bluuebunny/crossref_metadata_2025 huggingface dataset:
Axial Buckling of Cylindrical Shells With Prismatic Imperfections
Authors: Bhatia P. , Babcock C. D.
Published: November 2010

The effect of prismatic imperfections on the buckling load of circular cylindrical shells under axial compression is examined by considering the problem as one of interaction between panels forming the shell. The imperfections are in the form of flat spots. Numerical results are presented to show the effect of shell geometric parameters and the number, size, and the type of flat spots on the buckling load.
Stresses at the Intersection of Sphere and Cylinder by a Variant Finite-Difference Method
Authors: Fayed Mustafa Hassan
Published: November 2010

The aim of this paper is the determination of stresses at the intersection of cylinder with the sphere using a variant finite-difference technique. Mesh lines are drawn on the cross section of the body which are roughly parallel and perpendicular to the boundary, and which the author calls natural meshes. Discretization of the governing differential equations must be carried out to reduce the continuous problem to a discrete problem, this discretization converts the problem into a set of linear simultaneous equations for the functions under consideration at a set of mesh points. The derivatives to be inserted in the governing equations and boundary conditions are found by writing Taylor series expansions at a point in terms of five neighboring points in the case where the point is an internal point (four for a boundary point). By an elimination process the derivatives can be eliminated for each point, and we are left with the unknown functions only.
Displacement Analysis of Spatial Six-Link, 5R-C Mechanisms
Authors: Duffy J. , Rooney J.
Published: November 2010

Input-output displacement equations of degree 16 are derived for spatial six-link RRRRCR and RRCRRR2 mechanisms. The derivation of these equations provides the solution to one of the most formidable problems in the theory of analysis of spatial mechanisms. The subsequent displacement analysis is derived by extending Be´zout’s reduction (1764) of the degree of a pair of equations in a single unknown, to equations with two unknowns. Numerical results were verified using a physical model. The input-output equations contain as special cases eighth-degree polynomials for spatial six-link 4R-P-C slider-crank mechanisms.
Transients in High Spin Gyroscopic Systems
Authors: Sethna P. R. , Balachandra M.
Published: November 2010

Transient motions of nonlinear gyroscopic systems with large conserved momenta or with rotors with large angular velocities are studied by asymptotic methods of analysis. The general results are applied to the study of a damped heavy top and a single axis stable platform.
A Theory of Optical Second Harmonic Generation Via Symmetry and Group-Theoretic Methods in Mechanics
Authors: Tsui Y. T.
Published: November 2010

Based on classical Lorentz theory of electrons, one can construct anisotropic coupled equations of motion of anharmonic Lorentz oscillator, which conform to crystal symmetry operations. The solution of the aforementioned coupled equations yields second harmonic component when the driving electric field contains fundamental harmonic only. The physical model of this theory is that electrons oscillate simultaneously and sinusoidally in the xy plane with frequency ω and along the z-direction with frequency 2ω.
Flow-Rate Estimates for Rectilinear Pipe Flow
Authors: Wheeler L.
Published: November 2010

A means is established for finding upper and lower bounds on the flow rate of viscous incompressible fluids in straight pipes. Bounds are derived for a class of flow regions having as cross section a strip or annulus, and used to deduce an approximation appropriate to such sections when they are thin. Explicit error-bound results are included.
General Bounding Theorems for the Quasi-Static Deformation of a Body of Inelastic Material, With Applications to Metallic Creep
Authors: Ponter A. R. S.
Published: November 2010

General displacement and work bounds are derived for the small-deflection quasi-static deformation of a body composed of a material which exhibits both elastic and inelastic strains. The bounds are described in terms of functional properties of the constitutive relationships. The results are specialized to an elastic/perfectly plastic and nonlinear viscous material and known results are recovered. Special emphasis is given to problems associated with the analysis of creep deformation of metallic structures.
Stresses and Deformations in a Cylindrical Shell Lying on a Continuous Rigid Support
Authors: Vinet R. , Dore´ R.
Published: November 2010

This paper develops a theoretical tool to predict rigorously the different types of contact between a cylindrical shell and a continuous rigid support for the complete range of pressure, vessel, and support parameters. The technique consists in comparing the actual angle of opening of the support with two limiting angles. These angles represent the upper bounds of the support for contact to take place on two lines only at the tips of the support or on three lines at the tips and at the center of the support. Using Flu¨gge’s equations and considering variations in the circumferential direction, it is shown that the type of contact depends on the internal pressure of the fluid, the geometrical parameters of the shell, and on the angle of opening of the support. The analysis also indicates that separation between the shell and the support is always to be expected in the circumferential direction. Results for the limiting angles of the support are presented graphically. The radial displacements and the circumferential bending moment are given for a specific example.
Instability Analysis of Thin Rectangular Plates Using the Kantorovich Method
Authors: Grimm T. R. , Gerdeen J. C.
Published: November 2010

The extended Kantorovich method is used to obtain solutions for a large number of previously unsolved elastic buckling problems of thin rectangular plates. In the present work, this method is specially adapted to a numerical method of solution. Verification of the solution method is made by solving a large number of plate buckling problems with known classical solutions. Included among the new problems solved are plates with a variety of boundary conditions, plates on elastic foundations, and plates with a variable inplane compressive load applied to only one edge, together with several different in-plane prestress configurations to increase the magnitude of the critical stress.
Instability of an Elastic Strip Hanging in an Airstream
Authors: Datta S. K. , Gottenberg W. G.
Published: November 2010

The stability of a long, thin elastic strip hanging vertically in a downward flowing airstream was considered. Experimentally it was observed that the strip remained essentially motionless or at most developed a small amplitude bounded oscillation as the air speed was increased until a critical speed was attained beyond which violent oscillations of the free-ended strip occurred. A linear approximate analysis was performed for this problem which accounted for shape-induced lift and bending stiffness of the strip and which closely predicted critical air speeds for this instability. The critical air speed was studied as a function of the length, width, and thickness of the rectangular strip.
Finite-Element Analysis of Thin Elastic Shells With Residual Energy Balancing and the Role of the Rigid Body Modes
Authors: Fried I.
Published: November 2010

The thin cylindrical and spherical shells are computationwise distinct owing to the presence in the first and the absence in the latter of extensional modes. Introduction by numerical integration or allied means of discrete extensional modes in the cylindrical shell element considerably improves the discretization accuracy. Balancing the (residual) extensional energy with the discretization errors removes the radius-to-thickness ratio from the condition number of the stiffness matrix. No such computational contrivances are needed for the spherical shell whose global stiffness matrix is as well conditioned as that of a flat membrane, regardless of large radius-to-thickness ratios.
A Continuum Mixture Theory of Heat Conduction in Laminated Composites
Authors: Nayfeh Adnan H.
Published: November 2010

A continuum mixture theory with microstructure is developed for heat conduction in laminated wave guides. The theory leads to simple governing equations for the actual composite which retain the integrity of the diffusion process in each constituent but allow them to coexist under some defined interactions. The utility of the resulting equations is demonstrated by studying both harmonic and transient temperature pulses. In the case of harmonic loadings the results are found to correlate well with some existing exact solutions. For transient loadings, solutions are derived by means of Laplace transform techniques. Analytical inversion of the transforms is possible only for the limiting cases of “weak” and “strong” thermal coupling. The limit of strong interaction leads to the coalescence of both temperatures; in this case the composite behaves like a single but higher-order continuum. For the general coupling case, however, results are demonstrated by a direct numerical inversion of the transforms.
Numerical Solution of the Three-Dimensional Navier-Stokes Equations With Applications to Channel Flows and a Buoyant Jet in a Cross Flow
Authors: Chien J. C. , Schetz J. A.
Published: November 2010

The steady, three-dimensional, incompressible Navier-Stokes equations written in terms of velocity, vorticity, and temperature are solved numerically for channel flows and a jet in a cross flow. Upwind differencing of the convection term was used in the computation for convergence and simplicity. Comparisons were made with experimental results for laminar flow in the entrance region of a square channel, and good agreement was obtained. The method was also applied to a turbulent, buoyant jet in a cross-flow problem with the Boussinesq approximation and a constant Prandtl eddy viscosity model. Good agreement with experiment was obtained in this case also.
Residual Thermal Stresses in a Solid Sphere Cast From a Thermosetting Material
Authors: Levitsky Myron , Shaffer Bernard W.
Published: November 2010

Expressions are developed for the residual thermal stresses in a solid sphere cast from a chemically hardening thermosetting material in a rigid spherical mold. The description of the heat generation rate and temperature variation is derived from a first-order chemical reaction. Solidification is described by the continuous transformation of the material from an inviscid liquidlike state into an elastic solid, with intermediate properties determined by the degree of chemical reaction. Residual stress components are obtained as functions of the parameters of the hardening process and the properties of the hardening material. Variation of the residual stresses with a nondimensionalized reaction rate parameter and the relative compressibility of the hardened material is discussed in detail.
On the Three-Dimensional Theory of Cracked Plates
Authors: Folias E. S.
Published: November 2010

This paper discusses a method for solving three-dimensional mixed-boundary-value problems which arise in elastostatics. Specifically, the method is applied to a plate of finite thickness which contains a finite, through the thickness, line crack. The analysis shows that (a) in the interior of the plate only the stresses σx, σy, σz, τxy are singular of order 1/2; (b) in the vicinity of the corner point all the stresses are singular of order |(1/2) + 2ν|; (c) as the thickness h → ∞ the plane strain solution is recovered and; (d) as ν → 0 the plane stress solution is recovered. Finally, it is found that in the neighborhood of the corner points, even though the displacements are singular for certain values of the Poisson’s ratios, the derived stress field satisfies the condition of local finite energy.
Harmonic Waves in Layered Composites: Comparison Among Several Schemes
Authors: Nemat-Nasser S. , Minagawa S.
Published: November 2010

For harmonic waves in layered elastic composites the results obtained by means of the Rayleigh quotient based on displacement and the Rayleigh quotient based on stress, are compared with those obtained by a new quotient recently proposed by one of the authors, in an effort to examine reasons for the astonishing accuracy of the new quotient for this class of problems. This comparison leads to a scheme for obtaining improved test functions which then give very accurate lower and upper bounds for the wave frequencies. Results are illustrated by numerical examples.
Scattering of Plane Waves by a Propagating Crack
Authors: Chen E. P. , Sih G. C.
Published: November 2010

Scattering of plane harmonic waves by a running crack of finite length is investigated. Fourier transforms were used to formulate the mixed boundary-value problem which reduces to pairs of dual integral equations. These dual integral equations are further reduced to a pair of Fredholm integral equations of the second kind. The dynamic stress-intensity factors and crack opening displacements are obtained as functions of the incident wavelength, angle of incidence, Poisson’s ratio of the elastic solid and speed of crack propagation. Unlike the semi-infinite running crack problem, which does not have a static limit, the solution for the finite crack problem can be used to compare with its static counterpart, thus showing the effect of dynamic amplification.
The Exact Solution of the Translational Acceleration of a Low Modulus Elastic Medium in Rigid Spherical Shells—Implications for Head Injury Models
Authors: Chandran K. B. , Liu Y. King , von Rosenberg D. U.
Published: November 2010

The exact solution in the form of a finite series has been obtained for the problem of low modulus elastic medium contained in rigid spherical shells subjected to translational acceleration about its diametrical axis. Laplace transformation technique and the shifting theorem were used to obtain the Green’s functions for the potentials when the external acceleration is a Dirac delta function. The solutions are formally extended to external accelerations which are general functions of time by the convolution integral. The shear stress distribution for a unit step function acceleration is illustrated. The results obtained are used to judge the adequacy of this and other similar models for the study of closed head injury mechanism.
Application of Spencer’s Ideal Soil Model to Granular Materials Flow
Authors: Morrison H. L. , Richmond O.
Published: November 2010

In 1964, Spencer proposed a model for plane deformation of soils based upon the concept that the strain at any point may be considered as the resultant of simple shears on the two surface elements where Coulomb’s yield condition is met. Gravitation and acceleration terms were neglected in his full field equations. These terms are included in the present treatment, however, since they play an essential role in granular materials flow problems. It is shown that the field equations remain hyperbolic, and the characteristic equations are derived. In addition, a streamline equation, similar to Bernoulli’s classical equation for fluid flow, is derived and used together with the continuity equation to obtain one-dimensional approximate solutions to some typical hopper and chute problems. A solution is obtained for the nonsteady flow from a wedge-shaped hopper when the gate is suddenly opened, including an equation for the minimum slope necessary to prevent arching. Another solution is obtained for the profile of a hopper which has constant wall pressure. Still another solution is obtained for the relationship between the height of a chute and its exit velocity, and it suggests that the maximum trajectory usually is obtained with a horizontal exit since an upward-sloping exit requires a velocity jump at the minimum point in the chute, similar to a hydraulic jump in fluid flow. All of these solutions are ideal in the sense that they include no wall resistance to the flow, and therefore represent maximum flow rates.
Multiple Diffractions of Elastic Shear Waves by a Rigid Rectangular Foundation Embedded in an Elastic Half Space
Authors: Dravinski M. , Thau S. A.
Published: November 2010

A rigid rectangular foundation, embedded in an elastic half space, is subjected to a plane, transient, horizontally polarized shear (SH) wave. Embedment depth of the foundation and the angle of the incidence of the plane wave are assumed to be arbitrary. The problem considered is of the antiplane-strain type. The Laplace and Kontorovich-Lebedev transforms are employed to derive the equation of motion for the foundation during the period of time required for an SH-wave to traverse the base width of the obstacle twice. Therefore this solution includes the process of multiple diffractions at the corners of the foundation.
Transmission and Reflection of Extensional Stress Pulses at the Junction of a Straight Bar and a Helix
Authors: Haines D. W. , Chang N.
Published: November 2010

We present the analytical and experimental study of a mechanical pulse filter. The filter is an unbounded assembly composed of a straight bar joined tangentially to a helix. The Fourier time transform of the pulses and the complex frequency response of the assembly are employed to obtain the analytical solutions. It is shown that for the assembly to be effective as an extensional pulse filter, the pulse duration should be longer than the ring mode period, i.e., the time required for a pulse traveling with the extensional bar velocity to travel around one turn of the helix. Experimental results are presented which verify the analytical solution.
Deviations From the Linear Transport Laws and Corrections to the Onsager Reciprocal Relations
Authors: Scheffler W. A. , Dahler J. S. , Ibele W. E.
Published: November 2010

An extension of the linear transport laws is derived from first principles of statistical mechanics. The resulting transport laws include both relaxation and nonlinear terms. It is found when these terms are included the Onsager reciprocal relations are no longer valid. Therefore, the development gives the limit of validity of the Onsager relations, as well as expressing the transport coefficients as correlation functions of the dynamical variables. In order to show the validity of the procedure used, a functional integral is derived as a first-order approximation for the transition probability. This integral when evaluated verifies the assumption of Onsager and Machlup for the transition probability for the linear transport laws.
Harmonic Holes—An Inverse Problem in Elasticity
Authors: Bjorkman G. S. , Richards R.
Published: November 2010

A fundamental problem in elasticity is investigated: to determine the geometry of a boundary from prescribed conditions that must be satisfied by the final field stresses. For the planar problem the hole shape termed “harmonic” is the one which satisfies a specific design requirement that the first invariant of the original field remains everywhere unchanged. Using the complex variable technique a general functional equation for the hole geometry is obtained in integral form simply in terms of the original free field and hole boundary loading. The biaxial field is considered as an example with a uniformly distributed normal stress applied to the unknown hole boundary. It is shown that for this field, a properly proportioned and oriented elliptic hole satisfies the design requirement and simultaneously produces the minimum stress concentration for any possible unreinforced hole shape. For an unloaded boundary, this optimum hole exists only when the principal stresses in the original field have the same sign.
Uniaxial Creep Behavior of Metals Under Cyclic Temperature and Stress or Strain Variations
Authors: Paslay P. R. , Wells C. H.
Published: November 2010

The application of recovery creep theory to the prediction of cyclic loading and heating response of a specific high temperature alloy is illustrated for four different cyclic shapes. It is shown that a satisfactory approximation to the quasi-steady state cyclic response of the material after a number of loading cycles can be obtained from a single computation by comparison with the results of cycle-by-cycle integration. The special form of recovery creep theory employed assumes isotropic hardening and therefore does not predict a symmetrical creep strain response under symmetrical stress cycling.
Nonlinear Dynamic Buckling of Sandwich Panels
Authors: Adi Murthy N. K. , Alwar R. S.
Published: November 2010

Nonlinear dynamic buckling of simply supported rectangular sandwich panels with isotropic cores and with initial curvature under transverse loads is analyzed. The large deflection sandwich panel equations proposed by Reissner are solved using a trigonometric series spacewise and by Houbolt scheme for timewise integration. The resulting nonlinear algebraic equations are solved by Newton’s iterative method to yield the deflection coefficients at all time intervals. The present investigation essentially deals with the influence of dynamic loads on the snap-through behavior of sandwich panels. The effect of the initial curvature and core modulus is studied in detail. Static snap-through collapse loads are also calculated and compared with dynamic loads. As a check for the present analysis the results obtained for the static case for a homogeneous plate are compared with the available results. It has been shown that for a given sandwich panel with a given initial curvature, the dynamic snap-through loads can be estimated directly from the static snap-through loads without actually resorting to dynamic analysis.
Stress-Focusing Effect in a Uniformly Heated Cylindrical Rod
Authors: Ho Chih-Horng
Published: November 2010

A long cylindrical rod is considered brought suddenly to a uniform temperature rise over its cross section. Stress-focusing effects occur when stress waves reflect from the outer surface of the rod and proceed radially inward to the axis. The focusing effect can cause a very high peak dynamic stress in both tension and compression in the rod. The magnitude of the peak stress depends upon the magnitude of the temperature rise and the effective heating duration. For instantaneous heating, the infinite peak of stress propagates outward from the center while these peaks are finite for nonzero heating duration. The solutions are carried out by using Laplace transform on time and presented as infinite series summations after the end of heating.
Attenuation of Concentrated Loads in a Thin Moving Elastic Strip
Authors: Patula E. J.
Published: November 2010

The effect of strip velocity on the attentuation distance of concentrated loads for a thin, moving, infinite, elastic strip is considered. The strip is loaded at infinity with a uniform tensile stress. The range of velocity of interest is from zero to the lowest wave velocity in the strip. The results indicate that the attenuation distance decreases with increased strip velocity. Furthermore, the attenuation distance is larger for symmetric loadings than for unsymmetric loadings. As the limiting strip velocity is approached, the solution degenerates in such a manner that the attenuation distance approaches a finite limiting value. The limiting strip velocity is below the lowest wave velocity of the strip. Finally, a procedure for determining the stress and displacement distributions is presented.
Elasticity Solution of Deep Beam Under Settlement of Supports
Authors: Prasad S. N. , Chiu P. K.
Published: November 2010

The present study investigates the two-dimensional stresses and displacements in a finite rectangle whose one set of parallel edges is given a relative tangential displacement by means of rigidly attached planes. The other set of parallel edges is free from tractions. The problem is formulated in terms of a singular integral equation of the first kind, which yields the correct singular behavior of stresses at the corners. The integral equation is solved numerically by employing Gauss-Jacobi quadrature in conjunction with certain collocation technique. Numerical results of quantities of practical interests are shown graphically and also compared with the classical bending analysis.
The Vibrations of an Infinite Orthotropic Layered Cylindrical Viscoelastic Shell in an Acoustic Medium
Authors: Berger B. S.
Published: November 2010

In the following a numerical solution is given for the vibration of an orthotropic layered cylindrical viscoelastic shell in an acoustic medium. The acoustic fluid is modeled through a finite-difference scheme. Numerical results for the elastic shell in an acoustic medium agree with previous solutions.
Hamilton, Ritz, and Elastodynamics
Authors: Bailey C. D.
Published: November 2010

The theory of Ritz is applied to the equation that Hamilton called the “Law of Varying Action.” Direct analytical solutions are obtained for the transient motion of beams, both conservative and nonconservative. The results achieved are compared to exact solutions obtained by the use of rigorously exact free-vibration modes in the differential equations of Lagrange and to an approximate solution obtained through the application of Gurtin’s principles for linear elastodynamics. A brief discussion of Hamilton’s law and Hamilton’s principle is followed by examples of results for both free-free and cantilever beams with various loadings.
Analysis of Adhesively Bonded Joints Between Panels of Composite Materials
Authors: Renton W. J. , Vinson J. R.
Published: November 2010

A mathematical model is developed and methods of analysis are formulated for determining the structural response of the single-lap and symmetric-lap joints composed of generally orthotropic material systems. Analytical results are compared in both instances with experimental data and excellent correlation is seen to exist.
Determination of Global Regions of Asymptotic Stability for Difference Dynamical Systems
Authors: Hsu C. S. , Yee H. C. , Cheng W. H.
Published: November 2010

In this paper certain global properties of dynamical systems governed by nonlinear difference equations are studied. When an asymptotically stable equilibrium state or periodic solution exists, it is desirable to be able to determine a global region of asymptotic stability in the state space. In this paper an effective method is presented for the determination of such a region. It will be seen that once certain features of the backward mapping have been properly delineated, the development of the method becomes a rather simple one. The method is mainly presented for second-order systems but the basic ideas are also applicable to higher-order systems. Through the development of the theory and examples, one also sees that, in general, the region of asymptotic stability for a nonlinear difference system is of extremely complex shape.
The Elastic Moduli of a Fiber-Reinforced Composite
Authors: Mal A. K. , Chatterjee A. K.
Published: November 2010

A composite consisting of a homogeneous isotropic elastic matrix containing infinitely long parallel circular cylinders is considered. The cylindrical fibers have identical physical properties and are firmly bonded to the matrix with uniform spatial distribution. Only plane problems are considered. Approximate formulas for the three average elastic moduli of the composite are derived by retaining the interaction between the fibers. The interaction effects are explicitly calculated as functions of the spacing between the fibers. Numerical results for a specific composite model are given.
Pressure-Shear Waves in 6061-T6 Aluminum Due to Oblique-Plate-Impact
Authors: Abou-Sayed A. S. , Clifton R. J.
Published: November 2010

Results are reported for experiments employing two types of oblique-plate-impact configurations. One, a symmetric configuration, uses 6061-T6 Aluminum plates for both targets and projectiles. The second, an asymmetric configuration, uses a 6061-T6 Aluminum projectile and a fused silica target. The experimental results are compared to analytical solutions based on an elastic-viscoplastic model for the aluminum alloy and a hyperelastic model for fused silica. The normal velocity-time profile for the symmetric configuration shows close agreement with the predicted one. Results from the asymmetric configuration indicate the utility of using fused silica as a window material for determining the dynamic plastic flow characteristics of the projectile material.
High Velocity Impact Calculations in Three Dimensions
Authors: Johnson G. R.
Published: November 2010

A three-dimensional analysis is presented for high velocity impact problems. A Lagrangian finite-element technique is formulated for tetrahedron elements subjected to large strains and displacements. The effects of material strength and compressibility are included to account for elastic-plastic flow and wave propagation. The strains and strain rates in each element are determined from the displacements and velocities of the nodes. The strains, strain rates, and material properties are used to determine the elastic stresses, plastic deviator stresses, hydrostatic pressure, and artificial viscosity. The stresses are equated to concentrated forces acting on concentrated masses at the nodes, and the nodal equations of motion are numerically integrated. Illustrative examples are also included.
The Stability of an Isolated Rectangular Surface Embedded in Uniform Subsonic Flow
Authors: Ellen C. H.
Published: November 2010

This paper examines the stability of a rectangular surface lying in isolation in an inviscid fluid in uniform subsonic motion when the surface, in its undeformed state, lies in a plane with its edges aligned parallel and perpendicular to the flow direction. The problem is formulated in the form of an integral equation which is solved approximately using the one-term Galerkin method so that expressions for the stability parameter are determined in the form of asymptotic series for the high and low aspect ratio limits. Surfaces supported on all edges as well as those whose edges are only partially supported are investigated. The results are compared with those for an infinite array of panels and an isolated panel replacing part of a rigid surface.
Natural Structural Shapes of Shallow Arches
Authors: Stadler W.
Published: November 2010

This paper serves as a further illustration of the concept of natural structural shapes, a concept in optimal structural design. Natural shapes occur as solutions of a multicriteria control problem with criteria “mass” and “stored energy” of the deformed structure. The corresponding optimality concept is that of Pareto-optimality. This general approach is applied to the calculation of optimal initial shapes of uniform shallow arches. The resultant problem is a so-called unbounded problem in multicriteria control theory; there are no state constraints. The solution consists of a family of optimal shapes. The subsequent specification of additional constraints such as the maximum allowable deflection, stress, mass, and the like, then yields a particular member of the family. The solutions to the minimum weight and the minimum of the maximum deflection problem appear as limiting cases.
The Possible Motions of a Rigid Body With One Fixed Point
Authors: Zare K. , Levinson D. A.
Published: November 2010

A recently developed theory is used to establish criteria for determining regions of possible motions in a reduced configuration space for a rigid body having one fixed point. Such regions are plotted for a numerical example and their qualitative features are examined.
Timoshenko Beam Theory Is Not Always More Accurate Than Elementary Beam Theory
Authors: Nicholson J. W. , Simmonds J. G.
Published: November 2010

A counterexample involving a homogeneous, elastically isotropic beam of narrow rectangular cross section supports the assertion in the title. Specifically, a class of two-dimensional displacement fields is considered that represent exact plane stress solutions for a built-in cantilevered beam subject to “reasonable” loads. The one-dimensional vertical displacement V predicted by Timoshenko beam theory for these loads can be regarded as an approximation to either the exact vertical displacement v at the center line, or a weighted average of v over the cross section, or a quantity defined to make the virtual work of beam theory equal to that of plane stress theory. Regardless of the interpretation of V and despite the presence of an adjustable shear factor, Timoshenko beam theory for this class of problems is never more accurate than elementary beam theory.
Capillary Breakup of a Liquid Jet With a Random Initial Perturbation
Authors: Lafrance P. , Ritter R. C.
Published: November 2010

Experiments were performed to measure the size of drops resulting from the capillary breakup of laminar liquid jets. Random noise was used to perturb the jet and an electro-optical instrument was used to measure drop sizes. Drop size distributions show two peaks as predicted by nonlinear theory. The large group has a mean size as predicted by the most unstable perturbation mode, in agreement with the commonly accepted but previously untested assumption.
The Theory of Static Loads in Bins
Authors: Cowin S. C.
Published: November 2010

The classical formula for the pressure in deep bins containing granular material is derived here employing considerably weaker assumptions than previous derivations. Three important points are established in this rigorous derivation. First, it is shown that the classical formula due to Janssen is a lower bound on the average pressure the granular material can exert on a bin wall rather than necessarily the actual stress. Second, it is shown that Janssen’s assumption of constant vertical stress over the bin’s horizontal cross section is not necessary to obtain his classical formula. Third, it is shown that the coefficient introduced by Janssen should be interpreted as the ratio of the horizontal stress averaged over the lateral boundary perimeter to the vertical stress averaged over the horizontal cross-sectional area of the bin.
A Star-Shaped Array of Curvilinear Cracks in an Infinite Isotropic Elastic Medium
Authors: Theocaris P. S. , Ioakimidis N. I.
Published: November 2010

The problem of a symmetrical star-shaped array of curvilinear cracks in an infinite isotropic elastic medium is reduced, by using the complex potential technique of Muskhelishvili [1], to a complex Cauchy-type singular integral equation on one of the cracks together with a complex condition of single-valuedness of displacements. This equation can be solved numerically by reduction to a system of linear equations after application of the Lobatto-Chebyshev numerical integration method for the approximation of the integrals involved in it and an appropriate selection of the points of collocation. An application to some cases of circular-arc-shaped cracks is made.
Nonlinear Stability Analysis of an Eccentrically Loaded Two-Bar Frame
Authors: Kounadis A. N. , Giri J. , Simitses G. J.
Published: November 2010

A completely nonlinear stability analysis, based on a variational approach, is performed on a simple geometrically perfect, two-bar frame, which is loaded eccentrically in a direction parallel to one of the bars (Roorda’s frame). The effects of eccentricity and slenderness ratio are fully assessed. The results are compared to those of Koiter, obtained by employing his initial postbuckling analysis, and to Roorda’s experimental findings. Significant new conclusions concerning the response of the frame are discussed herein, thus giving a better insight into its behavior.
Stability of Elastically Restrained Timoshenko Cantilevers With Attached Masses Subjected to a Follower Force
Authors: Kounadis A. N.
Published: November 2010

In this investigation, the individual and primarily the coupling effects on the critical load are assessed for a variety of parameters, such as elastic spring supports, concentrated masses (positioning, translational, and rotational inertia) as well as transverse shear deformation and rotatory inertia of the column. The problem, in its most general form, is reduced to a system of two-coupled partial-differential equations subject to the appropriate boundary conditions. A solution methodology is developed and successfully demonstrated through numerous examples.
Transient Motion of an Elastic Shell of Revolution in an Acoustic Medium
Authors: Berger B. S.
Published: November 2010

A numerical solution for the transient vibration of an arbitrary shell of revolution, surrounded by an acoustic medium, has been formulated in terms of the conformally mapped acoustic equations, fluid shell boundary conditions and spectral representation of the shell displacements. The technique readily includes the boundary condition at infinity, internal shell structure and is exact to within those approximations implicit in the finite-difference method.
Wheel Rotations and Trailer Dynamics
Authors: Taylor D. L.
Published: November 2010

An evaluation is made of the usual assumption which neglects wheel rotations when obtaining equations of motion for simple vehicle dynamics problems. Using a simple example, a quantitative measure of this approximation is presented. The rotations of the wheels are shown to increase the effective inertia of the system, and thus could be of importance for low mass trailers. The change is easily calculated and can then be included or discarded at the discretion of the analyst.
Sufficient Conditions for Stability of Rotating Flows
Authors: Yang Cheng-I
Published: November 2010

This is a study of sufficient conditions for the stability of rotating flows and swirling flows of perfect conducting fluid with circular magnetic fields. Miles’ theorem [1] and Howard’s semicircle theorem [2] on the stability of stratified shear flows are extended to rotating flows with discontinuous swirl velocity. Some stronger sufficient conditions for stability are established. Some sufficient conditions for the stability and instability of the perfect conductive fluids subjected to a transverse circular magnetic field are also studied.
Simulation of Continuous Systems by Periodic Structures
Authors: Engels R. C. , Meirovitch L.
Published: November 2010

Many continuous systems can be approximated by periodic structures where periodic structures are structures consisting of identical substructures, connected to each other in identical manner. An efficient algorithm developed by these authors for the response of periodic structures is adapted to the treatment of continuous systems. The method is capable of deriving the response of damped or undamped systems subject to harmonic distributed loads. The length of the substructure can be made arbitrarily small without increasing the computational effort. Furthermore, the number of degrees of freedom of the substructure can be reasonably large.
Study of the Random Vibration of Nonlinear Systems by the Gaussian Closure Technique
Authors: Iyengar R. N. , Dash P. K.
Published: November 2010

A technique is developed to study random vibration of nonlinear systems. The method is based on the assumption that the joint probability density function of the response variables and input variables is Gaussian. It is shown that this method is more general than the statistical linearization technique in that it can handle non-Gaussian excitations and amplitude-limited responses. As an example a bilinear hysteretic system under white noise excitation is analyzed. The prediction of various response statistics by this technique is in good agreement with other available results.
Instantaneous Invariants in Three-Dimensional Kinematics
Authors: Kirson Y. , Yang A. T.
Published: November 2010

The paper generalizes the concepts of canonical systems and instantaneous invariants from planar to three-dimensional kinematics. It presents a systematic procedure to determine the instantaneous invariants. An example is included for illustration. The instantaneous invariants are derived on the basis of line coordinates, therefore they are useful for the characterization of higher-order intrinsic properties of a ruled surface—the path trajectory of an arbitrary line embedded in a rigid body in three-dimensional motion. It is hoped that this study may be useful for the rational design of spatial mechanisms for surface generation.
Rules and Methods of Stress and Stability Calculations in the Presence of Creep
Authors: Hoff N. J.
Published: November 2010

Formulas and methods are presented in a self-contained manner to help the analyst of stresses and stability in the design office to deal with problems that arise when elements of metal structures and machinery creep at high temperatures.
Dynamic Stress Concentration Around Two Coplanar Griffith Cracks in an Infinite Elastic Medium
Authors: Itou S.
Published: November 2010

The dynamic problem presented here is for an infinite elastic medium weakened by two coplanar Griffith cracks in which a self-equilibrated system of pressure is varied harmonically with time. The problem is reduced to dual integral equations and solved by a series-expansion method. The dynamic stress-intensity factors are computed numerically.
Natural Frequencies of Clamped Orthotropic Rectangular Plates With Varying Thickness
Authors: Sakata T.
Published: November 2010

The characteristic equation of a clamped orthotropic rectangular plate with thickness varying in one direction parallel to the side is derived analytically by the use of the double trigonometric series. By using the fundamental natural frequency determined from the characteristic equation, a formula is obtained numerically for estimating the fundamental natural frequency of a clamped orthotropic rectangular plate with thickness varying linearly in one direction. The accuracy of the formula and the influence of the flexural rigidity D1 on the natural frequency are discussed.
Bifurcations in Dynamical Systems With Internal Resonance
Authors: Sethna P. R. , Bajaj A. K.
Published: November 2010

Dynamical systems with quadratic nonlinearities and exhibiting internal resonance under periodic excitations are studied. Two types of transition from stable to unstable motions are shown to occur. One kind are shown to be associated with jump phenomena while the other kind are shown to be associated with Hopf bifurcations of the averaged system of equations. In the case of the latter, the motions are shown to be amplitude modulated motions at the excitation frequency with the amplitude of modulation determined by the motion of a point on a torus.
An Experimental Study of First-Passage Failure of a Randomly Excited Structure
Authors: Roberts J. B. , Yousri S. N.
Published: November 2010

Some experimental measurements of the mean and standard deviation of the first-passage time of randomly excited cantilevers are presented. It is shown that these results can be predicted satisfactorily by using a theoretical method based on the energy envelope of the structure, together with information on the energy loss per cycle. This information can be derived either from free decay tests or from data on specific damping factors. The prediction technique does not require the damping forces to be modeled in explicit form and enables nonlinear damping effects to be readily incorporated. Some predicted nonlinear effects are confirmed by the experimental results.
Propagation of a Pulse in a Nonhomogeneous Elastic Rod With Varying Cross Section
Authors: Vasudeva R. Y. , Bhaskara R. K.
Published: November 2010

The problem of propagation of a pressure pulse in a nonhomogeneous elastic rod with varying cross section is discussed. The cross section, the material density, and the elastic modulus of the rod are taken to be varying in a power law form along the length of the rod and the longitudinal displacement is obtained through a method due to Keller and Keller.
Experiments on Magnetoelastic Buckling in a Superconducting Torus
Authors: Moon F. C.
Published: November 2010

A 16 coil superconducting torus is used to study magnetoelastic instabilities in a set of current carrying elastic rings. The torus is a 1/75th model of a proposed magnetic fusion reactor. Up to 130 KA-turns were placed in the 30-cm-dia torus. Three different lateral constraint conditions on the elastic magnets are discussed. Both dynamic and static methods are used to determine the critical buckling currents. The coils are observed to pair up during buckling. A series of snap-type instabilities were observed near the critical buckling current for the lowest mode. A fair to good comparison between experimental and theoretical values of the buckling currents for all three modes is obtained when tension stiffening corrections are included.
Approximate Eigenvalues for Systems With Variable Parameters
Authors: Sinha S. C. , Chou C. C.
Published: November 2010

The paper deals with an approximate analytical technique for solving the boundary-value problems governed by second-order differential equations with variable coefficients. The variable coefficient appearing in the system equation is expanded in ultraspherical polynomials in the desired interval to construct simple equivalent functions such that the approximate differential equations thus obtained have known closed form solutions. If the variable coefficient is approximated by a constant, the solutions are the sine and cosine functions, while a linear approximation leads to a solution in terms of Bessel functions of 1/3 order or Airy’s functions. In particular, the method has been applied to calculate the critical buckling load for a column of exponentially varying moment of inertia. Results obtained by present approach agree with exact results to a much better accuracy than other approximate analytical methods available in the literature. The technique is quite general and does not require any restriction on system parameters.
Fluctuating Flow of a Viscoelastic Fluid in a Porous Channel
Authors: Bhatnagar R. K.
Published: November 2010

The problem of flow of a viscoelastic fluid characterized by the well-known Rivlin-Ericksen constitutive equations is discussed, when such a fluid is driven by an unsteady pressure gradient in the region between two parallel porous plates. It is assumed that on one plate the fluid is injected with certain constant velocity and that it is sucked off at the other with the same velocity. The governing differential equations, which do not involve the cross-viscosity parameter, are solved using a pertubation scheme treating the viscoelastic parameter to be small. The behavior of instantaneous velocity profiles, and magnitude and the phase lag of mass flux, which depend on the injection Reynolds number, the frequency parameter, and the viscoelastic parameter are discussed for various values of these parameters. Some very interesting departures of these from the corresponding flow of classical viscous fluids are reported when one or both of the injection Reynolds number and frequency parameter are small or large.
Axially Symmetric Radial Flow of Rigid/Linear-Hardening Materials
Authors: Durban D.
Published: November 2010

A closed-form solution has been discovered for axially symmetric radial flow of rigid/linear-hardening materials. It is assumed that the materials obey the von Mises flow rule and that the flow field is in steady state. Explicit expressions for the stress components and the radial velocity are given. The applicability of the solution to wire drawing or extrusion is discussed. Some approximate formulas are derived and shown to be in good agreement, within their range of validity, with experimental results for drawing.
Behavior of Thermal Effects and Velocity-Slip on Performance of Externally Pressurized Porous Incompressible Gas Thrust Bearing
Authors: Kapur V. K. , Yadav J. S.
Published: November 2010

In the present analysis, the interactions of thermal effects and velocity slip on the performance of externally pressurized porous incompressible gas thrust bearing have been studied. Numerical results for load capacity, mass flow rate, and static stiffness have been obtained and their behavior is illustrated in figures. The results for slip as well as no-slip condition have also been compared with the experimental results of Gargiulo and Gilmour [7].