bluuebunny/crossref_metadata_2025 huggingface dataset:
Nonlinear Creep Buckling of Some Simple Structures
Authors: Huang N. C.
Published: October 2011

In this paper, the creep buckling behavior of shallow Mises trusses and two-hinged sinusoidal low arches with sandwich cross section is studied. The material properties are assumed to be nonlinear viscoelastic and obeying the power creep law. The purpose of this study is to find the critical times, critical deflections, and postbuckling deflections of these structures. For Mises trusses, snap-through may be induced by direct compression or lateral buckling of the members. Analytical solutions are obtained. In the arch problem, both symmetrical and antisymmetrical bucklings are considered. Collocation method is used in the analysis, and numerical solutions are obtained.
Generalized Hypergeometric Function Solutions on the Transverse Vibration of a Class of Nonuniform Beams
Authors: Wang Han-Chung
Published: October 2011

With simple beam theory, solutions of normal functions for transverse vibration of a tapered beam are obtained in terms of generalized hypergeometric functions by the method of Frobenius. For the beams considered, the cross-sectional area and the area moment of inertia vary along the beam according to any two arbitrary powers of the longitudinal coordinate. The frequency equation is formulated, and the numerical results for many different tapered cantilever beams are presented.
Numerical Analysis of Combined Bending and Torsion of a Work-Hardening Plastic Square Bar
Authors: Miller P. M. , Malvern L. E.
Published: October 2011

An iterative scheme using a backward difference in the timelike variable is developed, which makes possible a numerical-analysis solution for the incremental plasticity theory formulation with hardly any extra computational effort than that required for total-strain theory; this permits easy comparison between the predictions of the two theories for a variety of bending-twist histories. Isotropic hardening is assumed, using comparable generalizations of the Ramberg-Osgood stress-strain law to combined-stress incremental and total-strain theories, for continuous loading with no unloading, and for a material assumed to have no initial elastic range, so that the entire cross section is plastic. Analysis, of a uniform prismatic square bar, continuously loaded from a stress-free state, by a bending couple in a plane of symmetry, and a twisting couple, shows that the predictions of the two theories agree when the ratio of curvature to angle of twist per unit length is held constant during the deformation, even though the stress path in stress space is nonradial. When the ratio of curvature to unit angle of twist varies during the deformation, the two theories predict different results.
Frequency-Dependent Almost Sure Stability Conditions for a Parametrically Excited Random Vibrational System
Authors: Gray A. H.
Published: October 2011

In this paper, a Lyapunov type of approach is used to obtain sufficient conditions for the almost sure stability of a particular parametrically excited random vibrational system. The result found utilizes the frequency spectrum of the random term.
Theory of a Thermal Fluxmeter in a Shear Flow
Authors: Tanner R. I.
Published: October 2011

It is known from some recent experiments that a thin, electrically conducting plate on an electrically insulating base gives a heat transfer rate to a laminar shear flow about twice that predicted from some simple boundary-layer theories. It is shown in this paper that close agreement with experiment results if the theory allows for (a) conduction through the base material, giving an effective increase in plate area; and (b) variable heat flux and temperature in the heated plate.
Separation and Stall of an Impulsively Started Elliptic Cylinder
Authors: Wang Chang-Yi
Published: October 2011

Separation and stall of an impulsively started elliptic cylinder at an angle of attack are investigated through the method of inner and outer expansions. The assumptions are large Reynolds numbers and small times. The interactions between the boundary layer and the outer inviscid flow are taken into consideration. Uniformly valid solutions are obtained for general two-dimensional cylinders. The movements of the separation points on an elliptic cylinder are calculated. Stall is found to be strongly dependent on the thickness ratio and the angle of attack of the cylinder but to be weakly dependent on the Reynolds number.
Induced One-Dimensional Waves in Elastic Nonconductors
Authors: Walsh E. K.
Published: October 2011

The influence of a propagating discontinuity in the extrinsic body force and heat supply on the amplitude of induced shock and acceleration waves is studied. These waves are considered in the sense of moving surfaces of discontinuity in certain field quantities associated with a motion of the body. In the case of acceleration waves, an explicit relation is derived for the amplitude of the wave in terms of the extrinsic forces and the material parameters. A similar relation is exhibited for shock waves of small amplitude. Only the one-dimensional case is considered here and the material is assumed to be a nonconductor of heat.
The Shear Coefficient in Timoshenko’s Beam Theory
Authors: Cowper G. R.
Published: October 2011

The equations of Timoshenko’s beam theory are derived by integration of the equations of three-dimensional elasticity theory. A new formula for the shear coefficient comes out of the derivation. Numerical values of the shear coefficient are presented and compared with values obtained by other writers.
On the Contact of Two Axisymmetric Plates
Authors: Essenburg F. , Gulati S. T.
Published: October 2011

The general problem of the contact of two axisymmetric plates is considered. By way of specific examples, the ability of the Reissner theory to overcome the difficulties inherent in the application of the classical theory to such problems is demonstrated.
Stresses in an Infinite Strip Containing a Semi-Infinite Crack
Authors: Knauss W. G.
Published: October 2011

Stresses in an infinitely long strip of finite width containing a straight semi-infinite crack have been calculated for the case that the clamped boundaries are displaced normal to the crack. The solution is obtained by the Wiener-Hopf technique. The stresses are given in the form of asymptotic expansions in the immediate crack tip vicinity and for a larger region of interest in graphical form. The effect of prescribing displacements on the boundary close to a crack instead of stresses far away is discussed briefly. Together with an asymptotic solution for a small crack, the result is used to estimate the stress field around a crack of arbitrary length in an infinite strip. The usefulness of this crack geometry in laboratory investigations of fracture mechanics is pointed out.
Recent Developments in Calculation Methods for Turbulent Boundary Layers With Pressure Gradients and Heat Transfer
Authors: Rotta J. C.
Published: October 2011

A review is given of the recent development in turbulent boundary layers. At first, for the case of incompressible flow, the variation of the shape of velocity profile with the pressure gradient is discussed; also the temperature distribution and heat transfer in incompressible boundary layers are treated. Finally, problems of the turbulent boundary layer in compressible flow are considered.
Point Load on a Shallow Elliptic Paraboloid
Authors: Forsberg Kevin , Flu¨gge Wilhelm
Published: October 2011

The present work is a study of a thin shallow shell having a specific type of deviation from axial symmetry, i.e., the portion of an elliptic paraboloid near its vertex. The singular solutions to the homogeneous shallow-shell equations are expressed as power series in terms of a parameter γ, which is a measure of the deviation of the shell geometry from axial symmetry. These singular solutions can be directly related to concentrated loading at the vertex of the shell. The solution converges in the range γ = 0 (sphere) to γ = 1/2 (cylinder). Detailed graphical results are presented for the stress resultants and radial deflection of a shell subjected to a point load at its vertex.
On the Stability of the Impact Damper
Authors: Masri S. F. , Caughey T. K.
Published: October 2011

The exact solution for the symmetric two-impacts-per-cycle motion of the impact damper is derived analytically, and its asymptotically stable regions are determined. The stability analysis defines the zones where the modulus of all the eigenvalues of a certain matrix relating conditions after each of two consecutive impacts is less than unity.
Diffractions of Horizontal Shear Waves by a Parabolic Cylinder and Dynamic Stress Concentrations
Authors: Thau S. A. , Pao Yih-Hsing
Published: October 2011

Diffractions of horizontally polarized shear waves by a parabolic cylinder are studied by using the expansion of solutions to the wave equation in terms of Weber’s functions. The parabolic cylinder is either empty or filled with rigid material. Also, the problems of a semi-infinite line crack and a semi-infinite rigid ribbon as two limiting cases are treated. Displacements and stresses are calculated near the base of the parabola. In the case of a line crack or a rigid ribbon, the singular behavior of stresses is shown to be of the order of (kr)−1/2, where k is the wave number and r the distance from the tip.
Three-Dimensional Stress Concentration Around a Cylindrical Hole in a Semi-Infinite Elastic Body
Authors: Youngdahl C. K. , Sternberg E.
Published: October 2011

This paper contains a three-dimensional solution, exact within classical elastostatics, for the stresses and deformations arising in a half-space with a semi-infinite transverse cylindrical hole, if the body—at infinite distances from its cylindrical boundary—is subjected to an arbitrary uniform plane field of stress that is parallel to the bounding plane. The solution presented is in integral form and is deduced with the aid of the Papkovich stress functions by means of an especially adapted, unconventional, integral-transform technique. Numerical results for the nonvanishing stresses along the boundary of the hole and for the normal displacement at the plane boundary, corresponding to several values of Poisson’s ratio, are also included. These results exhibit in detail the three-dimensional stress boundary layer that emerges near the edges of the hole in the analogous problem for a plate of finite thickness, as the ratio of the plate thickness to the diameter of the hole grows beyond bounds. The results obtained thus illustrate the limitations inherent in the two-dimensional plane-strain treatment of the spatial plane problem; in addition, they are relevant to failure considerations and of interest in connection with experimental stress analysis.
Nonlinear Elastic Buckling and Parametric Excitation of a Cylinder Under Axial Loads
Authors: Yao John C.
Published: October 2011

Two nonlinear problems relating to buckling and parametric excitation of thin elastic cylindrical shells are considered. In the first, time-dependent end displacements are specified and, in the second, time-dependent end loads are specified. The effects of large deflections, initial imperfections, inertia forces, viscous damping, and the elasticity of a testing machine are taken into account. New results from this nonlinear formulation show, for the first problem, favorable agreement with the experimental results of L. R. Ispravnikov, and clear deviations from the linear-theory predictions for the second problem.
Wave Propagation in an Elastic Nonhomogeneous Bar of Finite Length
Authors: Lindholm U. S. , Doshi K. D.
Published: October 2011

The case of an elastic disturbance propagating in a nonhomogeneous bar of finite length is solved by using the principle of virtual work. The nonhomogeneity is prescribed as a continuously varying modulus of elasticity with position in the bar. The density is assumed constant. Numerical results are presented for a finite-length pressure pulse in a free-free bar giving a comparison between the homogeneous and nonhomogeneous solutions.
The Vibration of Unsymmetrical Rotating Shafts
Authors: Ariaratnam S. T.
Published: October 2011

This paper deals with the vibration of heavy unsymmetrical shafts possessing unequal flexural rigidities in the principal directions and running in symmetrical bearings. The existence of several bands of whirling speeds is shown and the effects of stationary and rotary viscous damping on the free and forced vibrations of the shaft are discussed.
Theory for Moderately Large Deflections of Thin Sandwich Shells
Authors: Wempner G. A.
Published: October 2011

This paper presents equations which govern moderately large deflections of thin sandwich shells. These equations account for the bending resistance of the facings and orthotropy; they are compared with previous formulations.
Plastic Deformation of Impulsively Loaded Straight Clamped Beams
Authors: Humphreys John S.
Published: October 2011

A series of tests was conducted on flat steel beams of various sizes and material properties, using sheet explosive to provide sufficiently high uniform impulsive loading to produce significant plastic deformation. The beams were attached to a ballistic pendulum for measurement of applied impulse, and were photographed with a Fastax camera during deformation. The resulting final deformations are compared with the rigid-plastic theory of Symonds and Mentel, which is seen to give upper bounds that are in general higher by about 20–30 percent than the deformations observed. A fairly good first approximation to maximum deflection for engineering purposes is in fact obtained simply by using rigid-plastic beam theory (including axial constraints).
Pressures and Flow Rates in Extruders With Axially Variable Geometry
Authors: Tangorra G.
Published: October 2011

The problem of predicting pressures and flow rates for extruders with geometrical parameters arbitrarily variable along the axis is considered for isothermal, Newtonian conditions. A graphical method is applied to an actual case of a truncated, cone-shaped extruder. Experimental results are reported. The same general procedure, but with further simplified formulas, is applied subsequently to cases of extruders having diameter, pitch, and thread depth linearly variable along the axis.
On a Simplified Method for Solving Impulsively Loaded Structures of Rate-Sensitive Materials
Authors: Perrone Nicholas
Published: October 2011

In an attempt to assess more completely rate-sensitive material effects, two fundamental structural elements are analyzed: A wire with an impulsively loaded end mass, and an impulsively loaded ring. The ring and wire are made of perfectly plastic, rate-sensitive materials. In each case, exact and approximate solutions are obtained for an exponential rate-sensitivity law. The results suggest that very good approximations to the exact solutions may be found by utilizing a rate-insensitive material with constant yield stress equal to the initial dynamic yield stress.
Vibrations of Dynamical Systems With Quadratic Nonlinearities
Authors: Sethna P. R.
Published: October 2011

General two-degree-of-freedom dynamical systems with weak quadratic nonlinearities are studied. With the aid of an asymptotic method of analysis a classification of these systems is made and the more interesting subclasses are studied in detail. The study includes an examination of the stability of the solutions. Depending on the values of the system parameters, several different physical phenomena are shown to occur. Among these is the phenomenon of amplitude-modulated motions with modulation periods that are much larger than the periods of the excitation forces.
Application of Irreversible Thermodynamics in Finite Viscoelastic Deformations
Authors: Lianis George
Published: October 2011

In this paper, Onsager’s principle of irreversible thermodynamics is applied to viscoelastic materials subjected to finite deformation. The constitutive equation of Ref. [10] for small dynamic strains superposed on a finite static deformation is used. The state of the resulting deformation can be considered as a small deviation from an equilibrium reference state. The latter is the state of equilibrium of a material subjected to a finite deformation in which the material is maintained for a long time.
Dynamic Bond Stress in a Composite Structure Subjected to a Sudden Pressure Rise
Authors: Payton R. G.
Published: October 2011

The model studied in this paper is that of a composite structure represented by two elastic rods, of uniform cross section, which are bonded together along their generators. The rods are semi-infinite in length and are suddenly loaded by a pressure step applied over the end of the structure. The resulting elastic waves which are generated in each of the rods cause a dynamic bond shearing stress which is proportional to the difference between the two rod displacements. An integral solution is obtained for the bond stress and is evaluated numerically. The bond stress is composed of a static and a dynamic part and it is found that the peak bond stress, which occurs at the loaded end, is dominated by the static stress. Results are shown graphically for a particular rod configuration as well as the parametric dependence of the peak bond stress on the rod composite-stiffness ratio. Several limiting cases for the stiffness parameter and elastic wave-speed ratio parameter are investigated analytically and some asymptotic formulas are given which describe the small and large time behavior of the dynamic-bond stress.
Bending of Rectangular Plates With Finite Deflections
Authors: Bauer Frances , Bauer Louis , Becker William , Reiss Edward L.
Published: October 2011

A previously developed iterative procedure is applied to obtain numerical solutions of the von Ka´rma´n equations for rectangular plates subjected to a uniform normal pressure. On the simply supported boundary, it is assumed that the normal membrane stress and the tangential membrane displacement vanish. Solutions are obtained for a wide range of values of the loading parameter and the aspect ratio. Boundary layers develop both as the loading parameter and the aspect ratio increase. The stresses and deflections are examined and compared with an “asymptotic” solution which can be valid only in the interiors of long plates. A comparison is also made with previously obtained approximate solutions.
On the Generation of Residual Stresses in Thermoviscoelastic Bodies
Authors: Lee E. H. , Rogers T. G.
Published: October 2011

The development of residual stress distributions in thermoviscoelastic materials due to surface cooling is considered. They arise because the nonuniform thermal contraction generates irreversible viscoelastic deformation, which tends to become permanent as the temperature falls due to the rapid growth of relaxation times with temperature reduction. Examples of a cooled solid sphere of polymethylmethacrylate are evaluated, and the results are compared with previous analyses based on an elastic-inviscid fluid model. For application in design to generate beneficial residual stress distributions, the need to assess the entire stress history is pointed out, and relevant features of the phenomenon are discussed.
Theory of Vibratory Bending for Elastic and Viscoelastic Layered Finite-Length Beams
Authors: DiTaranto R. A.
Published: October 2011

The vibrational characteristics, natural frequencies, and associated composite loss factor of a finite-length laminated beam having alternate elastic and viscoelastic layers, are investigated. An auxiliary equation which accounts for the effect of the viscoelastic layers is derived. The use of this equation in conjunction with the ordinary bending equations encountered for homogeneous beams, allows one to solve static and dynamic bending problems for laminated beams in the same manner as for homogeneous beams. The resulting equations are complex expressions since the shear modulus of the viscoelastic material is a complex quantity. The use of the auxiliary equation in conjunction with the loading equation for a freely vibrating beam yields a sixth-order, complex, homogeneous differential equation. The solution of this equation, subject to satisfying the boundary conditions, yields the desired natural frequencies and associated composite loss-factors.
Parametric Excitation of a Nonlinear System
Authors: Tso W. K. , Caughey T. K.
Published: October 2011

A study has been made on the parametric excitation of a nonlinear system with hardening springs. In the parametric excitation of linear systems, the only subharmonic predicted is a subharmonic of order 1/2. However, in the parametric excitation of non-linear systems, it is shown that higher order subharmonics can exist, depending both on the amplitude and frequency of the parametric excitation.
The Steady-State Response of the Double Bilinear Hysteretic Model
Authors: Iwan W. D.
Published: October 2011

The steady-state response of a one-degree-of-freedom double bilinear hysteretic model is investigated and it is shown that this model gives rise to the jump phenomenon which is associated with certain nonlinear systems. The stability of the steady-state solution is discussed and it is shown that the model predicts an unbounded resonance for finite excitation.
On the Flexural Motions of Plates at the Cut-Off Frequency
Authors: Chao C. C. , Pao Yih-Hsing
Published: October 2011

Mindlin’s equations of plates in flexural motion degenerate at the cut-off frequency of the lowest thickness shear mode. In this paper it is shown that, by introducing two displacement potentials, the original equations of motion can be transformed into one wave equation and one biharmonic equation. Based on these two equations, the reflection of a plane flexural wave at the free edge of a plate at this cut-off frequency is reexamined.
Viscoelastic Boundary Damping of Beams and Plates
Authors: Mentel T. J.
Published: October 2011

A series of experiments on boundary, damped beams are described which identify separately the effectiveness of axial and transverse motions of the embedded beam ends in producing energy dissipation. A comparatively elementary level of theoretical analysis is shown to be adequate in explaining most of the experimental results. A subsequent series of experiments is then described which tests the damping effectiveness of a small inset of viscoelastic adhesive at the supports of beams and plates, the inset design being motivated by the results of the first experiments. The principal characteristics of the inset design are determined experimentally and a supporting theory (for beams and circular plates) is outlined.
Bilinear Theories in Plasticity and an Application to Two-Dimensional Wave Propagation
Authors: Aggarwal H. R. , Soldate A. M. , Hook J. F. , Miklowitz Julius
Published: October 2011

The Koehler and Seitz bilinear theory is generalized and related to a similar theory given by Swainger. It is shown that, in contradistinction to the corresponding Hencky theory, the generalized theory depends partially on the strain path, and further leads to linearization of the governing equations. An alternative form analogous to the generalized Hooke’s law is given. Displacement equations of motion for the bilinear model are derived and explicit expressions for plastic wave velocities obtained. Dynamic equations for cases previously considered in the literature are compared. As an application, the initial stress discontinuities for the problem of scattering of a plane compressional step wave by a rigid, perfectly dense cylinder are obtained.
Catastrophic Thermoplastic Shear
Authors: Recht R. F.
Published: October 2011

Dynamic plastic behavior of materials is influenced by internally generated temperature gradients. These gradients are a function of thermophysical properties as well as strain rate and shear strength. Criteria are presented for the prediction of catastrophic shear in materials. Catastrophic shear occurs when the local rate of change of temperature has a negative effect on strength which is equal to or greater than the positive effect of strain-hardening. Catastrophic slip is an influential deformation mechanism during high-speed machining and ballistic impact. Structural failure may occur during dynamic loading of components which are designed without regard to the specific sensitivity of certain materials to catastrophic shear.
Wave Propagation in a Two-Layered Medium
Authors: Jones J. P.
Published: October 2011

Elastic wave propagation in a medium consisting of two finite layers is considered. Two types of solutions are treated. The first is a Rayleigh train of waves. It is seen that for this case, when the wavelength becomes short, the waves approach two Rayleigh waves plus a possible Stoneley wave. When the wavelength becomes large, there are two waves; i.e., a flexural wave and an axial wave. Calculations are presented for this case. The propagation of SH waves is treated, but no calculations are presented.
The Elastic Moduli of Fiber-Reinforced Materials
Authors: Hashin Zvi , Rosen B. Walter
Published: October 2011

Bounds and expressions for the effective elastic moduli of materials reinforced by parallel hollow circular fibers have been derived by a variational method. Exact results have been obtained for hexagonal arrays of identical fibers and approximate results for random array of fibers, which may have unequal cross sections. Typical numerical results have been obtained for technically important elastic moduli.
Sandwich Shells of Arbitrary Shape
Authors: Schmidt Robert
Published: October 2011

Differential equations are derived for sandwich shells of arbitrary shape. The weak core is assumed to be elastic, orthotropic, and deformable in all directions. The face layers obey the Kirchhoff hypothesis. The core and the face layers are rigidly connected to each other at their natural boundaries.
Buckling of a Thin-Walled Circular Cylindrical Shell Heated Along an Axial Strip
Authors: Hoff Nicholas J. , Chao Chi-Chang , Madsen Wayne A.
Published: October 2011

The elastic stability of a thin-walled circular cylindrical shell is investigated by means of the small-deflection theory when the shell is subjected to such nonuniform heating as causes a uniform axial compressive stress to arise in a band of width 2b while the rest of the shell is free of stress. The critical value of the compressive axial stress is found to be equal to the critical stress of the same circular cylindrical shell when subjected to uniform axial compression provided the band is not extremely narrow. In the latter case the critical stress of the band is higher than that of the uniformly compressed shell.
Nonsimilar Normal Mode Vibrations of Nonlinear Systems Having Two Degrees of Freedom
Authors: Rosenberg R. M. , Kuo J. K.
Published: October 2011

When a nonlinear system having several masses vibrates in normal modes, the time histories of the motion of these masses are, in general, different in wave shape (although in certain special nonlinear systems they differ at most in amplitude, but not in shape). When the wave shapes differ, the normal mode vibration is called nonsimilar. In this paper, nonsimilar normal mode vibrations are analyzed with respect to wave shape and stability. The systems considered are those lying close to systems having similar normal mode vibrations. An example is worked out in detail, and a comparison with an experimental study is reported.
The Performance of a Crossed-Field Magneto-Aerodynamic Accelerator
Authors: Krupka R. M. , Kezios S. P.
Published: October 2011

A one-dimensional theory of the performance of a crossed-field, magneto-aerodynamic accelerator is presented and the results are summarized in the form of design charts. With the aid of these charts, the synthesis characteristics of engineering applications may readily be accomplished, utilizing graphical construction techniques. Design charts are available which cover a range of initial Mach numbers of 0.1 to 0.9 in intervals of 0.1 and 2 to 10 in intervals of 1. Design charts for initial Mach numbers of 0.5 and 2 are presented herein and their utility is demonstrated with reference to several numerical examples.
Stress Analysis of a Helical Coil
Authors: Stein Irving
Published: October 2011

The solution for the torsional-stress problem in a small-angle helical coil of rectangular cross section is derived. The exact solution is then approximated for validity at small coil indices. This work complements the solution of Gohner,2 which is valid at larger coil indices.
Solution of Viscoelastic Stress Analysis Problems Using Measured Creep or Relaxation Functions
Authors: Lee E. H. , Rogers T. G.
Published: October 2011

Stress analysis problems for linear viscoelastic material behavior are solved on the basis of integral operator stress-strain relations. These characterize the material by relaxation modulus functions or creep compliances which are directly measurable over finite time ranges, and completely describe material behavior for stress determinations for the same duration. The stress analysis theory can lead to integral equations which are shown to be soluble with high accuracy by simple finite-difference numerical integration procedures. Examples are presented and compared with solutions obtained by other methods. A possible improved technique for relaxation modulus and creep compliance measurements is suggested, based on the method presented for numerical solution of the integral equations.
On Thermally Stressed Elastic-Plastic Shells
Authors: Onat E. T. , Yamantu¨rk S.
Published: October 2011

The elastic-plastic behavior of rotationally symmetric sandwich shells is considered in the presence of the thermal effects arising from thermal straining and the temperature dependence of the yield strength. The mathematical nature of the problem is discussed in some detail for the case of cylindrical shells.
Strongest Columns and Isoperimetric Inequalities for Eigenvalues
Authors: Tadjbakhsh I. , Keller J. B.
Published: October 2011

We consider the problem of determining what shape column has the largest critical buckling load of all columns of given length and volume. This problem was previously solved for a column hinged (pinned) at both ends. We solve it for columns clamped at one end and clamped, hinged, or free at the other end, assuming that all cross sections of the column are similar and similarly oriented. We also prove that the column previously obtained in the hinged-hinged case is actually strongest and not merely stationary. Graphs of the areas of the strongest columns as functions of distance along the columns are given for the various cases. The results are also expressed as isoperimetric inequalities for eigenvalues of second-order ordinary differential equations with various boundary conditions. Certain additional inequalities of this type are also obtained.
Diffraction of Pulses by Cylindrical Obstacles of Arbitrary Cross Section
Authors: Friedman M. B. , Shaw R.
Published: October 2011

The two-dimensional problem of the diffraction of a plane acoustic shock wave by a cylindrical obstacle of arbitrary cross section is considered. An integral equation for the surface values of the pressure is formulated. A major portion of the solution is shown to be contributed by terms in the integral equation which can be evaluated explicitly for a given cross section. The remaining contribution is approximated by a set of successive, nonsimultaneous algebraic equations which are easily solved for a given geometry. The case of a square box with rigid boundaries is solved in this manner for a period of one transit time. The accuracy achieved by the method is indicated by comparison with known analytical solutions for certain special geometries.
The Buckling of Cylindrical Shells Under Longitudinally Varying Loads
Authors: Weingarten V. I.
Published: October 2011

Two problems illustrating the effect of nonuniformity of loading on the buckling characteristics of circular cylinders are investigated. The first problem deals with the effect of linearly varying axial compressive stress, such as would be produced by the weight of the propellant in a solid-propellant engine case. The results indicate that the ratio of the maximum critical compressive stress induced by the shear load to the critical uniform compressive stress varies from 1.9 for the curvature parameter Z equal to 0 to 1.0 as Z becomes infinite. In particular, the increase in stress is less than 20 per cent for Z greater than 100. The stability of thin cylinders loaded by lateral external pressure, varying linearly in the longitudinal direction, is also investigated. The results indicate that for Z greater than 100, the buckling coefficients are proportional to Z1/2.
Geared Five-Bar Motion: Part I—Gear Ratio Minus One
Authors: Freudenstein F. , Primrose E. J. F.
Published: October 2011

Algebraic, geometric, and kinematic properties are derived for the curve generated by a point on the axis of the joint connecting the two floating links of a geared five-bar mechanism having a gear ratio of minus one.
Stress Distribution in a Nonhomogeneous Elastic Plane With Cracks
Authors: Erdogan Fazil
Published: October 2011

The problem of two semi-infinite elastic planes with different elastic properties bonded to each other along a finite number of straight-line segments and subjected to loads at infinity is formulated and the solution of the problem is reduced to the evaluation of ordinary integrals. The solutions for the cases with one and two bonding segments are given. For the general case, the stress state near the crack tips is analyzed and it is shown that the stress singularity is in the form of r−1/2, r being the distance from the crack tip. Finally, the stress-intensity factors, which are used in the fracture mechanics and which can be taken as the measure of the strength of stress singularities, are expressed in terms of the complex stress function.
On the Approximate Solution of Viscous-Flow Problems
Authors: Schetz J. A.
Published: October 2011

The need for a general technique for the approximate solution of viscous-flow problems is discussed. Existing methods are considered and a new method is presented which results in simple closed-form solutions. The accuracy of the method is demonstrated by comparisons with the results of known exact solutions, and finally the general technique is employed to determine a new solution for the fully expanded two-dimensional laminar nozzle problem.
On the Boundedness of the Dimensionless Index of Performance of a Nernst Effect Generator
Authors: Angrist S. W.
Published: October 2011

The author, in an earlier paper, analyzed a Nernst effect generator by the usual thermodynamic methods and found that a bound of unity arises on the dimensionless quantity θT where θ is given as the square of the product of the Nernst coefficient and magnetic field divided by the thermal conductivity and electrical resistivity. By application of the appropriate equations of semiconductor theory this bound is shown to be justified for four limiting cases: Weak magnetic fields considering both extrinsic and intrinsic materials, and strong magnetic fields considering both extrinsic and intrinsic materials.
Buckling of Simply Supported Oblique Plates
Authors: Yoshimura Y. , Iwata K.
Published: October 2011

Based on the general theory of thin plates and shells previously developed by the first author, which holds also for oblique coordinate system, the problem of buckling of simply supported parallelogram plates is treated. Numerical values of the critical stresses of buckling under compression and shear are calculated, respectively, for plates having angles between 45 and 135 deg, and for side ratios 1 and 2.
Analysis of the Motion of a Flexible Shaft Inside a Guide Tube
Authors: Massoud M. F.
Published: October 2011

A general method for analysis of the behavior of a flexible frictionless shaft of any arbitrary configuration running inside of a guide tube with negligible clearance and transmitting torque is presented. The method is applied to two configurations: (a) Segment of a plane circular arc. (b) Segment of a helical arc. The first configuration was discussed partially in a Russian publication where the solution for the angular displacement of an unloaded shaft was derived from first principles. The theory also is applied to the analysis of a switching device composed of a Wire-In-Tube with corrections to the solution given there.
Ballistic Perforation Dynamics
Authors: Recht R. F. , Ipson T. W.
Published: October 2011

Analytical equations of the types required to define ballistic perforation dynamics are developed. These equations concern both blunt and sharp-nosed fragments, perforating plates normally and at oblique impact angles. Residual velocities are defined in terms of magnitude and direction. Analytical models and confirming experimental data, which are presented here, specifically concern the ballistic velocity-impact range to about 25 percent of the velocity of longitudinal sonic waves in the impacting materials.
Fundamentals of the Theory of Rotating Fluids
Authors: Howard L. N.
Published: October 2011

This paper gives an expository survey of some of the principal mathematical models which have been used in the theory of rotating fluids, together with a discussion of several explicit examples. Some of these examples are related to geophysical fluid dynamics; others more directly to laboratory studies. In all cases the examples have been selected to illustrate some of the most important physical phenomena which are characteristic of rotating flows and distinguish them from other fluid motions. Physical concepts, such as the Taylor-Proudman effects, the Ekman boundary layer, and Rayleigh’s analogy, which have proved useful in obtaining a general understanding of rotating fluids, are presented and discussed.
Application of Nonstationary Shot Noise in the Study of System Response to a Class of Nonstationary Excitations
Authors: Lin Y. K.
Published: October 2011

The response of a linear system to the excitation of a nonstationary random process is studied. The random excitation considered belongs to a general class which may be generated by passing a nonstationary shot noise throuh a linear filter. The behaviors of different filters are discussed. In principle the covariance and the variance functions of an arbitrary excitation process can be simulated by properly choosing a filter and a non-stationary strength function in the shot noise. It is shown that, even with a first-order filter, the variance function of a complicated process such as a typical earthquake can be well reproduced, and the determination of the structural response to such excitations becomes relatively simple.
Dynamical Compliance of Rectangular Foundations on an Elastic Half-Space
Authors: Thomson William T. , Kobori Takuji
Published: October 2011

Equation for the compliance of the ground, considered as an elastic half-space under a rectangular foundation slab, is developed for harmonic forces normal to the ground. Displacement of the center of the slab for several rectangular shapes is evaluated numerically and plotted as a function of the frequency. A closed-form solution for the limiting case of zero frequency is shown to agree exactly with the static problem of Love [7].
The Elastic Plane With a Circular Insert, Loaded by a Radial Force
Authors: Dundurs J. , Hete´nyi M.
Published: October 2011

The problem treated is that of a plate of unlimited extent containing a circular insert and subjected to a concentrated radial force in the plane of the plate. The elastic properties of the insert are different from those of the plate, and a perfect bond is assumed between the two materials. The solution is exact within the classical theory of elasticity, and is in a closed form in terms of elementary functions. Explicit formulas are given for the components of stress in Cartesian co-ordinates, and also in polar co-ordinates at the circumference of the insert.
Stresses and Deflections in an Elastically Restrained Circular Plate Under Hydrostatic Normal Pressure Over a Segment
Authors: Bassali W. A. , Hanna N. O. M.
Published: October 2011

This paper is concerned with the application of complex variable analysis to establish exact expressions for the small deflections occurring in a thin isotropic circular plate subject to hydrostatic transverse pressure distributed over a segment of the plate. The general boundary conditions taken at the edge of the plate include those for the simply supported and rigidly clamped boundaries as particular cases. In the latter case the solution is obtained in a closed form. Explicit formulas are given for the boundary values of the bending and twisting moments and shearing forces. Expressions are also developed for the corresponding values on the axis of symmetry. When the hydrostatic pressure extends over a half of the plate or over the entire plate, the problem is investigated in detail and numerical results are presented in the form of tables and graphs. The results obtained are of practical significance in connection with the design of cylindrical tanks and boilers.
A Steepest-Ascent Method for Solving Optimum Programming Problems
Authors: Bryson A. E. , Denham W. F.
Published: October 2011

A systematic and rapid steepest-ascent numerical procedure is described for solving two-point boundary-value problems in the calculus of variations for systems governed by a set of nonlinear ordinary differential equations. Numerical examples are presented for minimum time-to-climb and maximum altitude paths for a supersonic interceptor and maximum-range paths for an orbital glider.
Crack-Tip, Stress-Intensity Factors for Plane Extension and Plate Bending Problems
Authors: Sih G. C. , Paris P. C. , Erdogan F.
Published: October 2011

A complex variable method for evaluating the strength of stress singularities at crack tips in plane problems and plate bending problems is derived. The results of these evaluations give Irwin’s stress-intensity factors for plane problems and analogous quantities for bending problems, a form familiar to the practitioner of “fracture mechanics.” The methods derived are integrated with the complex variable approach of Muskhelishvili to obtain the stress-intensity factors for various basic examples applicable to the extension and bending of plates with through-the-thickness cracks. The results suggest the possibility of extension of the Griffith-Irwin fracture theory to arbitrary plane extensional and/or bending problems in plates.
On Surface Constraints in Plate Problems
Authors: Essenburg F.
Published: October 2011

The general problem of an axisymmetric circular plate, partially constrained from deflection by a smooth, rigid surface of revolution, is considered and the Reissner plate-theory solution is obtained. A specific example involving a clamped circular plate, concentrically loaded by a paraboloid of revolution, illustrates the importance of the inclusion of the effect of transverse shear deformation (even in the case of a thin plate).
The Elastic Plane With a Circular Insert, Loaded by a Tangentially Directed Force
Authors: Hete´nyi M. , Dundurs J.
Published: October 2011

The problem treated is that of a plate of unlimited extent containing a circular insert and subjected to a concentrated force in the plane of the plate and in a direction tangential to the circle. The elastic properties of the insert are different from those of the plate, and a perfect bond is assumed between the two materials. The solution is exact within the classical theory of elasticity, and is in a closed form in terms of elementary functions. Explicit formulas are given for the components of stress in Cartesian co-ordinates, and also in polar co-ordinates at the circumference of the insert.
Free Vibration of a Simply Supported Bar With a Linearly Variable Height of Cross Section
Authors: Krynicki E. , Mazurkiewicz Z.
Published: October 2011

The problem of vibration of nonhomogeneous bars or bars of variable cross section1 leads to differential equations, which are generally unsolvable by formal integration. It is known that functional coefficients occur in these equations, which make it difficult, if not impossible, to obtain exact solutions by simple integration. Several exact solutions obtained for a few special cases and also some interesting approximate solutions are mentioned in the paper.
Contact Stress Analysis of Normally Loaded Rough Spheres
Authors: Goodman L. E.
Published: October 2011

The Hertz analysis of contact stresses is extended to include the effects of friction on the interface between two elastic spheres compressed along the line connecting their centers. The problem is shown to be one of a class which requires incremental formulation. Stress functions of interest in connection with the analysis of the shear-loaded half-space in the linear theory of elasticity are developed. The distribution of shear stress needed to prevent relative slip of surficial points after they enter the contact region is found to be finite everywhere in the region. The ratio of this shear stress to the coexisting normal stress component is shown to exhibit a singularity at the edge of the contact region. This implies that when elastically dissimilar spheres are pressed together microscopic slip must occur in a narrow annulus at the boundary of the contact region.
Transient Coupled Thermoelastic Boundary Value Problems in the Half-Space
Authors: Boley B. A. , Tolins I. S.
Published: October 2011

The propagation of mechanical and thermal disturbances in a half-space is studied by means of the solution of some transient boundary value problems, according to the coupled thermoelastic theory. The problems considered are those of a half-space under step time variations of strain, temperature, or stress uniformly distributed over the free surface. The coupled solution of Danilovskaya’s problem is thus included. The solution is obtained by the use of Fourier sine transforms, and the behaviors at short and long times, as well as the propagation of discontinuities, are studied.
Crack-Extension Force for a Part-Through Crack in a Plate
Authors: Irwin G. R.
Published: October 2011

The crack stress-field parameter K and crack-extension force G at boundary points of a flat elliptical crack may be derived from knowledge that normal tension produces an ellipsoidal crack opening. Rough correction procedures can be employed to adapt this result for application to a part-through crack in a plate subjected to tension. Experimental measurements suggest this adapted result has a useful range of accuracy.
A Digital Computer Program for the General Axially Symmetric Thin-Shell Problem
Authors: Sepetoski W. K. , Pearson C. E. , Dingwell I. W. , Adkins A. W.
Published: October 2011

This paper describes the development of a general computer program to handle arbitrary thin shells of revolution subject to radially symmetric loading or temperature variation. An elimination method is used to solve the set of difference equations obtained from the basic differential equations; a feature of the method is that “edge effect” difficulties that can arise with conventional differential-equation routines are avoided. The program is quite flexible and permits discontinuities in shell geometry or loading. The results of applying the program to several classical problems of known solution are given. These results permit the examination of computational accuracy for varying boundary conditions and mesh sizes. Finally, some program solutions of unconventional problems are presented.
Impulsive Motions
Authors: Kane T. R.
Published: October 2011

A method for the determination of changes induced in the time derivatives of the generalized coordinates of a mechanical system by the action of impulsive forces is presented. Several supplementary theorems are stated, and an illustrative problem is solved.