected to a seismic dislocation source has been formulated in the companion paper with the use of first-order perturbation (Born-type approximation) technique. The total wave field is obtained as a superposition of the mean and the scattered wave fields, which are generated, respectively, by a series of double couples of body forces equivalent to the seismic dislocation source and by fictitious body forces equivalent to the existence of the lateral inhomogeneities in the layered half-space. The responses in both the mean and the scattered wave fields are found with the aid of an integral transform technique and wave propagation analysis. The characteristics of the scattered waves and their effects on the mean waves or corresponding induced ground and/or underground mean responses are investigated in this paper. In particular, coupling phenomena between P-SV and SH waves and wave number shifting effects between the mean and the scattered wave responses are presented in detail. With the lateral inhomogeneities being assumed as a homogeneous random field, a qualitative analysis is provided for estimating the effects of the lateral inhomogeneities on the ground motion, which is related to a fundamental issue: whether a real earth medium can or cannot be approximately considered as a laterally homogeneous layer. The effects of the lateral inhomogeneities on the ground motion time history are also presented as a quantitative analysis. Finally, a numerical example is carried out for illustration purposes.
Dynamic Crack Propagation in a Layered Medium Under Antiplane Shear
Authors: Ma Chien-Ching , Ing Yi-Shyong
Published: February 2008

In this study, the transient analysis of dynamic antiplane crack propagation with a constant velocity in a layered medium is investigated. The individual layers are isotropic and homogeneous. Infinite numbers of reflected cylindrical waves, which are generated from the interface of the layered medium, will interact with the propagating crack and make the problem extremely difficult to analyze. A useful fundamental solution is proposed in this study, and the solution can be determined by superposition of the fundamental solution in the Laplace transform domain. The proposed fundamental problem is the problem of applying exponentially distributed traction (in the Laplace transform domain) on the propagating crack faces. The Cagniard’s method for Laplace inversion is used to obtain the transient solution in time domain. The exact closed-form transient solutions of dynamic stress intensity factors are expressed in compact formulations. These solutions are valid for an infinite length of time and have accounted for contributions from all the incident and reflected waves interaction with the moving crack tip. Numerical results of dynamic stress intensity factors for the propagation crack in layered medium are evaluated and discussed in detail.
Circular Rigid Punch With One Smooth and Another Sharp Ends on a Half-Plane With Edge Crack
Authors: Hasebe Norio , Qian Jun
Published: February 2008

A circular rigid punch with friction is assumed to contact with a half-plane with one end sliding on the half-plane and another end with a sharp corner. The contact length is determined by satisfying the finite stress condition at the sliding end of the punch. The crack is initiated near the end with a sharp corner where infinite stresses exist. Coulomb’s frictional force is supposed to act on the contact region. The cracked half-plane is mapped into a unit circle by using a rational mapping function, and the problem is transformed into a standard Riemann-Hilbert problem, which is solved by introducing a Plemelj function. The contact length, the stress intensity factors of the crack, and the resultant moment about the origin of the coordinates on the contact region are calculated for different frictional coefficients, Poisson’s ratios of the half-plane, crack lengths, and distances from the crack to the punch, respectively. The stress distributions on the contact region are also shown.
Weight Functions for Notches: Constructive and Variational Definition
Authors: Kirchner H. O. K.
Published: February 2008

Weight functions for notches or cracks, which express the intensity of the stress singularity at the tip as functionals of the loadings present, can be defined either as combination of eigenfunctions or as variational derivatives of energies. The two definitions are equivalent.
Experimental Identification Technique of Vibrating Structures With Geometrical Nonlinearity
Authors: Yasuda Kimihiko , Kamiya Keisuke , Komakine Munenobu
Published: February 2008

A new experimental identification technique of a two-dimensional vibrating elastic structure with geometrical nonlinearity is considered. First it is shown that the governing equations given in the form of nonlinear partial differential equations can always be transformed to those given in the form of nonlinear ordinary differential equations called the modal equations, and hence identification is reduced to determination of the modal equations. Then a technique for determining the parameters of the modal equations through use of experimental data is proposed. Numerical simulation is conducted for typical cases, and applicability of the technique is confirmed.
On the Nonaxisymmetric Loading of Nonhomogeneous Annular Plates of Variable Thickness
Authors: Yeh Kai-yuan , Kue Jien-huo , Rimrott F. P. J.
Published: February 2008

In this paper, the stepped reduction method is used to find general solutions for the nonaxisymmetric bending of arbitrary axisymmetric nonhomogeneous annular plates of variable thickness under an arbitrary nonaxisymmetric temperature field and an arbitrary nonaxisymmetric distributed load. In spite of a large number of steps, eventually only two simultaneous algebraic linear equations with two unknowns have to be solved. As an example, the bending of a circular plate, whose solution is known, is carried out by the proposed approach, and it is shown that results obtained by the proposed method compare well with previous solutions obtained by other methods and hence prove the accuracy of the proposed method.
Closed-Form Forced Response of a Damped, Rotating, Multiple Disks/Spindle System
Authors: Shen I. Y.
Published: February 2008

This paper is to study forced vibration response of a rotating disk/spindle system consisting of multiple flexible circular disks clamped to a rigid spindle supported by two flexible bearings. In particular, the disk/spindle system is subjected to prescribed translational base excitations and externally applied loads. Because of the bearing flexibility, the rigid spindle undergoes infinitesimal rigid-body rocking and translation simultaneously. To model real vibration response that has finite resonance amplitudes, the disks and the bearings are assumed to be viscously damped. Equations of motion are then derived through use of Rayleigh dissipation function and Lagrange’s equation. The equations of motion include three sets of matrix differential equations: one for the rigid-body rocking of the spindle and one-nodal-diameter disk modes, one for the axial translation of the spindle and axisymmetric disk modes, and one for disk modes with two or more nodal diameters. Each matrix differential equation contains either a gyroscopic matrix or a damping matrix or both. The causal Green’s function of each matrix differential equation is determined explicitly in closed form through use of matrix inversion and inverse Laplace transforms. Closed-form forced response of the damped rotating disk/spindle system is then obtained from the causal Green’s function and the generalized forces through convolution integrals. Finally, responses of a disk/spindle system subjected to a concentrated sinusoidal load or an impulsive load are demonstrated numerically as an example.
Simulation of Rough, Elastic Contacts
Authors: Kalker J. J. , Dekking F. M. , Vollebregt E. A. H.
Published: February 2008

Frictionless rough contact problems have been studied in great detail by J. A. Greenwood and his co-workers. The only thing that actually seems missing is a simulated figure of the real contact between two rough bodies. Such a figure will be provided. Frictional rough elastic contact, on the other hand, seems to be terra incognita, and we intend to explore it. We will use two-dimensional rough bodies, because then we can simulate many asperities, and also because three-dimensional does not differ very much from two-dimensional in frictional contact, while finally the figures resulting from two-dimensional are clearer and more transparent as well as more realistic. On the other hand, two-dimensional calculations yield only qualitative results; for quantitative results one needs three-dimensional computations.
On Balance and Variational Formulations of the Equation of Motion of a Body Deploying Along a Cable
Authors: Crellin E. B. , Janssens F. , Poelaert D. , Steiner W. , Troger H.
Published: February 2008

The equation of motion of a body moving along a vertically hanging cable by deploying the cable from the body or retrieving the cable in the body is derived. The derivation of the equation is given both by means of balance principles and a variational principle. Due to the fact that this system is not conservative the derivation by means of the variational principle requires the introduction of the Carnot energy loss concept. Its explanation is the main objective of this paper. The motion of the free falling folded string and a horizontally moving folded string modelling a whip are treated as examples.
Coefficient of Restitution for Collinear Collisions of Elastic-Perfectly Plastic Spheres
Authors: Thornton C.
Published: February 2008

Based on a simplified theoretical model for the normal contact interaction of two elastic-perfectly plastic spheres, an analytical solution is provided for the coefficient of restitution. The solution is expressed in terms of the ratio of impact velocity to yield velocity rather than in terms of material properties such as the yield stress which is difficult to reliably ascertain for many materials.
Free-Edge Stress Singularity in a Two-Dimensional Unidirectional Viscoelastic Laminate Model
Authors: Lee Sang Soon
Published: February 2008

This paper concerns the stress singularity at the interface corner between the perfectly bonded fiber and the matrix of a unidirectional two-dimensional laminate model subjected to a uniform transverse tensile strain. The matrix is assumed to be a linear viscoelastic material. The standard Laplace transform and the Mellin transform techniques are employed to get the characteristic equation and the order of singularity is obtained numerically for a given viscoelastic model. The time-domain boundary element method is used to investigate the behavior of stresses for the whole interface. It is shown that the order of singularity increases with time while the free-edge stress intensity factor is relaxed with time.
An Analysis of the Plane-Strain Compression of Viscoplastic Materials
Authors: Adams M. J. , Briscoe B. J. , Corfield G. M. , Lawrence C. J. , Papathanasiou T. D.
Published: February 2008

A theoretical analysis for the plane-strain compression of viscoplastic materials with a Tresca wall boundary condition is described. The analysis is based upon the incorporation of a viscoplastic associated flow rule into the cycloidal solution originally developed for rigid-perfectly plastic materials. The evolution of the calculated stress field suggests that the influence of strain rate hardening is similar to that reported previously for strain hardening. The calculated strain fields are elliptical in form and are consistent with those measured for a viscoplastic paste. Previous analyses of the compression of viscoplastic materials have employed the lubrication approximation for fluid flows with a resulting kinematic inconsistency in the predicted velocity fields.
Contact Pressures as an Elastic Roller Crosses a Scratch
Authors: Greenwood J. A.
Published: February 2008

The Westergaard method of plane elastic analysis is used to obtain an exact solution to the problem of an elastic roller crossing a gap, intended to represent a scratch, on a rigid half-space.
A Kelvin Theorem and Partial Work of Impulsive Forces
Authors: Ivanov A. P.
Published: February 2008

A rigid body under the action of several impulsive forces is considered. A Kelvin theorem provides a simple rule to calculate the total work done by all impulsive forces, but it is not necessarily applicable to the independent work done by each impulse. It is shown that there exist two cases when the partial work can be determined by the same Kelvin formula. Otherwise, the problem has no algebraic solution.
Surface Displacements due to a Steadily Moving Point Force
Authors: Barber J. R.
Published: February 2008

Closed-form expressions are obtained for the normal surface displacements due to a normal point force moving at constant speed over the surface of an elastic half-space. The Smirnov-Sobolev technique is used to reduce the problem to a linear superposition of two-dimensional stress and displacement fields.
Stress Singularity in Three-Phase Bonded Structure
Authors: Koguchi Hideo , Inoue Tadanobu , Yada Toshio
Published: February 2008

The plane problem of three-phase materials consisting of three isotropic homogeneous wedges with arbitrary angles, which are with two interfaces and two free surfaces, is analyzed under arbitrary normal and shearing tractions by the theory of elasticity. An eigenequation to examine the order of stress singularity at the apex in the three-phase bonded structure is analytically derived. In particular, this paper emphasizes to investigate the order of singularity in the stress field at the apex when materials of both side regions against intermediate region in three regions are identical. For several bonded wedge geometries, it is demonstrated how the order of stress singularity varies with material pairs. Finally, it is shown that the bonding order of materials also influences on the order of stress singularity in the three-phase bonded structure.
The Boundary Contour Method for Three-Dimensional Linear Elasticity
Authors: Nagarajan A. , Mukherjee S. , Lutz E.
Published: February 2008

This paper presents a novel variant of the boundary element method, here called the boundary contour method, applied to three-dimensional problems of linear elasticity. In this work, the surface integrals on boundary elements of the usual boundary element method are transformed, through an application of Stokes’ theorem, into line integrals on the bounding contours of these elements. Thus, in this formulation, only line integrals have to be numerically evaluated for three-dimensional elasticity problems—even for curved surface elements of arbitrary shape. Numerical results are presented for some three-dimensional problems, and these are compared against analytical solutions.
Localization due to Damage in Two-Direction Fiber-Reinforced Composites
Authors: Hild F. , Larsson P.-L. , Leckie F. A.
Published: February 2008

Fiber pull-out is one of the fracture features of fiber-reinforced ceramic matrix composites. The onset of this mechanism is predicted by using continuum damage mechanics, and corresponds to a localization of deformation. After deriving two damage models from a uniaxial bundle approach, different configurations are analyzed through numerical methods. For one model some very simple criteria can be derived, whereas for the second one none of these criteria can be derived and the general criterion of localization must be used.
A Method to Determine the Plane-Strain Yield Locus for Ductile Crystals
Authors: Nikolic R. R.
Published: February 2008

This paper presents a new method for determining the plane-strain yield surfaces based on the application of the lower bound limit theorem of the theory of plasticity. The method is very simple and by use of linear programming optimization routine the points of the yield surface in the stress space are generated automatically.
A Split Hopkinson Bar Technique to Evaluate the Performance of Accelerometers
Authors: Togami T. C. , Baker W. E. , Forrestal M. J.
Published: February 2008

We developed a split Hopkinson bar technique to evaluate the performance of accelerometers that measure large amplitude pulses. A nondispersive stress pulse propagates in an aluminum bar and interacts with a tungsten or steel disk at the end of the bar. We measure stress at the aluminum bar-disk interface with a quartz gage and measure acceleration at the free end of the disk with an accelerometer. The rise time of the incident stress pulse in the aluminum bar is long enough and the disk length is short enough that the response of the disk can be approximated closely as rigid-body motion; an experimentally verified analytical model supports this assumption. Since the cross-sectional area and mass of the disk are known, we calculate acceleration of the rigid disk from the stress measurement and Newton’s Second Law. Comparisons of accelerations calculated from the quartz gage data and measured acceleration data show excellent agreement for acceleration pulses with the peak amplitudes between 20,000 and 120,000 G (1 G = 9.81m/s2), rise times as short as 20 μs, and pulse durations between 40 and 70 μs.
A General Orthotropic von Mises Plasticity Material Model With Mixed Hardening: Model Definition and Implicit Stress Integration Procedure
Authors: Kojic´ M. , Grujovic´ N. , Slavkovic´ R. , Zˇivkovic´ M.
Published: February 2008

A general orthotropic von Mises plasticity model, with an extension of the Hill’s yield criterion to include mixed hardening, is introduced in the paper. Material constants and equivalent stress-equivalent plastic strain curves are defined in a way to suggest their experimental determination. The model represents a special case of a general anisotropic metal plasticity model proposed by the authors. An implicit stress integration procedure, representing an application of the governing parameter method (GPM) introduced by the first author, is presented. The GPM is briefly described, and the computational procedure, together with calculation of the consistent tangent moduli, are given in some detail for a general three-dimensional deformation, with direction of application to plane stress/shell conditions. Numerical examples illustrate applicability of the model and effectiveness of the computational algorithm.
On the Definition of the Deformed Reference Surface of Rubber-Like Shells of Revolution
Authors: Yu¨kseler R. F.
Published: February 2008

A comparative analysis of rubber-like shells of revolution which undergo arbitrarily large rotations and strains is presented. The comparison is made between two alternative definitions of the deformed reference surface: (i) The deformed reference surface is composed of the same particles as the undeformed reference surface. (ii) The deformed reference is taken as the surface of mass of the shell (the dynamic consistency condition) according to which (i) is not necessarily valid. The results obtained from the buckling analysis of circular neo-Hookean plates under radial loads using various approaches strengthen the latter definition relative to the former one.
Melnikov Process for Stochastically Perturbed, Slowly Varying Oscillators: Application to a Model of Wind-Driven Coastal Currents
Authors: Simiu E.
Published: February 2008

The stochastic Melnikov approach is extended to a class of slowly varying dynamical systems. It is found that (1) necessary conditions for chaos induced by stochastic perturbations depend on the excitation spectrum and the transfer function in the expression for the Melnikov transform; (2) the Melnikov approach allows the estimation of lower bounds for (a) the mean time of exit from preferred regions of phase space, and (b) the probability that exits from those regions cannot occur during a specified time interval. For a system modeling wind-induced currents, the deterministic Melnikov approach would indicate that chaotic transport cannot occur for certain parameter ranges. However, the more realistic stochastic Melnikov approach shows that, for those same parameter ranges, the necessary conditions for exits during a specified time interval are satisfied with probabilities that increase as the time interval increases.
Transition From Soliton to Chaotic Motion Following Sudden Excitation of a Nonlinear Structure
Authors: Davies M. A. , Moon F. C.
Published: February 2008

The existence of a transition from soliton-like motions to spatially and temporally disordered motions in a periodic structure with buckling nonlinearity is demonstrated. An experiment consisting of nine harmonic oscillators coupled with buckling sensitive elastica was constructed. This experiment is modeled using a modified Toda lattice. As has been shown in previous work, the experiment and the model show strong sensitivity to initial conditions. Here we show that this sensitivity may be related to a transition from relatively ordered solitary wave motion, immediately following the impact, to disordered motions at a later time. Some of the behavior of the observed wave structures is explained using Toda’s analytical results; however, the reasons for the break-up of the waves and their role in the generation of spatio-temporal disorder is not fully understood. We speculate that some type of transient chaotic motion is responsible for the observed behavior. These findings are relevant to aircraft, ship, and space structures that are subjected to large dynamic loads.
Prediction of Mode Parameters and Moment-Rotation Curves for Crushed Thin-Walled Trapezoidal Tubes in Bending
Authors: Park M. S. , Lee B. C.
Published: February 2008

In the context of kinematic models, a general procedure for the bending crush analysis of thin-walled members is proposed and applied to the trapezoidal and rectangular tubes in bending. The main emphasis of this study is given to the determination of collapse mode parameters and the prediction of post-collapse behaviors of the structural member. The mode shapes are determined by minimizing plastic energy rate of the members. Moment-rotation curves are obtained by differentiating the absorbed plastic energy with respect to the rotation angle. For small rotation angles the solution is modified by considering elastic buckling and plastic collapse moments. Through several examples a full range of post-collapse response of the thin-walled members is shown to be effectively calculated by the proposed method without making any recourse to experimental data.
Derivation of a Thin Film Equation by a Direct Approach
Authors: Huang F. Y. , Mote C. D.
Published: February 2008

A new model of the thin viscous fluid film, constrained between two translating, flexible surfaces, is presented in this paper: The unsteady inertia of the film is included in the model. The derivation starts with the reduced three-dimensional Navier-Stokes equations for an incompressible viscous fluid with a small Reynolds number. By introduction of an approximate velocity field, which satisfies the continuity equation and the no-slip boundary conditions exactly, into weighted integrals of the three-dimensional equations over the film thickness, a two-dimensional thin film equation is obtained explicitly in a closed form. The 1th thin film equation is obtained when the velocity field is approximated by 21th order polynominals, and the three-dimensional viscous film is described with increasing accuracy by thin film equations of increasing order. Two cases are used to illustrate the coupling of the film to the vibration of the structure and to show that the second thin film equation can be applied successfully to the prediction of a coupled film-structure response in the range of most applications. A reduced thin film equation is derived through approximation of the second thin film equation that relates the film pressure to transverse accelerations and velocities, and to slopes and slope rates of the two translating surfaces.
Dynamic Analysis of Nonuniform Beams With Time-Dependent Elastic Boundary Conditions
Authors: Lee Sen Yung , Lin Shueei Muh
Published: February 2008

The dynamic response of a nonuniform beam with time-dependent elastic boundary conditions is studied by generalizing the method of Mindlin-Goodman and utilizing the exact solutions of general elastically restrained nonuniform beams given by Lee and Kuo. The time-dependent elastic boundary conditions for the beam are formulated. A general form of change of dependent variable is introduced and the shifting polynomials of the third-order degree, instead of the fifth-order degree polynomials taken by Mindlin-Goodman, are selected. The physical meaning of these shifting polynomial functions are explored. Finally, the limiting cases are discussed and several examples are given to illustrate the analysis.
Chaotic Vibration in Fluid-Stiffness-Controlled Instability of a Tube Row in Crossflow
Authors: Chen S. H. , Chen S. S.
Published: February 2008

The fluid-elastic instability of tube arrays in heat exchangers may become chaotic, especially when clearances exist between tubes and supports. When chaotic motion appears in tube arrays, significant sliding between the tubes and supports may be induced. An analytical model, consisting of a row of rigid tubes with three tubes supported by springs, is presented. Bifurcation diagrams, Poincare´ maps, power spectral densities, and tube orbits are used to investigate the conditions under which the unpredictable motion can arise. The emphasis is on fluid-stiffness-controlled instability.
Exact Stationary Solutions of Stochastically Excited and Dissipated Integrable Hamiltonian Systems
Authors: Zhu W. Q. , Yang Y. Q.
Published: February 2008

It is shown that the structure and property of the exact stationary solution of a stochastically excited and dissipated n-degree-of-freedom Hamiltonian system depend upon the integrability and resonant property of the Hamiltonian system modified by the Wong-Zakai correct terms. For a stochastically excited and dissipated nonintegrable Hamiltonian system, the exact stationary solution is a functional of the Hamiltonian and has the property of equipartition of energy. For a stochastically excited and dissipated integrable Hamiltonian system, the exact stationary solution is a functional of n independent integrals of motion or n action variables of the modified Hamiltonian system in nonresonant case, or a functional of both n action variables and α combinations of phase angles in resonant case with α (1 ≤ α ⩽ n – 1) resonant relations, and has the property that the partition of the energy among n degrees-of-freedom can be adjusted by the magnitudes and distributions of dampings and stochastic excitations. All the exact stationary solutions obtained to date for nonlinear stochastic systems are those for stochastically excited and dissipated nonintegrable Hamiltonian systems, which are further generalized to account for the modification of the Hamiltonian by Wong-Zakai correct terms. Procedures to obtain the exact stationary solutions of stochastically excited and dissipated integrable Hamiltonian systems in both resonant and nonresonant cases are proposed and the conditions for such solutions to exist are deduced. The above procedures and results are further extended to a more general class of systems, which include the stochastically excited and dissipated Hamiltonian systems as special cases. Examples are given to illustrate the applications of the procedures.
Chaos in a Spacecraft Attitude Maneuver Due to Time-Periodic Perturbations
Authors: Gray G. L. , Dobson I. , Kammer D. C.
Published: February 2008

We use Melnikov’s method to study the chaotic dynamics of an attitude transition maneuver of a torque-free rigid body in going from minor axis spin to major axis spin under the influence of small damping. The chaotic motion is due to the formation of Smale horseshoes which are caused by the oscillation of small subbodies inside the satellite. The equations of motion are derived and then transformed into a form suitable for the application of Melnikov’s method. An analytical criterion for chaotic motion is derived in terms of the system parameters. This criterion is evaluated for its significance to the design of artificial satellites.
Viscoelastic Minimum Principles Revisited
Authors: Hazanov S.
Published: February 2008

A problem of viscoelastic counterparts for the elastic minimum theorems is considered. A theorem is proved that gives a general algorithm for the construction of such viscoelastic minimum functionals. The established results are applied for the theoretical evaluation of the effective properties of inhomogeneous viscoelastic materials. As an example, simple bounds on the effective properties of viscoelastic composites are obtained.
The Surface Crack Problem for a Plate With Functionally Graded Properties
Authors: Erdogan F. , Wu B. H.
Published: February 2008

In this study the plane elasticity problem for a nonhomogeneous layer containing a crack perpendicular to the boundaries is considered. It is assumed that the Young’s modulus of the medium varies continuously in the thickness direction. The problem is solved under three different loading conditions, namely fixed grip, membrane loading, and bending applied to the layer away from the crack region. Mode I stress intensity factors are presented for embedded as well as edge cracks for various values of dimensionless parameters representing the size and the location of the crack and the material nonhomogeneity. Some sample results are also given for the crack-opening displacement and the stress distribution.
The Elastic Field Resulting From Elliptical Hertzian Contact of Transversely Isotropic Bodies: Closed-Form Solutions for Normal and Shear Loading
Authors: Hanson M. T. , Puja I. W.
Published: February 2008

This analysis presents the elastic field in a half-space caused by an ellipsoidal variation of normal traction on the surface. Coulomb friction is assumed and thus the shear traction on the surface is taken as a friction coefficient multiplied by the normal pressure. Hence the shear traction is also of an ellipsoidal variation. The half-space is transversely isotropic, where the planes of isotropy are parallel to the surface. A potential function method is used where the elastic field is written in three harmonic functions. The known point force potential functions are utilized to find the solution for ellipsoidal loading by quadrature. The integrals for the derivatives of the potential functions resulting from ellipsoidal loading are evaluated in terms of elementary functions and incomplete elliptic integrals of the first and second kinds. The elastic field is given in closed-form expressions for both normal and shear loading.
Minimizing Stress Levels in Piezoelectric Media Containing Elliptical Voids
Authors: Park S. B. , Carman G. P.
Published: February 2008

In this paper we present an analytical solution to calculate the stress concentrations around an elliptical void in a piezoelectric medium subjected to electrical loading. We show that the stress concentrations can be eliminated if the material properties satisfy a certain mathematical relation. While a trivial solution exists for this problem, we demonstrate that other families of solutions exist (optimal) to minimize/eliminate the stresses. The optimal families are shown to be independent of geometry and therefore are universally applicable to a specific material system. The optimal families do not limit the deformation profile and represent admissible solutions to the problem. Numerical studies demonstrate that the entire stress field in the medium vanishes and not just at the critical locations as dictated by the mathematics. Finally, we numerically demonstrate that the optimal properties are also applicable to the crack problem.
A Spherical Inclusion in an Elastic Half-Space Under Shear
Authors: Jasiuk I. , Sheng P. Y. , Tsuchida E.
Published: February 2008

We find the elastic fields in a half-space (matrix) having a spherical inclusion and subjected to either a remote shear stress parallel to its traction-free boundary or to a uniform shear transformation strain (eigenstrain) in the inclusion. The inclusion has distinct properties from those of the matrix, and the interface between the inclusion and the surrounding matrix is either perfectly bonded or is allowed to slip without friction. We obtain an analytical solution to this problem using displacement potentials in the forms of infinite integrals and infinite series. We include numerical examples which give the local elastic fields due to the inclusion and the traction-free surface.
A Tensegrity Structure With Buckling Compression Elements: Application to Cell Mechanics
Authors: Coughlin M. F. , Stamenovic´ D.
Published: February 2008

A tensegrity structure composed of six slender struts interconnected with 24 linearly elastic cables is used as a model of cell deformability. Struts are allowed to buckle under compression and their post-buckling behavior is determined from an energy formulation of the classical pin-ended Euler column. At the reference state, the cables carry initial tension balanced by forces exerted by struts. The structure is stretched uniaxially and the stretching force versus axial extension relationships are obtained for different initial cable tensions by considering equilibrium at the joints. Structural stiffness is calculated as the ratio of stretching force to axial extension. Predicted dependences of structural stiffness on initial cable tension and on stretching force are consistent with behaviors observed in living cells. These predictions are both qualitatively and quantitatively superior to those obtained previously from the model in which the struts are viewed as rigid.
Dynamic Constitutive and Failure Behavior of a Two-Phase Tungsten Composite
Authors: Zhou M. , Clifton R. J.
Published: February 2008

The constitutive response and failure behavior of a W-Ni-Fe alloy over the strain rate range of 10-4 to 5 X 105 s-1 is experimentally investigated. Experiments conducted are pressure-shear plate impact, torsional Kolsky bar, and quasi-static torsion. The material has a microstructure of hard tungsten grains embedded in a soft alloy matrix. Nominal shear stress-strain relations are obtained for deformations throughout the experiments and until after the initiation of localization. Shear bands form when the plastic strain becomes sufficiently large, involving both the grains and the matrix. The critical shear strain for shear band development under the high rate, high pressure conditions of pressure-shear is approximately 1–1.5 or 6–8 times that obtained in torsional Kolsky bar experiments which involve lower strain rates and zero pressure. Shear bands observed in the impact experiments show significantly more intensely localized deformation. Eventual failure through the shear band is a combination of grain-matrix separation, ductile matrix rupture, and grain fracture. In order to understand the effect of the composite microstructure and material inhomogeneity on deformation, two other materials are also used in the study. One is a pure tungsten and the other is an alloy of W, Ni, and Fe with the same composition as that of the matrix phase in the overall composite. The results show that the overall two-phase composite is more susceptible to the formation of shear bands than either of its constituents.
Optimal Bounds on Plastic Deformations for Bodies Constituted of Temperature-Dependent Elastic Hardening Material
Authors: Giambanco F. , Palizzolo L.
Published: February 2008

Bounds are investigated on the plastic deformations in a continuous solid body produced during the transient phase by cyclic loading not exceeding the shakedown limit. The constitutive model employs internal variables to describe temperature-dependent elastic-plastic material response with hardening. A deformation bounding theorem is proved. Bounds turn out to depend on some fictitious self-stresses and mechanical internal variables evaluated in the whole structure. An optimization problem, aimed to make the bound most stringent, is formulated. The Euler-Lagrange equations related to this last problem are deduced and they show that the relevant optimal bound has a local character, i.e., it depends just on some fictitious plastic deformations produced in the same region of the body where the bounded real plastic deformations are considered. The bounding technique is also generalized to the case of loads arbitrarily varying in a given domain. An application is worked out.
A Theory for Reduced Order Control Design of Plate Systems
Authors: Wang Q. , Liew K. M.
Published: February 2008

This paper describes the theory of wave domain control for the reduced control design of plate systems. A transformation, which changes the original system into an image system in which the control force is designed in wave domain control and wave control, is proposed such that the number of degrees-of-freedom of the undisturbed state in its image system is reduced. The control design in the original system is then derived by an inverse transformation. This work focuses on, first, proposing a new wave control theory and, second, applying the theory for structural control design.
Transient Analysis of a Subsonic Propagating Interface Crack Subjected to Antiplane Dynamic Loading in Dissimilar Isotropic Materials
Authors: Ing Yi-Shyong , Ma Chien-Ching
Published: February 2008

In this study, the transient stress fields and the dynamic stress intensity factor of a semi-infinite antiplane crack propagating along the interface between two different media are analyzed in detail. The crack is initially at rest and, at a certain instant, is subjected to an antiplane uniformly distributed loading on the stationary crack faces. After some delay time, the crack begins to move along the interface with a constant velocity, which is less than the smaller of the shear wave speed of these two materials. A new fundamental solution is proposed in this study, and the solution is determined by superposition of the fundamental solution in the Laplace transform domain. The proposed fundamental problem is the problem of applying exponentially distributed traction (in the Laplace transform domain) on the propagating crack faces. The exact full-field solutions and the stress intensity factor are found in the time domain by using the Cagniard-de Hoop method (de Hoop, 1958) of Laplace inversion. The near-tip fields are also obtained from the reduction of the full-field solutions. Numerical results for the dynamically extending crack are evaluated in detail. The region of the stress singular field dominated in the transient process is also discussed.
Steady-State Motion of a Line Mechanical/Heat Source Over a Half-Space: A Thermoelastodynamic Solution
Authors: Brock L. M. , Georgiadis H. G.
Published: February 2008

An asymptotic solution within the bounds of steady-state coupled thermoelastodynamic theory is given for the surface displacement and temperature due to a line mechanical/heat source that moves at a constant velocity over the surface of a half-space. This problem is of basic interest in the fields of contact mechanics and tribology, and an exact formulation is considered. The results may serve as a Green’s function for more general thermoelastodynamic contact problems. The problem may also be viewed as a generalization of the classical Cole-Huth problem and the associated Georgiadis-Barber correction. Asymptotic expressions are obtained by means of the two-sided Laplace transform, and by performing the inversions exactly. The range of validity of these expressions is actually quite broad, because of the small value of the thermoelastic characteristic length appearing in the governing equations.