bluuebunny/crossref_metadata_2025 huggingface dataset:
On Foundations That React in Compression Only
Authors: Weitsman Y.
Published: November 2010

In this paper it is assumed that tensile stresses cannot be transmitted across the interface between beams, or plates, and their supporting subgrade. The subgrade is represented by models that were proposed by Winkler and by Reissner. The absence of tensile stresses, across the interface between a beam and its foundation, may be accompanied by the formation of no contact regions under the beam. Within those no-contact regions the beam lifts up away from its foundation and the subgrade does not support the structure. The development of no-contact regions is examined in several examples that are presented in this paper. In all the examples the structure, beam or plate, is subjected to a single concentrated load.
Shear Deformation in Heterogeneous Anisotropic Plates
Authors: Whitney J. M. , Pagano N. J.
Published: November 2010

A bending theory for anisotropic laminated plates developed by Yang, Norris, and Stavsky is investigated. The theory includes shear deformation and rotary inertia in the same manner as Mindlin’s theory for isotropic homogeneous plates. The governing equations reveal that unsymmetrically laminated plates display the same bending-extensional coupling phenomenon found in classical laminated plate theory based on the Kirchhoff assumptions. Solutions are presented for bending under transverse load and for flexural vibration frequencies of symmetric and nonsymmetric lamninates. Good agreement is observed in numerical results for plate bending as compared to exact solutions obtained from classical elasticity theory. For certain fiber-reinforced composite materials, radical departure from classical laminated plate theory is indicated.
Resonance Response of Nonlinear Circular Plates Subjected to Uniform Static Load
Authors: Farnsworth C. E. , Evan-Iwanowski R. M.
Published: November 2010

The axisymmetric resonant frequency response of static pressure loaded, nonlinear clamped, circular plates have been investigated analytically and experimentally. In the analysis, the set of nonlinear partial differential equations of motion and compatibility are solved by applying Galerkin’s method with Dini-Bessel and Fourier-Bessel series expansions for the assumed solution forms. These expansions satisfy the boundary conditions exactly. The equations are solved to yield a second approximation for the first mode response and a first approximation for the second mode response. Experiments were conducted on a number of circular plates. The analytical and experimental results are found to be in good agreement for plates with β ⩽ 57.3. The agreement was only fair for plates with β > 57.3.
Response of a Plate Supported by a Fluid Half Space to a Moving Pressure
Authors: Yen D. H. Y. , Chou C. C.
Published: November 2010

The response of an elastic plate supported by a fluid half space to a steadily moving pressure is studied. The Timoshenko plate theory is used in the study. By the method of integral transforms, solutions for both the plate deflection and the interaction fluid pressure are obtained. The results are then compared in detail with those obtained previously using the classical plate theory.
The Free Plastic Compression of Pure Metals
Authors: Shankhla V. S. , Scrutton R. F.
Published: November 2010

The dynamic compression of a billet by the impact of a falling weight is analyzed with reference to the general plastic properties of pure metals. Theoretical results are compared with the results of published experimental data for pure lead. It is shown that, for lead, the form of the stress-strain curve is little influenced by changes in strain rate during deformation. The strain-hardening coefficient is however found to be strongly influenced by the temperature changes associated with the adiabatic deformation. The position of the maximum in the stress-strain curve is sensitive to the value of the initial strain rate. A method is suggested whereby isothermal stress-strain relationships may be extended to include the effects of adiabatic thermal softening.
Semimembrane Analysis of Cylindrical Shells Subjected to Wind Loading
Authors: Krajcinovic D.
Published: November 2010

The semimembrane analysis of cylindrical cantilever shells (silos) is presented. In addition to the beam action, the method accounts for the influence of cross-sectional distortion also. The procedure is simple and the stresses are derived in the form of simple formulas suitable for design purposes.
Forced Vibrations of Two Masses on an Elastic Half Space
Authors: Warburton G. B. , Richardson J. D. , Webster J. J.
Published: November 2010

The paper gives a theory for the response of two periodically excited masses with circular bases attached to the surface of an elastic half space. Results for two geometrically identical cylindrical masses, excited by a vertical harmonic force applied to one of the masses, illustrate the effect of the presence of a second mass upon the response of the excited mass and the conditions for which the response of the second mass is significant.
Stress Concentration Around a Hyperboloidal Notch Under Tension in a Transversely Isotropic Material
Authors: Chen W. T.
Published: November 2010

An elastic solid is composed of a transversely isotropic material bounded by a single-sheeted hyperboloid of revolution, which is traction free. This solid is subjected to a finite tensile force at infinity. A closed-form solution based upon the potential functions approach is obtained. Numerical examples of the tensile stress at the narrowest section are presented.
Theory of Laminated Plates
Authors: Sun C. T.
Published: November 2010

A two-dimensional theory for laminated plates is deduced from the three-dimensional continuum theory for a laminated medium. Plate-stress equations of motion, plate-stress-strain relations, boundary conditions, and plate-displacement equations of motion are presented. The governing equations are employed to study the propagation of harmonic waves in a laminated plate. Dispersion curves are presented and compared with those obtained according to the three-dimensional continuum theory and the exact analysis. An approximate solution for flexural motions obtained by neglecting the gross and local rotatory inertia terms is also discussed.
Flow Over an Oscillating Plate With Suction or With an Intermediate Film: Two Exact Solutions of the Navier-Stokes Equations
Authors: Debler W. R. , Montgomery R. D.
Published: November 2010

The effect on the boundary layer of uniform blowing and suction across an oscillating plane, and the power input are determined. The change in power that is needed to oscillate a plate in an infinite fluid when an intermediate fluid film is present is also found.
Separation of Additive and Subtractive Moire´ Patterns
Authors: Clark J. A. , Durelli A. J.
Published: November 2010

Using a spatial filtering technique, moire´ patterns can be observed that correspond to different forms of the indicial equation describing the parametric properties of gratings and moire´. In particular both the additive and subtractive moire´s are obtained individually over the field. This method, combined with a previously developed method for obtaining spatial partial derivatives from deformed gratings, permits the experimental determination of the whole field of Cartesian shears and rigid rotations.
Experimental Determination of Some Kernel Functions in the Multiple Integral Method for Nonlinear Creep of Polyvinyl Chloride
Authors: Onaran K. , Findley W. N.
Published: November 2010

Kernel functions for mixed-time parameters in the multiple integral representation of the nonlinear viscoelastic behavior of polyvinyl chloride were determined from both two-step tension and two-step torsion creep experiments. First and second-order terms were used for tension and first and third-order terms were used for torsion to describe these kernel functions. Stepdown tests were needed for good accuracy of representation. Accuracy of prediction was good for stepdown but not stepup tests. The product form assumption for these kernel functions and the modified superposition method were also investigated. The latter gave the best overall predictability of the three methods, although the product form was nearly as satisfactory.
Reexamination of the Kolsky Technique for Measuring Dynamic Material Behavior
Authors: Jahsman W. E.
Published: November 2010

A one-dimensional wave propagation analysis is carried out to assess the validity of the Kolsky formulas [1] for average stress and strain in a specimen exhibiting bilinear elastic-plastic behavior when subjected to trapezoidal and triangular incident pulses. For this piecewise linear model, the method of characteristics relating stress and particle velocity rates coupled with loading-unloading boundary conditions connecting discontinuities in these same rates proves to be particularly convenient. For a specimen length which allows four complete reflections of the leading edge of the stress pulse before plastic deformation begins, a comparison is made between “reconstituted” stress-strain curves predicted by the Kolsky formulas and the reference bilinear curve. The reconstituted curves exhibit the following features: an underestimate of the initial elastic (primary) modulus; satisfactory agreement with the secondary modulus, particularly for the curve associated with the gentler trapezoidal stress pulse; and realistic “elastic” unloading again associated with the trapezoidal stress pulse. The analysis predicts some separation of the specimen from the bars near the end of the unloading process where influence on the reconstituted curve is small. It is concluded that when one-dimensional effects dominate, by careful selection of design parameters such as specimen length and pulse shape, one may use the Kolsky formulas with confidence in establishing the presence (or absence) of a strain-rate effect in elastic-plastic materials during plastic deformation.
On the Use of a Torsional Split Hopkinson Bar to Study Rate Effects in 1100-0 Aluminum
Authors: Duffy J. , Campbell J. D. , Hawley R. H.
Published: November 2010

The difficulties involved in the accurate measurement of the flow stress of materials at high rates of deformation are reviewed, and methods of overcoming these difficulties are discussed. It is concluded that the best experimental method is that in which a split Hopkinson bar is adapted for torsion testing, and the loading pulse is approximately square in shape and has a relatively short duration. A description is given of apparatus which was developed to achieve this type of loading, the input wave being generated explosively. This wave was found to contain large amplitude fluctuations, and to eliminate these a mechanical “pulse smoother” was used. The operation of this device is described, and the test procedure, method of calibration, and possible sources of inaccuracy are discussed. Results are presented for 1100-0 aluminum alloy deformed at strain rates of the order of 800 sec−1 and are compared with those obtained at a nominal strain rate of 10−4 sec−1; the results are also compared with those obtained in compressive tests by other workers.
Toward A Diffusing Continuum Theory of Composite Materials
Authors: Bedford A. , Stern M.
Published: November 2010

A theory of composite materials is proposed which is based on the continuum theory of mixtures. The constituents of a composite are modeled as superimposed continua which undergo individual deformations. Effects of structure on dynamical processes in composite materials are then simulated by specifying the coupling between the individual constituent motions. A novel feature of this model is the inclusion of diffusion with relative displacement coupling for perfectly bonded composites. A simple one-dimensional form of such a theory is presented, and, when compared with classical solutions for longitudinal wave propagation in laminated materials, predicts some aspects of the dynamical behavior extremely well.
An Improved Numerical Calculation Technique for Large Elastic-Plastic Transient Deformations of Thin Shells: Part 2—Evaluation and Applications
Authors: Morino L. , Leech J. W. , Witmer E. A.
Published: November 2010

Based upon the theoretical formulation presented in Part 1 of this paper, improvements in accuracy and computational efficiency are realized. Comparisons of predictions with experimental transient large deformations and strains show good agreement.
Time-Harmonic Waves Traveling Obliquely in a Periodically Laminated Medium
Authors: Sve C.
Published: November 2010

The dispersion relation is presented for time-harmonic waves propagating in an arbitrary direction in a periodically laminated medium. The analysis is based on two-dimensional equations of elasticity. Limiting phase velocities are presented for infinite wavelength for any angle of propagation in the form of a fourth-order determinant that illustrates the influence of an arbitrary angle. For the cases when the propagation is along or across the layers, the determinant reduces to two determinants of second order that yield the limiting phase velocities directly. Numerical results are presented to indicate the dependence of dispersion upon the angle of propagation. Also, a comparison with an approximate continuum theory is included; agreement is satisfactory for those angles where the dispersion is the strongest.
Theory of the Oscillating Viscometer for Slip Flow
Authors: Shah V. L.
Published: November 2010

The theory of the oscillating viscometer has been extended for a slip boundary condition. The cases considered here are: an infinite disk, an infinite cylinder, a sphere, and a pile of infinite disks. This study has prepared the way for the formulation of a new method for measuring the amount of slip experienced by bodies moving in gases outside the continuum regime. The theory of Kestin and Wang [11] has been extended to include slip at the boundary.
The Loading-Frequency Relationship in Multiple Eigenvalue Problems
Authors: Huseyin K. , Roorda J.
Published: November 2010

The free vibrations of a linear conservative system with multiple loading parameters are studied, attention being restricted to pure eigenvalue problems. It is shown that the smallest frequency and external loading parameters of such a system constitute a strictly convex (synclastic) surface which cannot have convexity toward the origin of the “parameter space.” It is further proved that in the case of systems with one degree of freedom only, the surface takes the form of a plane. The practical implications of these results regarding the estimation of the frequencies and/or the stability boundary of the system are discussed. Thus it is observed that, on the basis of the established theorems, lower bounds to the frequencies at any stage of external loading and/or upper bounds to the stability boundary are readily obtainable. A two-degree-of-freedom illustrative example is discussed.
A Direct Numerical Formulation of Galerkin’s Method for Nonlinear Lumped Systems
Authors: Johansen P. R. , Kohr R. H.
Published: November 2010

Use of Galerkin’s method for the approximate analysis of nonlinear lumped systems is considered. A numerical procedure for finding Galerkin solutions of initial value problems is developed and illustrated by two examples. The approach employs Galerkin’s method formulated as a two-point boundary-value problem. While solving the two-point problem, a recursion algorithm is obtained; the algorithm is applied to the Galerkin integral directly, and therefore analytical integration of the weighted equation residuals and solution of specific algebraic equations are not required. The numerical formulation renders Galerkin’s method systematic, and it extends the utility of the method.
A Minimum Principle for the Law of Dry Friction, With Application to Elastic Cylinders in Rolling Contact—Part 1: Fundamentals—Application to Steady Rolling
Authors: Kalker J. J.
Published: November 2010

In Part 1 of the present paper a minimum principle for the Coulomb-Amontons law of friction is derived. This minimum principle is uniform in the sense that no distinction is made between the slip and the no-slip conditions. The principle is applied to the two-dimensional contact problem in which the normal pressure is Hertzian. After discretization, the principle leads to a linear programming problem in the case of steady rolling as considered by Carter [1] and Bentall and Johnson [2]. Good agreement is found with these authors, and the force-creepage law for elastically dissimilar cylinders has been calculated completely. In the case of the nonsteady contact problem, which is treated in Part 2 and in which the traction evolves under the influence of a gross motion and loading program, the principle leads to a time sequence of linear programming problems. Such problems under several restrictions have been treated before by Kalker [3–5], without the aid of minimization techniques. In the present paper these restrictions are all removed. Numerical results are presented.
Pure Bending, Stretching, and Twisting of Anisotropic Cylindrical Shells
Authors: Reissner E. , Tsai W. T.
Published: November 2010

This paper considers the problem of determining stresses and deformations in elastic thin-walled, prismatical beams, subject to axial end forces and end bending and twisting moments, within the range of applicability of linear theory. The analysis, which generalizes recent work on the problem of torsion [1], is based on the differential equations of equilibrium and compatibility of thin shells in the form given by Gunther [2], together with constitutive equations given by the first-named author [3]. The technically most significant aspect of the work has to do with the analysis of the effect of anisotropy of the material, which is associated with previously not determined modes of coupling between stretching, bending, and twisting. Use of the general formulas of the theory is illustrated for a class of shells consisting of an “ordinary” material (unable to support stress moments with axes normal to the middle surface of the shell, and unable to undergo transverse shear deformation). Here explicit formulas are obtained for certain types of open as well as of closed-cross-section beams.
Rigid-Body Approximations to Turbulent Motion in a Liquid-Filled, Precessing, Spherical Cavity
Authors: Vanyo J. P. , Likins P. W.
Published: November 2010

Rigid-body approximations for turbulent motion in a liquid-filled, spinning and precessing, spherical cavity are presented. The first model assumes the turbulent liquid to spin and precess as a rigid solid sphere coupled to the cavity wall by a thin layer of massless viscous liquid. The second model replaces the layer of massless viscous liquid by a series of n concentric rigid spherical shells. The number and thickness of the shells can be varied so that the interior sphere varies from a negligible diameter to nearly the diameter of the cavity. Although these models do not provide solutions of the fluid equations of motion, they yield steady-state energy dissipation rates that compare favorably with existing experimental data associated with turbulent flow in such a cavity. The models also duplicate several other important features of rotating fluid flow theory. In particular, the motions of the concentric shells exhibit characteristics associated with a classic Ekman layer structure.
Response of Pressurized Cylindrical Shells Subjected to Moving Loads
Authors: Liao E. N. K. , Kessel P. G.
Published: November 2010

This paper presents a theoretical analysis of the dynamic response of a thin circular cylindrical shell, simply supported at both ends, of finite length, under initial biaxial stress and subjected to a radial point force that moves uniformly either along the axial direction or the circumferential direction. The analytical solutions are obtained in explicit form for the transient response of the first problem and the steady-state response of the latter problem. Critical speeds are given for both problems. Numerical results for both problems show the effects of the various relevant parameters. The effects of initial biaxial stress on the radial displacement and the critical velocities are presented. The behavior of cylinders beyond the lowest critical velocity is also pointed out.
Stability of General Hill’s Equation With Three Independent Parameters
Authors: Hamer K. , Smith M. R.
Published: November 2010

The stability of Hill’s equation with three independent parameters, two of which are small, is analyzed using a perturbation method. It is shown that, except for periodic terms of a special type, existing methods of determining stability boundaries fail. A new method, which works successfully to the first order of approximation, is described.
The Influence of a Free Surface on the Hydroelastic Stability of a Flat Panel
Authors: Weaver D. S. , Unny T. E.
Published: November 2010

This paper examines the influence of a parallel free surface on the hydroelastic stability of a flat panel. A quasi-two-dimensional approximation is made for the free surface displacement and the results compared with the more general but cumbersome three-dimensional solution. This comparison shows that the former approach is quite reasonable as well as being considerably simpler and more instructive. It is found that the free surface has no effect for depth ratios greater than about one half and is stabilizing for smaller depth ratios.
Thermal Stresses in an Orthotropic Elastic Semispace
Authors: Ako¨z A. Y. , Tauchert T. R.
Published: November 2010

The thermal stresses in an orthotropic semi-infinite elastic solid subject to plane strain are investigated. A general method of solution based upon displacement potentials is presented for the case of a steady-state temperature field. Results are presented for both stress-free and zero-displacement boundary conditions. The stresses are written in terms of Green’s functions, where the Green’s functions represent stresses induced by a line source of temperature on the bounding plane.
An Optical Method for Determining Opening-Mode and Edge Sliding-Mode Stress-Intensity Factors
Authors: Theocaris P. S. , Gdoutos E.
Published: November 2010

Interference of the two partially reflected light beams from the front and back surfaces of a cracked thin plexiglas plate yielded a fringe pattern, which depicted the thickness variations of the plate due to loading. The interferogram at the vicinity of the crack tip consisted of a dense fringe pattern, which represented the constrained zone. The dense pattern was separated from the remaining sparce pattern by a caustic. The caustic was created by the reflected light rays emerging from the plate, which were twice refracted through the thickness and reflected on the back face of the plate and which were retarded according to Maxwell and Neumann’s law. A general theory was developed where the dense fringe pattern was directly related to the complex intensity factor K* = KI − iKII, combining the opening mode together with the edge-sliding mode of fracture. In this way, any combination of the two modes may be studied by this reflected shadow method and the contribution of each mode to fracture can be evaluated. A series of experiments in cracked plexiglas plates under longitudinal tension were executed. The internal symmetric crack in each plate was inclined to the axis of application of the load by a different angle β, so that various combinations between KI and KII were obtained and checked with theory.
Variational Methods for Dispersion Relations and Elastic Properties of Composite Materials
Authors: Kohn W. , Krumhansl J. A. , Lee E. H.
Published: November 2010

The propagation of harmonic elastic waves through composite media with a periodic structure is analyzed. Methods utilizing the Floquet or Bloch theory common in the study of the quantum mechanics of crystal lattices are applied. Variational principles in the form of integrals over a single cell of the composite are developed, and applied in some simple illustrative cases. This approach covers waves moving in any direction relative to the lattice structure, and applies to structures of the Bravais lattice groups which include, for example, parallel rods in a square or hexagonal pattern, and an arbitrary parallelepiped cell. More than one type of inclusion can be considered, and the elastic properties and density of the inclusion and matrix can vary with position, as long as they are periodic from cell to cell. The Rayleigh-Ritz procedure can be applied to the solution of the variational equations, which provides a means of calculating dispersion relations and elastic properties of specific composite materials. Detailed calculations carried out on layered composites confirm the effectiveness of the method.
Eigenvalue Problems of Rectangular Plates With Mixed Edge Conditions
Authors: Keer L. M. , Stahl B.
Published: November 2010

The vibration and stability of plates with mixed edge conditions are considered in this paper. A simply supported rectangular plate which is clamped along the central portion on two opposite edges and a plate with partial clamping along one edge are analyzed. The problems are formulated as dual series equations and reduced to homogeneous Fredholm integral equations of the second kind. Comparisons with numerical results obtained by other investigators are made. Vibration and buckling mode shapes are illustrated. A vibration analysis of a plate simply supported adjacent to the corners is also made. This case is formulated as a coupled system of dual series equations which is reduced to a system of homogeneous integral equations. In all of the solutions given, the singularity is isolated and treated analytically.
Theory of the Dynamic Vibration Neutralizer With Motion-Limiting Stops
Authors: Masri S. F.
Published: November 2010

The exact solution for the steady-state motion of a dynamic vibration neutralizer with motion-limiting stops attached to a sinusoidally excited primary system is derived analytically, and its asymptotically stable regions are determined. Simulated motion on a digital computer and experimental studies with an analog computer corroborate the predictions of the theory. Results of the analysis are applied to modified vibration neutralizers, Lanchester dampers, and impact dampers. It is shown that the incorporation of properly designed motion-limiting stops into the auxiliary mass system will enhance the performance of the foregoing dampers.
On The Scattering of Spherical Elastic Waves by a Spherical Cavity
Authors: Moon F. C.
Published: November 2010

The distribution of scattered energy due to the interaction of spherical elastic dilatational waves with a spherical cavity is found to differ from that due to plane waves for long wavelengths even when the radius of curvature is much larger than the cavity radius.
Asymptotic Behavior of Eigenvalues for Finite, Inhomogeneous Elastic Rods
Authors: Nayfeh Adnan H.
Published: November 2010

Asymptotic expressions for the eigenvalues and the corresponding eigenfunctions for the free vibrations of an inhomogeneous elastic rod with a finite length are derived. The derivation is based on the assumption that the elastic parameters and their derivatives vary continuously along the rod. A method which consists of a perturbation about the solutions of the homogeneous cases is used.
A Generalized Isotropic Yield Criterion
Authors: Hosford W. F.
Published: November 2010

A generalized isotropic yield criterion of the form, (σ1−σ2)n+(σ2−σ3)n+(σ1−σ3)n21/n=Y where σ1 ≥ σ2 ≥ σ3 and 1 ≤ n ≤ ∞, is proposed. The corresponding flow rules, Lode variables, and effective strain functions are presented. Experimental and theoretical data on yielding under combined stresses can be described by a single parameter, n.
Transient Axisymmetric Motions of a Conical Bar
Authors: Mortimer R. W. , Schaller R. J. , Rose J. L.
Published: November 2010

Three bar-of-revolution theories are developed. The most inclusive theory is equivalent to the Mindlin-McNiven theory for circular bars in that it includes radial, axial shear, and longitudinal modes. By removing the axial shear mode in the foregoing, a theory equivalent to the Mindlin-Herrmann theory for circular bars is obtained. Finally, by eliminating all the radial effects in this latter theory, a simple theory incorporating only longitudinal effects is obtained. Each of these three theories is then specialized for a conical geometry and solved by the method of characteristics for the case of a longitudinal impact. The solutions for each of these theories are then compared to published surface meridional strain and internal strain data. In addition, the importance of impact pulse duration in establishing the validity of the approximate bar theories for impact problems is analytically indicated.
Dynamic Plastic Deformation of Circular Cylindrical Shells
Authors: Youngdahl C. K.
Published: November 2010

In order to determine the localized plastic deformation of a pipe or tube produced by a dynamic loading that exceeds the yield load only briefly, it is important to know the effect of the spatial and temporal shapes of the pressure pulse on the final deformation. This is particularly true in computer or laboratory simulations of reactor accidents, where it is impossible or impractical to reproduce the actual loading conditions. It is shown that the dynamic plastic deformation produced by an arbitrary load shape (spatial) and an arbitrary pulse shape (temporal) can be correlated by three parameters—the impulse, a load-shape parameter, and a pulse-shape parameter. These parameters are defined in terms of integrals of the pressure and are consequently insensitive to inaccuracies in experimental measurements.
A Large Deformation Elastic-Viscoplastic Analysis of a Thick-Walled Spherical Shell
Authors: Bodner S. R. , Partom Y.
Published: November 2010

A large deformation elastic-viscoplastic theory is formulated which considers both elastic and inelastic deformations to be present at all stages of loading and unloading. The theory does not require the assumption of a yield criterion or the prior determination of whether the material is loading or unloading. The theory is based on relating the essential parameters to state variables; the particular constitutive relations are motivated by the equations of “dislocation dynamics.” In the present formulation, thermal effects and properties representing the worked state of the material such as strain hardening are not considered. A numerical scheme for calculating deformations is developed and applied to a thick-walled spherical shell under internal pressure. Various numerical examples are presented.
The Stress Field in a Cylindrically Anisotropic Body Under Two-Dimensional Surface Tractions
Authors: Pagano N. J.
Published: November 2010

In this work, a general solution for the elastic stress field in a cylindrically anisotropic body, the hollow circular cylinder, under surface tractions which do not vary along the generator and which can be expressed in the form of a Fourier series, is presented. The form of the solution is sufficiently general to permit direct extension to an important class of composite structures, namely, laminated circular cylinders. Some of the peculiar effects of anisotropy are illustrated by the solution of a specific boundary-value problem—a circular hole in a large plate under tension.
Governing Equations for Vibrating Constrained-Layer Damping Sandwich Plates and Beams
Authors: Yan M.-J. , Dowell E. H.
Published: November 2010

For constrained-layer damping a simple differential equation for nonsymmetric sandwich plates or beams made of isotropic and homogeneous layers is deduced. The natural boundary conditions associated with this equation are also derived. Typical numerical results are presented including a preliminary comparison with experiment.
Dynamic Stability of Monosymmetrical Thin-Walled Structures
Authors: Ghobarah A. A.
Published: November 2010

A study is made on the dynamic stability of thin-walled beams of monosymmetrical cross section. Under the action of axial periodic loads, the parametric excitation of the coupled flexural-torsional type of vibrations is investigated. The nonlinear differential equations and the appropriate boundary conditions used in the analysis of the problem were obtained using the energy formulation. The effect of large angles of rotation and the effect of longitudinal deformations were taken into account. The parametric stability of a thin-walled beam of monosymmetrical split ring section is studied. The study included the establishment of the regions of parametric instability. The steady-state response and the transient growth of the amplitude of oscillations are investigated when the system is parametrically excited. Attention is focused on the response when the coupled flexural-torsional type of vibrations of predominant torsional characteristics is excited. The effect of viscous damping on the steady-state and the transient responses is also included in the analysis.
The Application of Newton’s Method to the Problem of Elastic Stability
Authors: Riks E.
Published: November 2010

The numerical solution of problems of elastic stability through the use of the iteration method of Newton is examined. It is found that if the equations of equilibrium are completed by a simple auxiliary equation, problems governed by a snapping condition can, in principle, always be calculated as long as the problem at hand is properly formulated. The effectiveness of the proposed procedure is demonstrated by means of an elementary example.
On a Laminated Orthotropic Shell Theory Including Transverse Shear Deformation
Authors: Dong S. B. , Tso F. K. W.
Published: November 2010

A constitutive relation for laminated orthotropic shells which includes transverse shear deformation is presented. This relation involves composite correction factors k112, k222 which are determined from an analysis of plane waves in a plate with the same layered construction. The range of applicability of the present theory and the quantitative effect of transverse shear deformation are evinced in a problem concerned with the natural oscillations of a three-layered freely supported cylinder.
Settlement of Powders in Vertical Channels Caused by Gas Escape
Authors: Johanson J. R. , Jenike A. W.
Published: November 2010

The paper discusses the settlement of powders in a vertical channel due to the escape of gas from the solid. The governing equations are discussed along with the methods of solution. Experimental results are presented confirming the theoretical work and the application of the results in predicting bin wall loadings is discussed.
Numerical Solutions of the Navier-Stokes Equations in Inlet Regions
Authors: McDonald J. W. , Denny V. E. , Mills A. F.
Published: November 2010

Numerical solutions of the Navier-Stokes equations are obtained for steady two-dimensional flow in the inlet region of both a tube and a channel. The entering flow is considered to be either uniform (u = constant, v = 0) or irrotational (u = constant, ω = 0). Values of Reynolds number Re = u0a/ν range from 0.75 to 2 × 106. An improved method for solving the stream function-vorticity equations of hydrodynamics has been developed. The method is stable at all Reynolds numbers and appears to be computationally superior to previous methods.
Determination of the Natural Frequencies of a Nearly Uniform System
Authors: Bergkvist H.
Published: November 2010

The equation giving the natural frequencies ωi of vibrations in a nearly uniform system is obtained from the knowledge of the natural frequencies of a uniform system and elementary determinant expansion. By inspection of the equation a sequence of frequency intervals is immediately found, each one containing one natural frequency. This fact makes the method superior to the classical Holzer method for this important type of vibratory system. A closer determination of the ωi:s, that sometimes could be needed, is easily performed by use of a simple desk-top calculator or even a slide rule, as is illustrated by some numerical examples in the Appendix.
The Dynamic Stress-Strain Behavior in Torsion of 1100-0 Aluminum Subjected to a Sharp Increase in Strain Rate
Authors: Frantz R. A. , Duffy J.
Published: November 2010

A modification of the torsional split Hopkinson bar is described which superimposes a high rate of shear strain on a slower “static” rate. The static rate of 5 × 10−5 sec−1 is increased to 850 sec−1 at a predetermined value of plastic strain by the detonation of small explosive charges; the rise time of the strain-rate increment is about 10 microsec. During deformation at the dynamic rate, direct measurement is made of the excess stress above the maximum static stress attained. Results for 1100-O aluminum show that the initial response to the strain rate increment is elastic, followed by yielding behavior reminiscent in appearance to an upper yield point. The incremental stress-strain curve always lies beneath the stress-strain curve obtained entirely at the higher strain rate but approaches it asymptotically with increasing strain. It is concluded that the material behavior is a function of strain, strain rate, and strain rate history.
Moving Load on a Fluid-Solid Interface: Supersonic Regime
Authors: Kennedy T. C. , Herrmann G.
Published: November 2010

The steady-state response of a semi-infinite solid with an overlying semi-infinite fluid subjected at the plane interface to a moving point load is determined for supersonic load velocities. The exact, closed-form solution valid for the entire space is presented. Some numerical results for the displacements at the interface are calculated and compared to the results obtained when no fluid is present.
Analysis of Transverse Cracks in an Orthotropic Strip With Edge Stiffeners
Authors: Lakshmikantham C.
Published: November 2010

The stress analysis of a central transverse crack in a stiffened orthotropic panel under tension is treated in this paper. The existing analytical techniques for the isotropic problem of a crack in an infinite strip, based on the well-known Schwarz alternating method for multiply connected domains, are applied to the present orthotropic problem. The ratio of stress-intensity factors for the finite plate to that of the infinite plate is obtained as a function of the crack length. The results are compared with the isotropic solution.
Solution of Levi Civita’s Problem by Infinite Matrix Inversion
Authors: Bentwich M.
Published: November 2010

The author proposes a new method by which one can solve for the two-dimensional irrotational fully cavitating flow past a cylinder of arbitrary cross section. Unlike the available solutions, it is in the form of two expansions each valid in part of the complex potential plane w = Φ + iΨ. The a priori unknown coefficients in the two expansions are linked by infinitely many linear algebraic equations. By inverting the associated matrix and utilizing the boundary condition, that represent the geometry of the wet surface, the coefficients in the expansions are evaluated and the solution is completed. Cases in which the wet surface is circular, the pressure along the free streamlines is constant, and the entire flow pattern is symmetric with respect to flow direction at infinity are considered in detail. Also, the well-known solution for the flow past a flat plate is compared to that obtained by the method of matrix inversion. Judging from these results, the convergence of the series appears to be very rapid. The author finally discusses the applicability of the method to cases in which the obstacle has a sharp leading edge, the pressure in the cavity is not uniform, or the flow pattern is not symmetric.
An Asymptotic Solution for the Laminar Flow of a Thin Film on a Rotating Disk
Authors: Rauscher J. W. , Kelly R. E. , Cole J. D.
Published: November 2010

An analysis on the basis of the Navier-Stokes equations is made of the flow of a liquid in a thin film on a rotating disk. Fluid flows outward in the radial direction due to the centrifugal force. An asymptotic solution valid for small values of the Rossby number is presented. Higher-order terms correcting for the effects of convection, Coriolis acceleration, radial diffusion, surface curvature, and surface tension are found and discussed on a physical basis.
The Evolution of a Self-Sustained Oscillation in a Nonlinear Continuous System
Authors: Mortell M. P. , Seymour B. R.
Published: November 2010

We consider a gas-filled tube into which there is an input of energy due to a pressure sensitive heat source. The system is linearly unstable to perturbations about the initial equilibrium state. Within nonlinear theory a disturbance grows until a shock forms. The shock can then act as a dissipative mechanism so that ultimately a time periodic oscillation may result. The small amplitude disturbance in the pipe is represented as the superposition of two simple waves traveling in opposite directions, and without interaction. Thereby, the problem is reduced to solving a nonlinear difference equation subject to given initial conditions. Then not only is the final periodic state described but also its evolution from the prescribed initial perturbation. The concept of critical points of a nonlinear difference equation is introduced which allows the direct computation of the periodic state. The effects of dissipation and of a retarded heater response are also treated.
Applications of the Theory of Impulsive Parametric Excitation and New Treatments of General Parametric Excitation Problems
Authors: Hsu C. S. , Cheng W.-H.
Published: November 2010

In this paper the stability theory of impulsive parametric excitation developed in [1] is first applied to three mechanical systems. Explicit and exact stability conditions are easily found and some typical stability charts are presented. Also presented in the paper is the use of this theory and a parallel theory involving step functions as approximate methods for treating periodic parametric excitations of more general nature. Exploratory studies along this line have led us to believe that these approximate methods have promise to be very powerful and practical tools for dealing with the stability of general high-order periodic systems.
Out-of-Plane Vibration and Stability of Curved Tubes Conveying Fluid
Authors: Chen S.-S.
Published: November 2010

A general theory is presented to account for the out-of-plane motion of uniformly curved tubes containing flowing fluid. The systems are grouped as conservative and nonconservative according to the support conditions. A general solution for the natural frequency is obtained and numerical results are presented. The effects of the flow velocity and Coriolis force on the natural frequency are discussed. It is shown that when the flow velocity exceeds a certain value, the tube becomes subject to the buckling-type instability for conservative cases and the fluttering-type instability for nonconservative cases. In the subcritical range of flow velocity, the conservative system performs free oscillations, while the nonconservative system performs damped oscillations.
A Perturbation Method for Low-Frequency Fluid-Structure Interaction Problems
Authors: Lou Y. K.
Published: November 2010

Perturbation methods have been used for electromagnetic scattering and diffraction problems in recent years. A similar method suitable for low-frequency fluid-structure interaction problems is presented. The essence of the method lies in the fact that approximate solutions for fluid-structure interaction problems can be obtained from a set of Poisson’s equations, rather than from the reduced wave equation. The method is particularly useful for those problems where the Poisson’s equation may be solved by the method of separation of variables while the reduced wave equation cannot. As an illustrative example, the vibrations of a submerged spherical shell is studied using the perturbation method and the accuracy of the method is demonstrated.
The Origin of Instability in Airlift Pumps
Authors: Hjalmars S.
Published: November 2010

A preliminary analysis is made of the well-known instability, occurring in airlift pumps, when at sufficiently high rise the ability of the pump as a self-controlling system breaks down, and a rapidly increasing oscillation of the flow sets in. It is shown that the instability is due to the fact that a small time-dependent perturbation of the stationary flow satisfies a difference-differential equation with time lag, of a kind well known from control theory. The theoretically computed values of the critical rise and the time period of oscillation are in satisfactory agreement with observation.
Three-Dimensional Study of the Nonrectilinear Trajectory of Air Bubbles Rising in Water
Authors: Mercier J. , Lyrio A. , Forslund R.
Published: November 2010

A three-dimensional photographic study of the nonrectilinear ascent of an air bubble in water is presented. A geometric model is developed which describes the trajectory in terms of a transformed coordinate system. The parameters of the model which describe the departure from linearity are found to be dependent on the equivalent spherical radius of the bubble.
Unsteady Nonuniform Flow in the Entrance of a Pipe
Authors: Noblesse F. , Farell C.
Published: November 2010

The laminar incompressible flow started from rest in the entrance of a pipe is analyzed using the integral form of the equations of continuity, momentum, and energy, together with a similarity hypothesis for the velocity profiles across the boundary layer. A first-order partial-differential equation for the growth of the boundary-layer thickness is obtained and solved by the method of characteristics. The flow is shown to depend critically on a dimensionless parameter which can be interpreted as the ratio of a characteristic time of the variation of the discharge to a time characteristic of the diffusion of viscous effects.
Dynamic Buckling of an Axially Compressed Cylindrical Shell With Discrete Rings and Stringers
Authors: Fisher C. A. , Bert C. W.
Published: November 2010

As an exploratory effort toward improving the crashworthiness of light aircraft cabins, a theoretical analysis was made to predict the dynamic buckling load and buckling time of a stiffened, thin-walled circular cylindrical shell. To provide for the large stiffener spacing in light aircraft, the stiffeners were considered as discrete elements by means of a Dirac delta procedure. The nonlinear governing equations were derived using Hamilton’s principle and the final equations were obtained by means of Galerkin’s method. Solution was carried out by using a Gauss-Jordan technique on the algebraic equations and a Runge-Kutta technique on the nonlinear differential equations. Numerical results are presented for an idealized model of a typical light aircraft cabin.
Stresses in a Transversely Isotropic Slab Having a Spherical Cavity
Authors: Atsumi A. , Itou S.
Published: November 2010

This paper deals with the analysis of the stress distribution arising in a transversely isotropic infinite slab with a symmetrically located spherical cavity under all-around tension. Difficulties in satisfying both boundary conditions on the surfaces of the slab and the surface of the cavity are successfully overcome by using the methods of Hankel transform and Schmidt-orthogonormalization. For some practical materials the influence of transverse isotropy upon stress distribution is presented in the form of curves.
The Effect of Plasticity and Crack Blunting on the Stress Distribution in Orthotropic Composite Materials
Authors: Tirosh J.
Published: November 2010

A detailed study of the plasticity and crack-tip blunting effects on toughening materials with rectilinear anisotropy is presented. The most important results are the prediction of the extent of plastic zone and the nature of stress distribution produced by the blunting effect in the tensile mode. The analysis was confirmed experimentally and numerically (finite-element method) on a unidirectional fiber-reinforced composite.
Waves in Prismatic Guides of Arbitrary Cross Section
Authors: Aalami B.
Published: November 2010

A formulation based on extended Rayleigh-Ritz is presented for waves and vibrations in orthotropic prismatic bars of arbitrary cross section. The scope and effectiveness of the method is demonstrated through case study of square guides. Basic features of the analysis such as accuracy are discussed.