bluuebunny/crossref_metadata_2025 huggingface dataset:
The Effects of Variable Properties on MHD Flow in Finite Ducts
Authors: Thomson W. J. , Bopp G. R.
Published: November 2010

Numerical solutions are obtained of the coupled partial differential equations which describe variable property MHD flow in finite rectangular ducts. The fluid properties are allowed to vary to the extent that electrical conductivity and viscosity are assumed to be temperature-dependent. It is shown that it is not possible to account for fluid property variations in terms of “weighted” fluid parameters such as average Hartmann numbers. Analysis leads to the conclusion that it is the nature of the current distributions in the duct which is important in predicting the behavior of nonisothermal MHD duct flow. It is possible that this conclusion may aid in the evaluation and correlation of experimental data. It is also shown that consideration of variable fluid properties results in friction factors and flow rates which differ from constant property solutions by as much as a factor of two and by 50 percent, even for small variations.
A Direct Numerical Method for Stress and Stress-Intensity Factor in Arbitrary, Cracked, Elastic Bars Under Torsion and Longitudinal Shear
Authors: Tirosh J.
Published: November 2010

A numerical method is proposed for a direct local determination of stresses in a general twisted and sheared cracked bar. Conceptually, the method employs the integral approach of the potential theory but is modified to yield the stress components without numerical differentiation or interpolation from a potential function. A general expression for the stress-intensity factor at the crack tip is formulated. It checks favorably with the corresponding theoretical solutions. Computer running time and storage requirements for typical problems indicate the comparative efficiency of the method in addition to its relatively high accuracy near the crack tip.
Asymmetric Buckling of Spherical Caps With Asymmetrical Imperfections
Authors: Kao R. , Perrone N.
Published: November 2010

The title problem has been solved using the nonlinear relaxation technique to treat the finite-difference representation of the differential equations governing cap response. For clamped spherical caps designated by λ = 6, buckling loads are somewhat lower for the same imperfection magnitudes than those obtained previously for asymmetric and axisymmetric buckling. The three differential equations of the Marguerre type are set up in terms of three displacement quantities as the dependent variables. The equations are formulated so as to allow arbitrary initial imperfections, boundary conditions, and loading. The computer program setup to solve these equations was checked by successfully solving simpler problems, the solutions of which are in the literature. Although the buckling loads for spherical caps with asymmetric initial imperfections appear reasonable, it is not possible to ascertain at this point whether the cap results are indicative of what the full shell might do.
The Separation of Membrane and Bending Shears in Shell With Two Birefringent Coatings
Authors: Schumann W. , Mylonas C. , Bucci R.
Published: November 2010

The determination of magnitude and principal direction of membrane and bending stress differences in plates or thin shells requires four independent items of information, such as the photoelastic retardations and principal directions in two birefringent coatings, one on each face. However, the superposition of a constant membrane and a linearly varying bending stress in general result in a change of direction of the total principal stress through the finite coating thickness. Such rotation of stress introduces considerable difficulties even in the direct determination of the photoelastic effect in known stress fields, and makes the inverse solution of stress distribution from birefringence impossible without additional techniques and data. This paper presents an explicit approximate inverse solution based on simple photoelastic observations in the two coatings, with only partial consideration of the effects of rotation. In its double, reversing path through a coating, polarized light is assumed to suffer the same changes as in a field of linearly varying stress of constant direction parallel to that at incidence and exit. The validity of the direct and inverse solutions was checked experimentally in square plates containing residual membrane stress and subjected to anticlastic bending of various magnitudes and directions. Agreement was very good, especially at the higher loads, even when large stress rotation occurred. Criteria for recognizing potentially inaccurate states with large rotation are also suggested. The proposed method should prove useful in the experimental study of shells.
Nonsteady Three-Dimensional Stagnation-Point Flow
Authors: Cheng E. H. W. , O¨zis¸ik M. N. , Williams J. C.
Published: November 2010

The equations of motion for the three-dimensional nonsteady flow of incompressible viscous fluid in the vicinity of a forward stagnation point are reduced to three ordinary differential equations for a potential flow field chosen to vary inversely as a linear function of time. The resulting ordinary differential equations contain two parameters C and D, the former characterizes the type of curvature of the surface around the stagnation point and the latter the degree of acceleration or deceleration of the potential flow. The simple stagnation-point problems which have been studied previously are obtainable as special cases of the present analysis by assigning particular values to C and D. Exact solutions have been computed numerically for the velocity field and the pressure distribution in the boundary-layer flow around the stagnation point of a three-dimensional blunt body for the values of the parameter C from 0–1.
Bolted Joint Interface Pressure for Thermal Contact Resistance
Authors: Bradley T. L. , Lardner T. J. , Mikic B. B.
Published: November 2010

One of the parameters needed to calculate the thermal contact resistance across a bolted joint is the interface pressure distribution between the plates of the joint [1, 2]. As part of a study [3] on thermal joint conductance, a three-dimensional photoelastic analysis using the stress freezing technique was used to predict the interface pressure. Nine bolted joint geometries were investigated using smooth flat plates of photoelastic material and equal thickness. The resulting interface pressure distributions which are presented are sufficiently accurate for the calculation of thermal contact resistance.
A Numerical Study of Axially Symmetric Flow Between Two Rotating Infinite Porous Disks
Authors: Jawa M. S.
Published: November 2010

This paper presents a numerical study of the axially symmetric flow between two rotating, contrarotating, and one-rotating another-stationary disks with, and without, porosity. The flow is considered only in the gap between the disks. The formulation is reduced to six-coupled first-order nonlinear ordinary differential equations which are solved with arbitrarily small truncation error. The effects of porosity, rate of rotation, and sense of rotation are evaluated; indicating, interalia, possible engineering applications. For example, it is found that seepage of fluid through the disks into the flow region increases the skin friction and increases the tendency of the disks to repel each other. The increase in the rate of rotation reinforces the force of attraction between the disks and weakens the skin friction; however, contrarotation has contrary effects.
The Hydrodynamic Drag on a Small Sphere in an Ionized Gas
Authors: Seymour E. V.
Published: November 2010

A theoretical and experimental study was made of the hydrodynamic drag on a small sphere moving relative to a plasma in local thermodynamic equilibrium. The results have application to velocity measurement in ionized gases using the technique of injecting small particles and following their motion as a function of time. The previously available sphere drag results for fluids with properties which vary linearly with temperature are shown to be in error by as much as 40 percent for an argon plasma at 13,000 deg K, for example, because large temperature gradients occur in the vicinity of the sphere where fluid properties vary nonlinearly with temperature. A new drag calculation for a sphere Reynolds number of zero has been made for an argon plasma taking into account nonlinear variations of transport properties with temperature. Sphere deflection measurements in an argon plasma have been made at Reynolds numbers between 0.3 and 1.5. The interpretation of these measurements in terms of sphere drag is subject to confirmation of the plasma transport properties used in the data reduction, but the difference between the measured drag and the drag calculated for zero Reynolds number appears to be approximately the same as in the classical case for invariant fluid properties.
Guided Surface Waves on an Elastic Half Space
Authors: Freund L. B.
Published: November 2010

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.
On the Finite Deflection Dynamics of Thin Elastic Beams
Authors: Lee S. Y.
Published: November 2010

A dynamic theory of thin beams undergoing large deflection but small strain is derived. Geometric nonlinearities are preserved but the material is assumed to behave linearly. Contributions due to rotatory inertia, shear deformation, and axial stress resultants are included. The resulting equations are analyzed by characteristic techniques. Wave-propagation speeds, jump properties, and their physical significances are discussed. A simplifying assumption generates a modified Timoshenko beam equation which is valid for large deformation.
Buckling and Postbuckling Behavior of Clamped Shallow Spherical Shells Under Axisymmetric Ring Loads
Authors: Akkas N. , Bauld N. R.
Published: November 2010

This paper presents the results of a numerical study of the buckling and initial post-buckling behavior of clamped shallow spherical shells under axisymmetric ring loads. This behavior is studied for a cap with fixed geometry when the location of the ring load is allowed to vary from the equivalent of a concentrated load at the apex to a location near the midpoint of the shell base radius, and for a fixed ring load location when the shell geometry is allowed to vary. It is found in both studies that a significant range of the geometric shell parameter λ exists such that buckling is accompanied by a loss in load-carrying capacity.
Axisymmetric Postbuckling and Nonsymmetric Buckling of a Spherical Shell Compressed Between Rigid Plates
Authors: Updike D. P. , Kalnins A.
Published: November 2010

The authors have previously shown that a thin, complete spherical shell compressed between two parallel rigid plates deforms initially with the polar portion of the shell flattened against the plates and that at a critical deformation the flat region may buckle into an axisymmetric inward dimple. The present paper presents an analysis of the stresses and deflections produced during axisymmetric postbuckling and determines the deformation states at which the shell may buckle into a nonsymmetric shape. The analysis accounts for finite deflections and rotations, but assumes that the material remains linearly elastic throughout the deformation. An experiment shows that both the primary axisymmetric bifurcation point and the secondary nonsymmetric bifurcation point are stable for a shell with R/h ≃ 40.
Asymptotic Formulas for the Buckling Stresses of Axially Compressed Cylinders With Localized or Random Axisymmetric Imperfections
Authors: Amazigo J. C. , Budiansky B.
Published: November 2010

Formulas are presented for the axial buckling stresses of long circular cylindrical shells having localized or random axisymmetric imperfections. The results are asymptotic in character, applicable only for sufficiently small magnitudes of the imperfections. The formulas found are discussed and compared with earlier results obtained by Koiter for the case of an imperfection in the shape of the axisymmetric buckling mode.
Predictions of Momentum Transfer Between Rotating Cylinders: The Narrow Gap Problem
Authors: Catton I. , Ayyaswamy P.
Published: November 2010

The contributions to momentum transfer by secondary motion, which arises beyond the marginal state of stability in a layer of fluid confined between rotating cylinders is calculated by an integral method. The procedure invokes the “shape assumption” due to Stuart. Results are presented in terms of an effective viscosity to molecular viscosity ratio that is a function of Taylor number. Comparison with experiment is found to be excellent over a wide range of values of the Taylor number (up to 1000 times the critical value).
Asymptotic Expansions of Guided Elastic Waves
Authors: Rulf B. , Robinson B. Z. , Rosenau P.
Published: November 2010

The problem of propagation of guided elastic waves near curved surfaces and in layers of nonconstant thickness is investigated. Rigorous solutions for such problems are not available, and a method is shown for the construction of high frequency asymptotic solutions for such problems in two dimensions. The method is applied to Love waves, which are SH-waves in an elastic layer, Rayleigh waves, which are elastic waves guided by a single free surface, and Lamb waves, which are SV-waves guided in a plate or layer with two free surfaces. The procedure shown breaks the second-order boundary-value problems which have to be solved into successions of simpler problems which can be solved numerically. Some numerical examples for Rayleigh waves are carried out in order to demonstrate the utility of our method. The method shown is useful for a large variety of guided wave problems, of which the ones we treat are just examples.
Limit Analysis of Nonsymmetrically Loaded Spherical Shells
Authors: Palusamy S. , Lind N. C.
Published: November 2010

Upper and lower bounds are found for limit loads on nonsymmetrically loaded spherical shells. The influence of geometrical and load parameters are discussed. The analytical results are compared with the results of tests on four steel models.
Magnetoelastic Buckling of Beams and Thin Plates of Magnetically Soft Material
Authors: Wallerstein D. V. , Peach M. O.
Published: November 2010

When a plate of magnetically soft material is supported with its wide surface normal to a uniform magnetic field, it will buckle when the field reaches a critical value. This paper formulates the problem quite generally for thin plates (including beams) and carries the solution as far as can be done without making specific assumptions as to plate geometry and constraints. The special case of wide cantilever beam, considered earlier by Moon and Pao, is carried through in detail. It is shown that if their theoretical result is modified to take account of the increased field intensity caused by the plate, agreement with experiment is within 20 percent.
Exact Analysis of a Thick Sandwich Conical Shell by Forward Integration
Authors: Seitz D. H.
Published: November 2010

A numerical method for stress analysis of three-layered, honeycomb-type sandwich plates and shells of arbitrary thickness is illustrated by application to a thick conical frustum. Results are demonstrated in a numerical example. The method features an exact elasticity analysis of the core including transverse shear and transverse normal stress. The facings are treated by classical shell theory. The numerical method used is forward integration.
An Estimator for the Standard Deviation of a Natural Frequency—Part 1
Authors: Schiff A. J. , Bogdanoff J. L.
Published: November 2010

An estimator for the standard deviation of a natural frequency in terms of second-order statistical properties of the parameters of the system is derived. Results for one simple example is presented in this part and are compared with theoretical and Monte Carlo results. Further results and discussion will be presented in Part 2, ASME Paper No. 71-WA/APM-8.
Application of Statistical Linearization Techniques to Nonlinear Multidegree-of-Freedom Systems
Authors: Iwan W. D. , Yang I-Min
Published: November 2010

A statistical linearization approach is applied to problems of the stationary random response of nonlinear multidegree-of-freedom dynamical systems. The approach is formulated in such a way that the resulting linear system parameters have a simple physical interpretation and can often be determined analytically. The accuracy of the approach is investigated by means of examples.
Large Amplitude Vibration of a Circular Plate With Concentric Rigid Mass
Authors: Chiang D. C. , Chen S. S. H.
Published: November 2010

Simplified nonlinear governing differential equations proposed by Berger and extended by Nash and Modeer are applied to obtain natural frequencies of a circular plate with concentric rigid part at its center in large amplitude vibrations. A modified Galerkin technique is used to derive a nonlinear differential equation of which the solution is given in terms of elliptic functions. The small amplitude vibration is treated as a special case of large amplitude vibration, while the free, large amplitude vibration of a flat circular plate is studied as a special case of large amplitude vibration of a circular plate with a concentric mass. The numerical results show that the effect of added concentric rigid mass to a circular plate is significant.
On the Sufficiency of the Energy Criterion for the Stability of Certain Nonconservative Systems of the Follower-Load Type
Authors: Leipholz H. H. E.
Published: November 2010

Using Galerkin’s method it is shown that in the domain of divergence, the nonconservative system of the follower-load type is always more stable than the corresponding conservative system. Hence, for nonconservative systems of the divergence type, the critical load of the corresponding conservative system becomes a lower bound for the buckling load, and the energy criterion remains sufficient for predicting stability. Moreover, it is proven that even for more general nonconservative systems, the energy criterion is sufficient under certain restrictions.
Free Vibrations of an Arbitrary Structure in Terms of Component Modes
Authors: Dowell E. H.
Published: November 2010

A method for the analysis of the free vibrations of an arbitrary structure in terms of component modes is presented based upon the use of the normal, free-free modes of the components in a Rayleigh-Ritz analysis with the constraint or continuity conditions between components enforced by means of Lagrange multipliers. Several examples are given and the advantages of such a procedure over more conventional methods are discussed.
On the Torsion of Elastic Half Spaces With Embedded Penny-Shaped Flaws
Authors: Low R. D.
Published: November 2010

The investigation is concerned with some of the effects of embedded flaws in an elastic half space subjected to torsional deformations. Specifically two types of flaws are considered: (a) a penny-shaped rigid inclusion, and (b) a penny-shaped crack. In each case the problem is reduced to a system of Fredholm integral equations. Graphical displays of the numerical results are included.
Nonlinear Flexural Vibrations of a Clamped Circular Plate
Authors: Kung G. C. , Pao Y.-H.
Published: November 2010

Nonlinear flexural vibration of a circular plate clamped at its edge are investigated both experimentally and theoretically. The investigation has been restricted to the first axisymmetric mode. The time-dependent part of the nonlinear plate equations are reduced to Duffing’s equation by applying a one-term Ritz-Galerkin’s procedure. Test results are in good agreement with the theoretical calculations which indicate a non-linearity of hardening type for large amplitude vibrations. The period of vibration decreases by 35 percent when the amplitude is twice the thickness of the plate. The “jumps” in the amplitude-frequency response curves are observed to occur during a transition of a few seconds and are accompanied by a beating phenomenon.
On the Use of Kinetic Energy to Determine Generalized Inertia Forces in Nonholonomic Systems
Authors: McGill D. J. , Shiau J.-F.
Published: November 2010

Use of kinetic energy K to directly compute generalized inertia forces Fr* is restricted to holonomic systems. In this paper, a subclass of simple nonholonomic systems is identified, for which the use of K to determine Fr* is indeed valid.
Reduction of a Gyrostat Problem to That of a Rigid Body
Authors: Kane T. R. , Chia B. S.
Published: November 2010

To determine the motion of a symmetric gyrostat under the action of a specialized body-fixed force, dynamical equations governing rotational motions are solved, and it is then shown how results available from a certain rigid-body problem can be used to complete the integration of the remaining kinematical and dynamical equations.
The Elastic Stability of Two-Parameter Nonconservative Systems
Authors: Huseyin K. , Plaut R. H.
Published: November 2010

The stability of a linear, elastic, circulatory system with two independent loading parameters is studied in general terms. The basic properties of the stability boundary are investigated and several theorems are established. It is shown that for a two-degree-of-freedom system which is capable of flutter instability the stability boundary is always convex toward the region of stability, in direct contrast with systems which cannot exhibit flutter. The practical significance of this result in obtaining lower and upper-bound estimates of the stability boundary is emphasized, and three illustrative examples are presented.
Sound Propagation in Non-Newtonian Fluids
Authors: Raichel D. R. , Kapfer W. H.
Published: November 2010

A perturbation analysis is applied to the basic hydrodynamic equations and developed to determine the non-Newtonian effects of a small-signal plane wave propagating through a viscous fluid which is continuous, homogeneous, and isotropic. With the emphasis on liquids, the analysis is applied to the case of a Powell-Eyring fluid (which specializes to the case of a Prandtl-Eyring model) in order to ascertain the magnitudes of second and third-order effects occurring as a result of viscous nonlinearity. It is established that the appearance of second and third harmonics, or “harmonic distortions” of the fundamental wave, can provide a measure of the deviation from Newtonian behavior that should prove useful in laboratory practice. For the purpose of demonstrating the sonic effects of non-Newtonian fluidity, numerical results are obtained for the specially assumed case of sound propagation in compressed water acting as a Powell-Eyring fluid. The second and third-order harmonic distortions are found as functions of fundamental wave frequency, signal strength, and viscous parameters.
A Numerical Solution for Laminar Entrance Flow in a Square Duct
Authors: Carlson G. A. , Hornbeck R. W.
Published: November 2010

The laminar entrance flow of an incompressible viscous fluid in a square duct is analyzed numerically. Two approximate mathematical models are considered, with the more exact model including the transverse momentum equations. Finite-difference representations are developed for the equations of both models, and solutions are obtained assuming a uniform inlet velocity distribution. Results are presented for the velocity and pressure distributions in the entrance region, and comparisons made with previous analytical and experimental work. The results provide new insight into the true three-dimensional character of the flow and are more accurate than previously available solutions.
Yield Surfaces for Perforated Materials
Authors: O’Donnell W. J. , Porowski J.
Published: November 2010

The sheet perforated with a uniform triangular pattern of round holes and subjected to in-plane stress of arbitrary biaxiality is investigated. Discontinuous fields of stress are employed to derive rigorous lower-bound limit stresses. Kinematically admissible velocity fields are also obtained, thus bounding the yield surface.
Transient Characteristics of Simple Systems to Modulated Random Noise
Authors: Barnoski R. L. , Maurer J. R.
Published: November 2010

Discussed are the mean-square response exceedance characteristics of a single-tuned system to amplitude modulated noise. The results bear on the accuracy of spectral estimates of nonstationary data, and subsequently, relate directly to the design, analysis, and testing of structural systems in environments as gusts, earthquakes, and ignition transients. For noise correlated as an exponentially damped cosine, the nonstationary response may exceed its stationary value by a factor in excess of two. A time-varying shaping filter explanation is offered for this behavior. For white noise, such exceedances do not occur.
Stability of a Pin-Ended Bar in Torsion and Compression
Authors: Walker J. A.
Published: November 2010

The stability of a uniform pin-ended bar having equal principal stiffnesses, subjected to combined torsion and compression, is studied via the direct method of Liapunov for cases in which the torque vector is circulatory; i.e., the torque vector does not bisect the angle between the undeformed and deformed axes of the bar. Liapunov functionals are presented and applied to both the case of a viscous environment and the case of a viscoelastic environment. Several simple stability and instability criteria are obtained in terms of the system parameters.
Unconditional Stability in Numerical Time Integration Methods
Authors: Krieg R. D.
Published: November 2010

Methods of numerical time integration of the equation M¯q¨ + K¯q = f are examined in this paper. A particular class of explicit time integration methods is defined and this class is searched for an unconditionally stable method. The class is found to contain no such method and, furthermore, is found to contain no method with a larger stable time step size than that characterized by the simple central difference time integration method.
Nonstationary Response of Linear Time-Varying Dynamical Systems to Random Excitation
Authors: Wan F. Y. M.
Published: November 2010

A direct time-domain method is used to analyze the titled problem. Special attention is paid to a system characterized by a general second-order equation with variable coefficients. The equation of flapping motion of a rigid rotor blade advancing in atmospheric turbulence belongs to this class. Steady-state mean-square response to ideal white noise and to exponentially correlated excitation is obtained by a perturbation series solution in a stiffness parameter. An upperbound of the same is derived. Explicit solution for the correlation matrix is obtained by the two-variable expansion method. Specialized to the rotor blade problem, the results have led to some new information concerning the blade behavior in a certain range of rotating speed. They have also served as useful check cases for computer programs developed for more general problems. Higher-order equations and their applications are also discussed.
On the Transverse Strength of Fiber-Reinforced Materials
Authors: Butler T. W. , Sullivan E. J.
Published: November 2010

Using plasticity limit theorems, transverse strengths for unidirectionally reinforced composites containing fibers with hexagonal cross sections are found and compared with earlier “exact” values found by Drucker for symmetric deformation. Using unsymmetric deformation modes, upper bounds are found which are lower than the values found by Drucker for volume fractions of fibers between 0.40 and 0.58. By extending the symmetric analysis, it has been found that for nonuniform hexagonal fiber sizes, the transverse limit strength is higher (for the same volume fraction) than for the uniform size case. Also, selected agglomerations can greatly increase transverse limit strengths.
Stresses in Laminated Composites Containing a Broken Layer
Authors: Ashbaugh N. E.
Published: November 2010

The stresses are determined around a crack in bimaterial laminated composite with elastic constituents. The crack is created by a broken layer and has a finite length. The solution presented in this paper applies to the problem where either the normal displacement or the normal stress can be prescribed. For the case when the normal stress is prescribed, a singular differential-integral equation is derived which the normal displacement of the crack surface must satisfy. A set of composite parameters is used which provide some pertinent information for this crack problem. To obtain numerical results a method which may have general application is used to reduce a singular differential-integral equation to a tractable form for computations. The results indicate that, as the ratio of shear modulus of the broken layer to shear modulus of adjacent material becomes large, the stresses which result from the presence of the crack lend to concentrate around the crack tips. Estimates of the stress-intensity factor which may be obtained without extensive numerical computation are also discussed.
Polycarbonate as a Model Material for Three-Dimensional Photoplasticity
Authors: Dally J. W. , Mulc A.
Published: November 2010

Polycarbonate is a polymer which exhibits extreme toughness, a pronounced yield behavior, and the ability to flow extensively prior to fracture. These characteristics coupled with its birefringent properties indicate its suitability as a model material for photoelastic analyses. This study treats the photoplastic response of polycarbonate which has been deformed well beyond the yield point and unloaded. The strain field associated with this permanent deformation is related to the birefringence by the conventional strain-optic law. The birefringence is permanently locked in the polycarbonate models on a molecular scale. The model can be sliced to isolate planes of interest and the method can be applied to study permanent strains in plastically deformed three-dimensional bodies.
Aerodynamic Effects Due to Configuration of X-Wire Anemometers
Authors: Strohl A. , Comte-Bellot G.
Published: November 2010

Two separate “reference” wires were arranged to act as an X-wire. First, the effects of the orientation of one of the wires with respect to the other, and of both wires with respect to the mean flow, were investigated. Then, components of typical hot-wire probes (stem, prongs, . . .) were being advanced toward the reference wires. The analysis of the response of the reference wires during the advancement uncovered (a) a perturbation induced on the RMS value v′ of the transverse component of the velocity fluctuation and on the Reynolds stress uv, (b) changes of the wire sensitivities, and therefore also (c) errors affecting the v′ and uv measurements performed with typical probes.
The Unsteady Aerodynamics of a Finite Supersonic Cascade With Subsonic Axial Flow
Authors: Verdon J. M.
Published: November 2010

A method is presented for determining the unsteady flow field and the aerodynamic response which occurs when a finite oscillating cascade is placed in a supersonic stream, which has a subsonic velocity component normal to the cascade. Solutions are obtained through the combined use of closed-form and numerical procedures. Computed results indicate that the finite cascade analysis should provide a reasonable indication of the influence of the cascade parameters on the response of the infinite array. A brief parametric study for a typical configuration reveals possible aerodynamic instabilities when the blades perform single-degree-of-freedom pitching oscillations over a broad range of frequencies and interblade phase angles.
Forced Plane Strain Motion of Cylindrical Shells—A Comparison of Shell Theory With Elasticity Theory
Authors: Pawlik P. S. , Reismann H.
Published: November 2010

A radially directed load is suddenly applied to a portion of the outer surface of a circular cylindrical shell which responds in a state of plane strain. An analytical solution for the resulting dynamic response is obtained within the context of linear elasticity theory, Flu¨gge shell theory, and an “improved” shell theory. A comparison of results for specific loading conditions indicates that the improved theory is far superior to the Flu¨gge theory in terms of predicting both the magnitude and characteristics of the response. However, as expected, neither shell theory satisfactorily predicts the wave character of the initial response.
Buckling of Rectangular Plates With General Variation in Thickness
Authors: Chehil D. S. , Dua S. S.
Published: November 2010

A perturbation technique is employed to determine the critical buckling stress of a simply supported rectangular plate of variable thickness. The differential equation is derived for a general thickness variation. The problem of bending, vibration, buckling, and that of dynamic stability of a variable thickness plate can be deduced from this equation. The problem of buckling of a rectangular plate with simply supported edges and having general variation in thickness in one direction is considered in detail. The solution is presented in a form such as can be easily adopted for computing critical buckling stress, once the thickness variation is known. The numerical values obtained from the present analysis are in excellent agreement with the published results.
Properties of Work-Hardening Materials With a Limit Surface
Authors: McLaughlin P. V.
Published: November 2010

Plastic behavior is investigated for a material which initially work-hardens, but eventually can have a limiting stress state at which continued straining is possible without increase in stress. Particular attention is paid to stability criteria and stress-strain relations at the limit surface when yield surfaces have vertices, and yield and limit surfaces are nonosculating. Under these circumstances, normality and convexity of yield surfaces do not imply that these are also properties of the limit surface. Conditions under which work-hardening materials are acceptable for use of limit analysis are presented.
Transient Thermoelastic Problem in a Polygonal Cylinder With a Circular Hole
Authors: Takeuti Y. , Noda N.
Published: November 2010

In our previous paper, we dealt with steady plane thermoelastic problems in a multiply connected domain by the method of five elementary stress functions. As an extension of this method to transient thermoelasticity, this paper is concerned with the uncoupled quasi-static transient plane thermoelastic problems in a polygonal cylinder with a circular hole.
The Morley-Koiter Equations for Thin-Walled Circular Cylindrical Shells: Part 2—Solution for a Line Loaded Cylinder With Close-Spaced Circumferential Grooves
Authors: Mangelsdorf C. P.
Published: November 2010

In Part 1, modified Donnell equilibrium equations were solved for the case of symmetrical loading and supports using Fourier series. An evaluation procedure for various boundary conditions was suggested. In Part 2, an application of the general solution is made for a shell with small circumferential grooves (or ribs) subjected to a longitudinal line load after approximations to allow for such groves are introduced. The solution is completed for boundary conditions of classical simple supports and relaxed simple supports and the results compared with experimental data.
A Refined Theory for Laminated Orthotropic Plates
Authors: Nelson R. B. , Lorch D. R.
Published: November 2010

A refined structural theory is presented which accurately models the static and dynamic behavior of laminated orthotropic plates. The refined theory extends classical theory to include transverse shear, transverse normal, and quadratic displacement terms in the kinematic assumption. Hamilton’s principle is used to formulate the displacement equations of motion with appropriate boundary and initial conditions. The composite correction factors kij are introduced in a manner consistent with their indifference to choice of reference surface, and are determined by a procedure in which plane wave solutions for the plate are adjusted to match corresponding exact solutions. Examples of homogeneous isotropic, orthotropic, and laminated orthotropic plates are presented to show the capability of the theory to accurately model the lower branches of the frequency spectrum of these plates for wavelength-thickness ratios greater than unity.
Contact of Inflated Membranes With Rigid Surfaces
Authors: Callegari A. J. , Keller J. B.
Published: November 2010

The equilibrium of an inflated cylindrical membrane in contact with two rigid cylindrical surfaces is considered. The cross section of the membrane consists of two circular arcs of radius R and an arc in contact with each surface. Equations for R and the end points of the contact regions are obtained. These equations are solved numerically for a membrane squeezed between parallel planes, and graphs of the results are shown. In addition we treat the case in which the cross section has ends which are attached to two points on one of the surfaces. In this case there are two solutions for certain values of the force on the planes, one of which is unstable.
Thermal Response of a Viscoelastic Rod Under Cyclic Loading
Authors: Mukherjee S.
Published: November 2010

Thermal response of a viscoelastic rod under cyclic loading is discussed by determining the stresses and temperature in a viscoelastic rod insulated on its lateral surface and driven by a sinusoidal stress at one end. Temperature dependence of the complex Young’s modulus of the rod and the effect of thermomechanical coupling are included in the analysis. A method of finite differences is used to directly determine the steady-state stresses and temperature without obtaining the complete time history of the process. The iterative algorithm used is very efficient and converges rapidly for a wide range of driving stress amplitudes and frequencies. It is found that rapid rise of temperature to dangerous levels occurs for relatively low values of driving stress amplitudes, especially if the driving frequency is close to one of the critical frequencies of the rod. Drastic softening of the rod leads to large strains. Thus failure of the rod could occur at low values of the driving stress.
Numerical Integration of Shell Equations Using the Field Method
Authors: Cohen G. A.
Published: November 2010

The “field method” for the numerical solution of even-order linear boundary-value problems in ordinary differential equations is formulated. This method converts the boundary-value problem into two successive initial-value problems, which may be solved by standard forward integration techniques. The method has been implemented in a computer program to calculate the static response of ring-stiffened branched shells of revolution to asymmetric loads. For such problems the field method eliminates the well-known numerical problem of “long subintervals”, as well as executing significantly faster than other numerical integration methods.
Dynamic Response of Linear Structures With Large Parameters
Authors: Dickerson J. R.
Published: November 2010

The response of a linear structure with large stiffness parameters is shown to behave as a rigid object under sufficiently smooth and bounded excitations.
The Effect of Initial Forces on the Hydroelastic Vibration and Stability of Planar Curved Tubes
Authors: Hill J. L. , Davis C. G.
Published: November 2010

The effect of initial forces on the vibration and stability of curved, clamped, fluid conveying tubes is analyzed by the finite-element technique. The tubes are initially planar with general center-line shapes approximated by constant curvature arcs. The effect of internal pressure is included. Numerical results are presented with, and without, the effects of the initial in-plane forces, for circular arcs S, L, and spiral configurations. Neglecting initial forces results in out-of-plane buckling, while including these forces prevents buckling within the elastic limit, in all configurations studied.
On Higher-Order Elastodynamic Plate Theories
Authors: Bache T. C. , Hegemier G. A.
Published: November 2010

A hierarchy of approximate elastodynamic plate theories is deduced from the three-dimensional equations of elasticity. The derivation is based upon asymptotic expansions in a parameter viewed as the ratio of plate half thickness to a dominant signal wavelength of motion. Approximate theories of any desired order of accuracy are contained in a single compact set of partial differential equations with the order of approximation determined by the order of truncation of the differential operators appearing in the equations. As examples, particular cases of free extensional and forced flexural vibrations are studied. Lower-order theories for these cases are compared to some existing approximate theories of the same order.
Modal Analysis of Floquet Waves in Composite Materials
Authors: Yang W. H. , Lee E. H.
Published: November 2010

A numerical method which admits discontinuous variable coefficients in the wave equation is employed for handling the wave propagation in composite materials. The resulting algebraic eigenvalue system is simplified by a rank–one matrix modification that reduces the computing time by at least one order of magnitude. The first five modes are accurately and efficiently computed as a demonstration of the method presented.
The Application of the Minimum Potential Energy Principle to Nonlinear Axisymmetric Membrane Problems
Authors: Tielking J. T. , Feng W. W.
Published: November 2010

The deformed configuration of nonlinear axisymmetric membranes is obtained by potential energy minimization via the Ritz method. The solution technique presented in this paper departs from the usual application of the potential energy principle in that the deformed configuration is minimizing instead of the displacement field. This approach is advantageous for problems in which the final configuration is easy to represent by a series of coordinate functions while the displacement field is complex and difficult to approximate. The potential energy functional minimized in the example problems is based on the Mooney strain-energy density for an incompressible material. In that no approximation is made in the large deformation extension ratios written in terms of final position, the solution may justifiably be compared to a numerical integration of the corresponding equilibrium equations. The energy solution is in excellent agreement with previously published solutions for the inflation of a circular membrane sheet. Solutions to two new example problems are presented.
On the Governing Equation for Quasi-Static Crack Growth in Linearly Viscoelastic Materials
Authors: Nuismer R. J.
Published: November 2010

An equation governing the initiation and growth of quasi-static fracture in a linearly viscoelastic material is derived using the thermodynamic power balance as a fracture criterion. It is found that this equation does not involve the time-dependent part of the viscoelastic material behavior but only the elastic portion. This is in direct contrast to the results obtained by Williams [1], Cherepanov [3, 4], and Knauss [5], all of whom use the same assumptions and fracture criterion as does the present paper. The apparent errors made in [1, 3-5] are pointed out and it is shown how, when the appropriate corrections are made, the results in each case become identical to those obtained in the present paper.
Large Displacement Analysis of Viscoelastic Beams and Frames by the Finite-Element Method
Authors: Yang T. Y. , Lianis G.
Published: November 2010

A finite-element displacement formulation and solution procedure are developed for the analysis of large displacement problems of viscoelastic beams and frames. The displacements considered are of the same order as the length of the beam member. The geometrical nonlinearity is accounted for by a midpoint-tangent incremental approach together with coordinate transformation at every step. The linear viscoelastic stress-strain relation in the form of hereditary integral is accounted for by the numerical integration with trapezoidal rule. Results are given for the displacements of a variety of beam and frame problems. For the simple case of cantilever beams, some alternative approximate solutions are available for comparison and reasonable agreement is indicated.
Moving Load on a Laminated Composite
Authors: Sve C. , Herrmann G.
Published: November 2010

A solution is presented for the dynamic response of a periodically laminated half plane that consists of alternating layers of two different materials and is subjected to a moving load. The laminations are parallel to the surface of the half plane, and the velocity of the load is steady and supersonic. An effective stiffness theory developed by Sun, Achenbach, and Herrmann is used to model the layered material, and the formal solution is obtained with the aid of Laplace transforms. A far-field solution is constructed with the head-of-the-pulse procedure, and several numerical examples are presented.
Transient Wave Propagation in a Symmetrically Layered Elastic Plate
Authors: Viano D. C. , Miklowitz J.
Published: November 2010

The response of a symmetrically layered plate subjected to symmetric step normal line face loads is determined. The solution, which is based on the equations of motion from linear elasticity, is obtained in the form of an infinite series of integrals with each term being the contribution from a branch of the underlying frequency equation. Through numerical analysis several of the lower branches of the frequency equation, which depend on layered plate ratios (four material and one thickness) are evaluated and used to write the transient response in the near field. Integrations based on the first five branches show the dominance of the lowest mode in the solution. Applying arguments of stationary phase to the spectrum, yields low frequency-long wave and high frequency-short wave approximations for use in obtaining the far field-long time disturbance. The former governs a front running “head of the pulse” for the layered plate, and the latter, later arriving Rayleigh and Stoneley waves.
Coupled Rocking and Translating Vibrations of a Buried Foundation
Authors: Thau S. A. , Umek A.
Published: November 2010

The plane strain model of a rigid building foundation embedded below the surface of an elastic half space is treated. The foundation is assumed to be vibrating freely with arbitrary transient time-dependences U(t) and V(t) in the horizontal and vertical directions, respectively, and to be rocking about its mass center with magnitude Ω(t). The total restraining reactions exerted upon the foundation by the surrounding medium are determined exactly during the initial time period for a P-wave to traverse the foundation base width. Thereafter the results become approximate. In this manner the coupled equations of motion for free vibrations of the foundation are obtained. A numerical example presents the impulse response matrix for U, V, and Ω. Peak responses are found to occur during the early time period where the results are exact.