bluuebunny/crossref_metadata_2025 huggingface dataset:
A Moving Boundary Problem in a Finite Domain
Authors: Dursunkaya Z. , Nair S.
Published: April 2008

The heat conduction and the moving solid-liquid interface in a finite region is studied numerically. A Fourier series expansion is used in both phases for spatial temperature distribution, and the differential equations are converted to an infinite number of ordinary differential equations in time. These equations are solved iteratively for the interface location as well as for the temperature distribution. The results are compared with existing solutions for low Stefan numbers. New results are presented for higher Stefan numbers for which solutions are unavailable.
Plane Punch Indentation of Anisotropic Elastic Half Space
Authors: Klintworth J. W. , Stronge W. J.
Published: April 2008

The stress distribution within a planar anisotropic half space is determined for normal or tangential displacements imposed over a small part of the surface. The general punch problem is then considered as a combination of these basic solutions. Results are presented for the normal, tangential, and rotary indentation of an arbitrarily-oriented half space by a flat frictional punch.
Internal Stress Arising From a Spherically Symmetric, Finite Plastic Strain and Yielding of a Hollow Sphere
Authors: Sakaki T. , Sugimoto K. , Kuroki T.
Published: April 2008

Internal stress arising from a spherically symmetric, finite plastic strain is obtained on the basis of the Eshelby’s theory on inclusions with stress-free strain. Using the internal stress, yielding of a thick-walled hollow sphere is discussed. From the present analysis, distribution of plastic strain in a yield zone and stress distribution are easily obtained, even if a hollow sphere has any type of flow curve. The present analysis is also applicable to forward and reverse loading.
A Dynamic Measuring Technique for Bulk Stiffness Constants as a Function of Temperature and Microstructure for U-6 wt pct Nb
Authors: Lowry D. R. , Wolfenden A. , Ludtka G. M.
Published: April 2008

Measurements of dynamic Young’s modulus (E) and shear modulus (G) have been made with the piezoelectric ultrasonic composite oscillator technique (PUCOT) on gamma solution heat treated specimens of U-6 wt pct Nb at 80 and 40 kHz, respectively. Three aging conditions were employed to permit measurements for four different microstructures from ambient to 647°C. Values of Poisson’s ratio (ν) were calculated from the measured values of E and G. The extreme ranges for E, G and ν extended from 171 to 55 GPa, from 66 to 17 GPa, and from 0.09 to 0.70, respectively.
Analysis of Simply-Supported Orthotropic Cylindrical Shells Subject to Lateral Impact Loads
Authors: Christoforou A. P. , Swanson S. R.
Published: April 2008

An analytic solution is given for the problem of simply-supported orthotropic cylindrical shells subject to impact loading. The closed-form solution has not been obtained previously. The analysis is based on an expansion of the loads, displacements, and rotations in a double Fourier series which satisfies the end boundary conditions of simple support. Each expansion is assumed to be separable into a function of time and a function of position. By neglecting in-plane and rotary inertia the problem becomes a second-order ordinary differential equation in time for the Fourier coefficients of the radial deflection. For a given loading impulse the solution can be found by invoking the convolution integral. The results show that for impact by a heavy mass, the solution is equivalent to that obtained by an approximate procedure of neglecting the mass of the shell, which leads to a simple simple-degree-of-freedom analysis. For problems of impact by smaller masses, the higher response frequencies of the cylinder become important. The results show the importance of dynamic effects in the predicted impact duration, peak force, and peak deflection relative to the quasi-static response. The results show that the response amplitude varies linearly with the impact velocity, but the response characteristics depend on the mass of the impactor and the mass and stiffness of the cylinder.
Modal Sensors/Actuators
Authors: Lee C.-K. , Moon F. C.
Published: April 2008

A piezoelectric laminate theory that uses the piezoelectric phenomenon to effect distributed control and sensing of structural vibration of a flexible plate has been used to develop a class of distributed sensor/actuators, that of modal sensors/actuators. The one-dimensional modal sensors/actuator equations are first derived theoretically and then examined experimentally. These modal equations indicate that distributed piezoelectric sensors/actuators can be adopted to measure/excite specific modes of one-dimensional plates and beams. If constructed correctly, actuator/observer spillover will not be present in systems adopting these types of sensors/actuators. A mode 1 and a mode 2 sensor for a one-dimensional cantilever plate were constructed and tested to examine the applicability of the modal sensors/actuators. A modal coordinate analyzer which allows us to measure any specific modal coordinate on-line real-time is proposed. Finally, a way to create a special two-dimensional modal sensor is presented.
Dynamic Stiffness of Cracked Interfaces
Authors: Sotiropoulos Dimitrios A.
Published: April 2008

Quantitative relationships are derived between the dynamic macromechanical stiffness and microparameters of planar interfaces containing distributed cracks. The derivation is based on the solution of the problem of elastic wave reflection by a plane with a continuous distribution of springs to model the cracked interface at the macrolevel. The dynamic spring stiffness is then, through averaging, related to crack-opening volumes and other microparameters. For linear springs and periodic crack distributions, numerical examples are presented for plain strain. The stiffness is shown to strongly depend on frequency.
On Interface Crack Growth in Composite Plates
Authors: Nilsson K.-F. , Stora˚kers B.
Published: April 2008

Analysis of fracture growth, and in particular at interfaces, is pertinent not only to load-carrying members in composite structures but also as regards, e.g., adhesive joints, thin films, and coatings. Ordinarily linear fracture mechanics then constitutes the common tool to solve two-dimensional problems occasionally based on beam theory. In the present more general effort, an analysis is first carried out for determination of the energy release rate at general loading of multilayered plates with local crack advance either at interfaces or parallel to such. The procedure is accomplished for arbitrary hyperelastic material properties within von Karman plate theory and the results are expressed by aid of an Eshelby energy momentum tensor. By a feasible superposition it is then shown that the original nonlinear plate problem may be reduced to that of an equivalent beam in case of linear material properties. As a consequence of the so-established principle, the magnitude of mode-dependent singular stress amplitude factors is then directly determinable from earlier two-dimensional linear beam solutions for isotropic and anisotropic bimaterials and relevant at determination of cohesive and adhesive fracture. The procedure is illustrated by an analysis of combined buckling and crack growth of a delaminated plate having a nontrivial crack contour.
Mori-Tanaka Estimates of the Overall Elastic Moduli of Certain Composite Materials
Authors: Chen Tungyang , Dvorak George J. , Benveniste Yakov
Published: April 2008

Simple, explicit formulae are derived for estimates of the effective elastic moduli of several multiphase composite materials with the Mori-Tanaka method. Specific results are given for composites reinforced by aligned or randomly oriented, transversely isotropic fibers or platelets, and for fibrous systems reinforced by aligned, cylindrically orthotropic fibers.
Unilaterally Supported Plates on Elastic Foundations by the Boundary Element Method
Authors: Sapountzakis E. J. , Katsikadelis J. T.
Published: April 2008

A boundary element solution is developed for the unilateral contact problem of a thin elastic plate resting on elastic homogeneous or nonhomogeneous subgrade. The reaction of the subgrade may depend linearly, or nonlinearly, on the deflection of the plate. The contact between the plate and the subgrade is unbonded. The subgrade surface is not necessarily plane, and miscontact between plate and subgrade due to initial gaps is also encountered. The solution procedure is based on the integral representation of the deflection for the biharmonic equation in which the unknown subgrade reaction is treated as loading term. The effectiveness of the proposed method is illustrated by several examples.
Modified Mixed Variational Principle and the State-Vector Equation for Elastic Bodies and Shells of Revolution
Authors: Steele Charles R. , Kim Yoon Young
Published: April 2008

A modified mixed variational principle is established for a class of problems with one spatial variable as the independent variable. The specific applications are on the three-dimensional deformation of elastic bodies and the nonsymmetric deformation of shells of revolution. The possibly novel feature is the elimination in the variational formulation of the stress components which cannot be prescribed on the boundaries. The result is a form exactly analogous to classical mechanics of a dynamic system, with the equations of state exactly in the form of the canonical equations of Hamilton. With the present approach, the correct scale factors of the field variables to make the system self-adjoint are readily identified, and anisotropic materials including composites can be handled effectively. The analysis for shells of revolution is given with and without the transverse shear deformation considered.
An Investigation of Dynamic Pulse Buckling of Thick Rings
Authors: Pegg N. G.
Published: April 2008

The occurrence of dynamic buckling of thick rings responding to an impulse load is investigated by analytical and numerical solutions to the equation of motion and by nonlinear finite element analyses. An extension to the linearized analytical solution is made using a finite difference scheme which incorporates a nonlinear moment-curvature relationship to model the effects of elastoplastic behavior and strain-rate reversal on the buckle formation. The finite element solution to the problem is formulated with the nonlinear code, ADINA. A comparison of the results shows that the numerical solutions (and, in particular, the ADINA solution) predict a significant reduction in the amplitude of buckling response and an increase in the predominant wavelength of response with time, in comparison to the linear analytical solution. A limited comparison to published experimental results of dynamic pulse buckling of thick rings is also given.
A Theory for Transverse Deflection of Poroelastic Plates
Authors: Taber Larry A.
Published: April 2008

A theory is presented for the bending of fluid-saturated poroelastic plates. The governing equations, based on linear consolidation theory, reduce to a single fourth-order integro-partial-differential equation to be solved for the transverse displacement of the middle surface. This equation resembles the classical plate equation but has an added convolution integral, which represents the viscous losses due to the flow of fluid relative to the solid. Laplace transform and perturbation solution methods are presented. The Laplace-transformed poroelastic plate equation and the first-order equation of the perturbation expansion have the forms of the standard plate equation. Results are given for a simply-supported rectangular plate with a time-dependent surface pressure.
A Projection Method Approach to Constrained Dynamic Analysis
Authors: Blajer W.
Published: April 2008

The paper presents a unified approach to the dynamic analysis of mechanical systems subject to (ideal) holonomic and/or nonholonomic constraints. The approach is based on the projection of the initial (constraint reaction-containing) dynamical equations into the orthogonal and tangent subspaces; the orthogonal subspace which is spanned by the constraint vectors, and the tangent subspace which complements the orthogonal subspace in the system’s configuration space. The tangential projection gives the reaction-free (or purely kinetic) equations of motion, whereas the orthogonal projection determines the constraint reactions. Simplifications due to the use of independent variables are indicated, and examples illustrating the concepts are included.
Transfer Functions of One-Dimensional Distributed Parameter Systems
Authors: Yang B. , Tan C. A.
Published: April 2008

Distributed parameter systems describe many important physical processes. The transfer function of a distributed parameter system contains all information required to predict the system spectrum, the system response under any initial and external disturbances, and the stability of the system response. This paper presents a new method for evaluating transfer functions for a class of one-dimensional distributed parameter systems. The system equations are cast into a matrix form in the Laplace transform domain. Through determination of a fundamental matrix, the system transfer function is precisely evaluated in closed form. The method proposed is valid for both self-adjoint and non-self-adjoint systems, and is extremely convenient in computer coding. The method is applied to a damped, axially moving beam with different boundary conditions.
Robustness of Nonlinear Systems Perturbed by External Random Excitation
Authors: Leng G. , Sri Namachchivaya N. , Talwar S.
Published: April 2008

The effect of external random excitation on nonlinear continuous time systems is examined using the concept of the Lyapunov exponent. The Lyapunov exponent may be regarded as the nonlinear/stochastic analog of the poles of a linear deterministic system. It is shown that while the stationary probability density function of the response undergoes qualitative changes (bifurcations) as system parameters are varied, these bifurcations are not reflected by changes in the sign of the Lyapunov exponent. This finding does not support recent proposals that the Lyapunov exponent be used as a basis for a rigorous theory of stochastic bifurcation.
Saint-Venant End Effects for Materials With Negative Poisson’s Ratios
Authors: Lakes R. S.
Published: April 2008

In this paper we analyze Saint-Venant end effects for materials with negative Poisson ’s ratios. We present an example of slow decay of stress arising from selfequilibrated stress at the end of a circular cylinder of elastic material with a negative Poisson’s ratio. By contrast, a sandwich panel containing rigid face sheets and a compliant core exhibits no anomalous effects for negative Poisson’s ratio, but exhibits slow stress decay for core Poisson’s ratio approaching 0.5. In sandwich panels with stiff but not perfectly rigid face sheets, slow decay of stress is known to occur; a negative Poisson’s ratio results in end stress decay, which is faster than it would be otherwise.
Finite Deformation Analysis of Pressure-Shear Plate Impact Experiments on an Elastohydrodynamic Lubricant
Authors: Ramesh K. T. , Clifton R. J.
Published: April 2008

Pressure-shear plate impact experiments on an elastohydrodynamio lubricant (5P4E) are interpreted by means of a full finite deformation analysis of stress wave propagation in an elastic/viscoplastic material. The elastic response is modeled as that of a neo-Hookean solid, modified to include compressibility in such a way that the shock velocity increases linearly with increasing particle velocity; the viscoplastic response is modeled by means of a thermal activation model in which the activation energy is taken to be pressure dependent. The parameters in the elasticity relation are determined from the rising part of the transmitted stress profiles, which are related to transit times for multiple reverberations through the thickness of the lubricant layer. The parameters in the viscoplastic model are determined from the shear stress transmitted after nominally homogeneous states of stress are established through the thickness of the lubricant. Good agreement between measured and computed wave profiles is obtained over the entire range of pressures used in the experiments.
Stress Distribution in an Edge-Stiffened Semi-infinite Elastic Plate Containing a Circular Hole
Authors: Lee Eung J. , Klang Eric C.
Published: April 2008

An edge-stiffened semi-infinite elastic plate containing a circular hole under tension at infinity has been studied using a conformal mapping technique. Melan ’s stiffener condition in Cartesian coordinates has been newly formulated as a resultant shear stress condition in bipolar coordinates. The solution is sought in series form, and by truncating the system of equations, it is numerically solved. Pertinent stress distributions are examined to illustrate the roll of the stiffener under the presence of a circular hole near the straight edge. It has been concluded that the stiffener contributes to indirectly suppressing the stress concentration around the hole.
Boundary Formulations for Three-Dimensional Continuum Structural Shape Sensitivity Analysis
Authors: Kane J. H. , Zhao G. , Wang H. , Guru Prasad K.
Published: April 2008

The direct, singular, boundary element analysis formulation is shown to provide a basis for a computationally efficient and accurate shape design sensitivity analysis approach for the structural response of three-dimensional solid objects. The theoretical formulation for surface displacement and traction component sensitivities, and all components of the stress tensor is presented along with a formulation for the recovery of displacement and stress components in the interior of the object under consideration. Discussion of computational issues related to the overall efficiency of these formulations is given, along with numerical results to demonstrate the accuracy and efficiency of this approach.
Determination of Stress Components From Thermoelastic Data Without Boundary Conditions
Authors: Ryall T. G. , Heller M. , Jones R.
Published: April 2008

Recent investigations have shown that the temperature variation caused by sinusoidal loading of a solid consists of two harmonic components. In this paper it is shown that by using an appropriate Airy stress function the separated stress components can be obtained, almost always, with knowledge of these two components. Since the second harmonic response is small compared to the noise level, the question of experimental design is examined. The problem of uniqueness is also studied. The close similarity between the second harmonic response and various energy parameters is also investigated and its role in structural optimization is discussed. The method is demonstrated on a particular example using simulated noisy data.
Closed-Form Vibration Analysis of Sagged Cable/Mass Suspensions
Authors: Cheng S.-P. , Perkins N. C.
Published: April 2008

A theoretical model is presented which describes the three-dimensional nonlinear motion of a sagged cable that supports an array of discrete masses. An asymptotic form of this general model is derived for the linear response of a cable/mass suspension having small equilibrium curvature and horizontal supports. While the asymptotic model remains rich enough to capture dominant sagged cable effects, it is simple enough to permit closed-form analysis. A free vibration analysis is pursued that leads to closed-form solutions for problems which, heretofore, were analyzed using purely numerical methods. Among the advantages of the present method is its ability to pro vide results for: (1) complex mass arrays, (2) high-order modes, and (3) dynamic cable tension. Examples highlight the key role played by mass array symmetry and lead to new conclusions regarding free vibration.
Dynamics of Flexible Beams and Plates in Large Overall Motions
Authors: Boutaghou Z. E. , Erdman Arthur G. , Stolarski Henryk K.
Published: April 2008

The dynamic response of flexible beams, plates, and solids undergoing arbitrary spatial motions are systematically derived via a proposed approach. This formulation is capable of incorporating arbitrary representation of the kinematics of deformation, phenomenon of dynamic stiffening, and complete nonlinear interaction between elastic and rigid-body dynamics encountered in constrained multibody systems. It is shown that the present theory captures the phenomenon of dynamic stiffening due to the transfer of the axial and membrane forces to the bending equations of beams and plates, respectively. Examples are presented to illustrate the proposed formulations.
A Fabric-Related Constitutive Model for Granular Materials
Authors: Jahedi J. , Mohammadi J. , Nair S.
Published: April 2008

A new anisotropic constitutive model for granular materials is developed. This model exhibits the noncoaxiality of the principal axes of stress and strain rate as a natural consequence of a kinematic hypothesis. A fabric reconstruction parameter ℬ plays an important role in this model. The pressure sensitivity parameter, μ, and two different hardening parameters often employed in modeling granular materials, come out to be expressible in terms of this fabric reconstruction factor. The stress criterion in this model is not friction based, and therefore the rolling of granules can be taken into account through the fabric paramater. Numerical results are presented on the basis of a phenomenological trial function for ℬ.
A Finite Deformation Theory of Viscoplasticity Based on Overstress: Part II—Finite Element Implementation and Numerical Experiments
Authors: Nishiguchi I. , Sham T.-L. , Krempl E.
Published: April 2008

A one-step time integration method is developed for the finite deformation theory of viscoplasticity based on overstress (FVBO) described in Part I. This time integration method is based on a forward gradient approximation and it leads to explicit expressions of the tangent operators suitable for finite element implementation. Numerical experiments and closed-form solutions for a hypoelastic material in homogeneous deformation states are presented. The FVBO is applied to the modeling of second-order effects in torsion. The numerical results show that a modification of the Jaumann rate and second-order terms of the inelastic rate of deformation are necessary to model the observed effects.
Asymptotic Crack-Tip Fields for Perfectly Plastic Solids Under Plane-Stress and Mixed-Mode Loading Conditions
Authors: Dong P. , Pan J.
Published: April 2008

In this paper, we first discuss some of the properties of the crack-tip sectors for perfectly plastic materials under plane-stress conditions. Then starting with the plane-stress mixed-mode crack-tip fields suggested by Shih (1973), we assemble these sectors in a slightly different manner from those in Shih (1973). The missing governing equations needed to completely specify the crack-tip fields for both near mode I and near mode II mixed-mode loadings are derived. The mode I crack-tip field, as the limit of the near mode I cases, differs from Hutchinson’s solution (1968) by the appearance of a small constant stress sector ahead of the crack tip. In addition, the relevance of the solutions of the near mode II cases to some interesting features of the mixed-mode crack-tip fields, as suggested by Budiansky and Rice (1973), is also discussed.
The First-Order Variation of the Displacement Field Due to Geometrical Changes in an Elliptical Crack
Authors: Nishioka T. , Atluri S. N.
Published: April 2008

Analytical expressions are derived for the derivatives of the crack-surface displacement field, with respect to the lengths of the major and minor axes, respectively, of an elliptical crack embedded in an infinite isotropic elastic solid, when the crack faces are subjected to arbitrary tractions. These results are shown to lead, in turn, to analytical expressions for weight functions for the stress intensity factors along the fronts of elliptical-shaped embedded or part-elliptical shaped surface flaws, when a simple two-parameter characterization of the stress intensity variation along the flaw border is used. In the case of part-elliptical surface flaws, a finite-element alternating method, based on the Schwartz-Neumann superposition technique, is proposed to determine the coefficients in the analytical expressions for crack-surface displacements, and their gradients with respect to the crack dimensions.
Elastodynamic Scattering From Penny-Shaped and Nonplanar Cracklike Flaws With Dissipation and Restoring Forces
Authors: Olsson Peter
Published: April 2008

Scattering from penny-shaped and nonplanar cracklike flaws, with a type of boundary condition which incorporates dissipation and restoring forces, is studied. Scattering cross-sections and energy absorption cross-sections are computed, and comparisons with open cracks are performed. A partially debonded inclusion, with the debonding in the form of a cracklike flaw, is also discussed. The method employed is a modified null field approach, incorporating some ideas previously used for treating scattering from nonplanar open or fluid-filled cracks. In the present context, the boundary conditions lead to great simplifications in the implementation of the method, in that part of the relevant matrices can be computed analytically.
A Convolution Approach for the Transient Analysis of Locally Nonlinear Rotor Systems
Authors: Chiang I. F. , Noah S. T.
Published: April 2008

A computationally efficient convolution method, based on discretized impulse response and transition matrix integral formulations, is developed for the transient analysis of complex linear structures interacting through strong local nonlinearities. In the formulation, the coupling forces due to the nonlinearities are treated as external forces acting on the coupled subsystems. Iteration is utilized to determine their magnitudes at each time increment. The method is applied to a generic rotor-housing model representing a turbopump of a space shuttle main engine (SSME). In that model, the local nonlinearity is due to clearances between the rotor bearing outer races and the carrier attached to the housing. As compared to the fourth-order Runge-Kutta numerical integration methods, the convolution approach proved more efficient and robust for the same accuracy requirement. This is due to the closed-form formulation of the convolution approach which allows for the use of relatively larger time increments and for a reduction in the roundoff errors.
Classical Vibration Analysis of Axially Moving Continua
Authors: Wickert J. A. , Mote C. D.
Published: April 2008

Axially moving continua, such as high-speed magnetic tapes and band saw blades, experience a Coriolis acceleration component which renders such systems gyroscopic. The equations of motion for the traveling string and the traveling beam, the most common models of axially moving materials, are each cast in a canonical state space form defined by one symmetric and one skew-symmetric differential operator. When an equation of motion is represented in this form, the eigenfunctions are orthogonal with respect to each operator. Following this formulation, a classical vibration theory, comprised of a modal analysis and a Green’s function method, is derived for the class of axially moving continua. The analysis is applied to the representative traveling string and beam models, and exact closed-form expressions for their responses to arbitrary excitation and initial conditions result. In addition, the critical transport speed at which divergence instability occurs is determined explicitly from a sufficient condition for positive definiteness of the symmetric operator.
Equations of Motion for Structures in Terms of Quasi-Coordinates
Authors: Quinn Roger D.
Published: April 2008

A form of Lagrange’s equations in terms of quasi-coordinates (Boltzmann/Hamel equations) is presented. Identities are introduced which permit a straightforward method for formulating the equations of motion for structures for which the kinetic and potential energies are explicit functions of angular orientation. This formulation may be utilized once the energies are expressed in matrix form as functions of angular velocities and coordinate transformation matrices. This method is particularly useful for a large class of problems in the dynamics of structures including spacecraft, robots, ground vehicles, and aircraft.
Two-Parameter Characterization of Elastic-Plastic Crack-Tip Fields
Authors: Betego´n C. , Hancock J. W.
Published: April 2008

Plane-strain elastic-plastic crack-tip fields have been modeled with modified boundary layer formulations based on the first two terms K and T, of the elastic field. These formulations match the appropriate full field solutions. Compressive T stresses reduce the stresses by an amount which is independent of radial distance, corresponding to the introduction of a second term in addition to the dominant plastic singularity. Geometries which maintain J-dominance are characterized by zero or positive T stresses, while geometries with negative T stresses can be described by a two-parameter characterization using J and T into full plasticity.
Pure Bending of Curved Beams of Thin-Walled Rectangular Box Section
Authors: Cook R. D.
Published: April 2008

A closed-form solution of the subject problem is presented. The analytical method resembles that used by Bleich (1933) to study curved beams of I or T section. It is found that the circumferential stress may be smaller than a perpendicular stress that arises from flexing of parts of the box. Accuracy of the solution is verified by comparison with finite element analyses.
Local Delamination Buckling in Layered Systems
Authors: Madenci E. , Westmann R. A.
Published: April 2008

This paper presents an analytical solution to the problem of local buckling induced by delamination of a layered plate. Delamination growth and buckling is an observed failure mode in laminated structures subjected to compressive loads. Previous analytical studies of the phenomenon rest upon simplifying structural and geometric approximations. The purpose of this paper is to present solutions for this problem using the classical three-dimensional theory of elasticity to predict the buckled equilibrium state. Solutions to the problem of a plate with a circular delamination subjected to axisymmetric and uniaxial in-plane compressive loadings are obtained using mathematical techniques appropriate for mixed boundary value problems.
The Usefulness of Elementary Theory for the Linear Vibrations of Layered, Orthotropic Elastic Beams and Corrections Due to Two-Dimensional End Effects
Authors: Duva J. M. , Simmonds J. G.
Published: April 2008

With the aid of formal asymptotic expansions, we conclude not only that elementary (Euler-Bernoulli) beam theory can be applied successfully to layered, orthotropic beams, possibly weak in shear, but also that, in computing the lower natural frequencies of a cantilevered beam, the most important correction to the elementary theory—of the relative order of magnitude of the ratio of depth to length—comes from effects in a neighborhood of the built-in end. We compute this correction using the fundamental work on semi-infinite elastic strips of Gregory and Gladwell (1982) and Gregory and Wan (1984). We also show that, except in unusual cases (e.g., a zero Poisson’s ratio in a homogeneous, elastically isotropic beam), Timoshenko beam theory produces an erroneous correction to the frequencies of elementary theory of the relative order of magnitude of the square of the ratio of depth to length.
Active Vibration Control of the Axially Moving String in the S Domain
Authors: Yang B. , Mote C. D.
Published: April 2008

A new method is presented for active vibration control of the axially moving string, one of the most common models of axially moving continua. The control is formulated in the Laplace transform domain. The transfer function of a closed-loop system, consisting of the plant, a feedback control law and the dynamics of the sensing and actuation devices, is derived. Analysis of the root loci of the closedloop system gives two stability criteria. Stabilizing controller design is carried out of both collocation and noncollocation of the sensor and actuator. It is found that all the modes of vibration can be stabilized and that in principle the spillover instability can be avoided. Also, the steady-state response of the stabilized string to periodic, external excitation is presented in closed form.
Optimal Control of Beams With Dynamic Loading and Buckling
Authors: Su Y.-A. , Tadjbakhsh I. G.
Published: April 2008

The vibration of beams can be suppressed by a set of discrete actuators associated with a causal optimal, coupled-modal control algorithm which is derived from minimizing a time-dependent weighted sum of the kinetic energy, potential energy, and the control effort. The control gains are functions of the control interval and couple the modes that participate in the control. The controller can be applied to control a beam subjected to a resonant cyclic load, a moving load, and a beam column subjected to a unit impuse at midspan before buckling.
Dynamic Spherical Cavity Expansion of Strain-Hardening Materials
Authors: Luk V. K. , Forrestal M. J. , Amos D. E.
Published: April 2008

We developed models for the dynamic expansion of spherical cavities from zero initial radii for elastic-plastic, rate-independent materials with power-law strain hardening. The models considered the material as incompressible and compressible. For an incompressible material, we obtained closed-form solutions, whereas the compressible results required the numerical solution of differential equations. A comparison of the numerical results from both models showed the effect of compressibility.
Dynamics of Multibody Systems With Known Configuration Changes
Authors: McPhee J. J. , Dubey R. N.
Published: April 2008

The equations of motion are derived for a system with inertial properties that are varying in time as a result of known relative motions between the rigid bodies comprising the system. This vector-dyadic formulation has been encoded into a computer program, making use of the conformal rotation vector for the representation of rotations. The numerical simulation of two different physical systems is presented in order to illustrate the dynamic effects of the changing inertial properties, and the usefulness of the encoded formulation for modeling these effects.
Fatigue, Fractals, and a Modified Miner’s Rule
Authors: Altus Eli
Published: April 2008

A Mechano Chemical Fatigue Model (MCFM) was recently developed. Two basic features of the model are studied here: (a) the fractal (self-similarity under magnification) property of the damage function, which is predicted by the model and (b) how it leads to a “Modified Miner’s Rule” (MMR), where the fatigue response is dependent on the loading order. Based on the simplest (basic) case of the model, the damage function is dependent on a single parameter when a Weibull strength distribution for the microscale elements (chains) is used. the MCFM proposes a rational explanation to a linear fatigue failure envelope for a two level (High-Low, Low-High) stress loading while the damage law is nonlinear. This is in contrast to the regular Miner Rule, where the damage progression is assumed linear. Applying multilevel cyclic loading the model shows a “fading memory“ response for a monotonically increasing stress. While for a decreasing stress steps there is an intermediate delay stage for which a constant damage rate is found. The microscopic basis of the MCFM enables a clear and direct physical interpretation of the macro behavior as related to the microscale damage mechanisms.
On the Extent of Dominance of Asymptotic Elastodynamic Crack-Tip Fields: Part I—An Experimental Study Using Bifocal Caustics
Authors: Krishnaswamy Sridhar , Rosakis Ares J.
Published: April 2008

The question of the domain of dominance of mode I asymptotic elastodynamic crack-tip fields is investigated experimentally for the cases of dynamically loaded stationary cracks as well as dynamically propagating cracks. The experiments reported are on three-point bend specimens loaded dynamically using a drop-weight tower. An optical configuration leading to a bifocal high-speed camera is proposed. This is used in conjunction with the method of caustics to obtain apparent dynamic stress intensity factor measurements simultaneously from two different regions around the crack tip. The results of this study indicate that three-dimensional and transient effects necessarily have to be taken into account in the interpretation of dynamic fracture experiments.
On the Extent of Dominance of Asymptotic Elastodynamic Crack-Tip Fields: Part II—Numerical Investigation of Three-Dimensional and Transient Effects
Authors: Krishnaswamy Sridhav , Rosakis Ares J. , Ravichandran G.
Published: April 2008

In Part I of this paper, the question of the extent of dominance of the mode I asymptotic elastodynamic crack-tip field (the KdI-field) was studied experimentally. Here, the results of two and three-dimensional elastodynamic finite element simulations of the drop-weight experiments are reported. The load records as obtained from the impact hammer and supports of the drop-weight loading device were used as boundary tractions in the numerical simulations. For the laboratory specimen studied, the results of the simulations indicate that the asymptotic elastodynamic field is not an adequate description of the actual fields prevailing over any sizeable region around the crack tip. This confirms the experimental results of Part I which showed that three-dimensional and transient effects necessarily have to be taken into account for valid interpretation of experimental results.
The Mode III Crack Problem in Bonded Materials With a Nonhomogeneous Interfacial Zone
Authors: Erdogan F. , Kaya A. C. , Joseph P. F.
Published: April 2008

In this paper the mode III crack problem for two bonded homogeneous half planes is considered. The interfacial zone is modeled by a nonhomogeneous strip in such a way that the shear modulus is a continuous function throughout the composite medium and has discontinuous derivatives along the boundaries of the interfacial zone. The problem is formulated for cracks perpendicular to the nominal interface and is solved for various crack locations in and around the interfacial region. The asymptotic stress field near the tip of a crack terminating at an interface is examined and it is shown that, unlike the corresponding stress field in piecewise homogeneous materials, in this case the stresses have the standard square root singularity and their variation is identical to that of a crack in a homogeneous medium. With application to the subcritical crack growth process in mind, the results given include mostly the stress intensity factors for some typical crack geometries and various material combinations.
Integral Equations Solution for Reinforced Mode I Cracks Opened by Internal Pressure
Authors: Fowser Scott W. , Chou Tsu-Wei
Published: April 2008

The problem of a series of collinear Mode I cracks loaded by a uniform internal pressure is solved by an integral equations technique. By superimposing the solution for an arbitrarily loaded Mode I crack with the solution for an edge loaded infinite strip, a system of integral equations is developed by making the superposition satisfy the required boundary conditions. Solving the integral equations by a least-squares Ritz method gives boundary values which may then be used with the Green’s functions solutions to calculate stress intensity factors for the cracks and the stress and displacement fields in the reinforcement and the cracked regions. By changing the boundary conditions at the reinforcement interface, integral equations modeling other situations such as imperfect bonding may be obtained.
Vibration of Circular Plates in Contact With Water
Authors: Kwak M. K.
Published: April 2008

This paper is concerned with the virtual mass effect on vibrating circular plates due to the presence of water. Natural frequencies in water can be estimated from natural frequencies in air by using the approximate formula, which mainly depends upon the so-called added virtual mass incremental factor. The added virtual mass incremental factor is a function of geometry, material properties of the plates and mostly boundary conditions of the plates, and water domain. For practical reasons, the added virtual mass incremental factor is likely to be nondimensionalized. In this paper, the nondimensionalized added virtual mass incremental factors for circular plates having simply-supported, clamped, and free edges are obtained by employing the integral transformation technique in conjunction with the dual integral equation method. It is found that the effect of water on the natural frequencies decreases with order.
Systems With Infinitesimal Mobility: Part I—Matrix Analysis and First-Order Infinitesimal Mobility
Authors: Kuznetsov E. N.
Published: April 2008

Structural and mechanical assemblies with infinitesimal mobility are studied by means of analytical statics, elaborating and capitalizing on the conceptual difference between virtual and kinematic displacements. The analysis is based on the resolution of a given load into two mutually orthogonal components, which allows the introduction of a statical-kinematic stiffness matrix. The issue of statical-kinematic duality is explored and extended to second-order analysis. It leads to the complementary exclusion condition between kinematic mobility and statical possibility of stable self-stress, and the ensuing statical criterion of immobility. A computationally efficient matrix method for detecting simple first-order mechanisms is presented and compared to an existing method based on the analysis of a certain reduced quadratic form.
On the Crucial Role of Imperfections in Quasi-static Viscoplastic Solutions
Authors: Belytschko T. , Moran B. , Kulkarni M.
Published: April 2008

The stability and structure of shear bands and how they relate to initial imperfections is studied within the framework of a one-dimensional boundary value problem. It is shown that in strain-softening viscoplasticity the structure of the band depends on the structure of the imperfection. A Fourier analysis shows that the width of the shear band depends directly on the width of the imperfection, suggesting that the imperfection scales the response of the viscoplastic material. For continuously differentiable imperfections, the shear band is continuously differentiable, whereas when the imperfection is C° at the maximum, the shear band is C°, and cusp-shaped. For step function imperfections, the shear band is shown to be a step function, but it is shown that this solution is unstable.
Torsional Stress Waves in a Circular Cylinder With a Modulated Surface
Authors: Kim Jin O. , Bau Haim H.
Published: April 2008

The paper describes a theoretical and experimental study pertaining to torsional stress wave motion in an axisymmetric waveguide whose cross-sectional area varies periodically as a function of the axial coordinate. Dispersion relations for the phase speed are obtained for both nonresonant and resonant conditions, using perturbation techniques for small amplitude, sinusoidal modulation. Resonant conditions exist when the modulation wave number is proportional to the sum or difference of wave numbers corresponding to various modes of the torsional stress wave. The experiments consist of measuring the stress wave speed in waveguides with threaded surfaces. The experimental observations verify the general trends predicted by the theory.
On Damping Mechanisms in Beams
Authors: Banks H. T. , Inman D. J.
Published: April 2008

A partial differential equation model of a cantilevered beam with a tip mass at its free end is used to study damping in a composite. Four separate damping mechanisms consisting of air damping, strain rate damping, spatial hysteresis, and time hysteresis are considered experimentally. Dynamic tests were performed to produce time histories. The time history data is then used along with an approximate model to form a sequence of least squares problems. The solution of the least squares problem yields the estimated damping coefficients. The resulting experimentally determined analytical model is compared with the time histories via numerical simulation of the dynamic response. The procedure suggested here is compared with a standard modal damping ratio model commonly used in experimental modal analysis.
Dynamic Pulse Buckling of Imperfection-Sensitive Shells
Authors: Lindberg Herbert E.
Published: April 2008

The theoretical basis of two related but distinctly different dynamic buckling criteria are summarized with the objective of demonstrating the range of applicability of each, so that together they cover the entire range of dynamic pulse loads from nearly impulsive loads to step loads of infinite duration. The example chosen is a cylindrical shell under elastic axial loads but the approach is applicable more generally. A critical amplification-of-imperfections criterion with a linear shell theory is shown to be applicable for short duration loads, for which a threshold nonlinear divergence criterion gives loads an order of magnitude too conservative. Conversely, the linear theory is inapplicable for long duration loads, for which critical loads are lower than the linear static buckling load because of imperfection sensitivity. In this range the threshold nonlinear divergence criterion is used. For loads of intermediate duration, an extended critical amplification criterion is used with equations that conservatively assume zero static buckling load but give an unchanged formula for critical load amplitude-duration combinations.
Structural Computation of an Assembly of Rigid Links, Frictionless Joints, and Elastic Springs
Authors: Pellegrino S. , Calladine C. R.
Published: April 2008

The aim of the paper is to set up a scheme for efficient computation of the small-displacement response of a plane assembly of rigid links, frictionless joints, and elastic springs to static external forces applied at the joints. The particular assembly of Fig. 1 is used as an example. The conventional “stiffness method”-which becomes singular when, as here, the links are rigid-is abandoned in favor of a method which describes the current state of the assembly in terms of the amplitudes of m (here = 3) independent infinitesimal modes of inextensional deformation of the assembly; and the calculation boils down to the solving of an m x m (here 3 x 3) set of algebraic equations. The method is particularly straightforward if the inextensional modes (as here) may be obtained by inspection; but a general algorithm is presented for obtaining the inextensional modes of an arbitrary assembly of the same general kind. A major advantage over the conventional stiffness method-which requires, of course, the replacement of rigid links by (stiff) elastic members is that the number of variables may be reduced substantially. This can be very important for large assemblies.
Predicting Rebounds Using Rigid-Body Dynamics
Authors: Smith Charles E.
Published: April 2008

The observation by Thomas Kane a few years ago, that long-used relationships for predicting post-collision motion of a system of rigid bodies can imply a significant increase in kinetic energy during collision, has revived interest in this type of problem. This paper is intended to clarify understanding of the sources of this difficulty, and to suggest an alternative to some of the previously used assumptions for making such predictions. An organization of the pertinent equations of kinetics is presented, which provides a more direct means of examining the aforementioned question and of obtaining rebound predictions.