0


RESEARCH PAPERS

J. Appl. Mech. 1976;43(4):531-536. doi:10.1115/1.3423924.

The analysis contains the derivation and a solution method for six nonlinear differential equations of motion which describe the c.g. position and orientations of the principal axes of a spinning discus moving in air. The aerodynamic pressure on the discus is obtained from existing experimental data on inclined plates and disk-shaped bodies; the effect on the moment due to the spinning motion is derived from the classical hydrodynamics of a rotating ellipsoid in a flow field. A case study, analyzed in the context of the 1972 World Olympics discus throw (which recorded 64.39 m or 211 ft 3 in.), showed that a fast-spinning discus will go farther than one not spinning by 13.8 m in this range. The optimum angle and optimum initial discus inclination are 35° and 26°. This combination of angles is found to be superior to the commonly accepted combination of 35° and 35°. The 35°/26° combination produced a gain in distance of 1.55 m over the 35° /35° combination. The results of the analyses presented here, including the effect of wind, agree closely with the experience of expert discus throwers.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):537-542. doi:10.1115/1.3423925.

The combined effects of convection and diffusion for dispersion on mass transport in fully developed laminar flow through circular tubes are investigated. The present method, which in general may be used to yield solutions at any arbitrary dimensionless time, in its zeroth-order approximation is identical to Taylor’s analysis for the average concentration. Solutions to the basic differential equation for an initial input of solute either concentrated at a section of the tube or uniformly distributed in the form of a slug of finite axial extension are developed. Numerical results for the former input are presented over a large range of dimensionless time and Peclet numbers. The time limitations of Taylor’s solution and Lighthill’s small time approximation [15] are placed on more reliable quantitative bases by comparison with the present calculations.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):543-547. doi:10.1115/1.3423926.

The production and dissipation of energy in a two-phase model for particle-fluid turbulent flow is considered. For plane parallel mean flow use of several scaling arguments yields a balance between production and drag dissipation for the particles, and between production and viscous dissipation for the fluid. A simple particle motion model is used to obtain estimates of the drag dissipation. Energy balance considerations are made for situations where drag reduction by the addition of particles is observed. Significant drag reduction is found to occur for sufficiently large Reynolds number. Discussion of the extra effectiveness of polymers for drag reduction is given within the framework of energy balance.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):548-550. doi:10.1115/1.3423927.

The energy stability limit is calculated for flow in a curved channel due to a pressure gradient acting around the channel. The energy limit is found among transverse disturbances and is of the same order for all channel radius ratios. The difference between the previously available linear limit and the energy limit increases dramatically as the instability mechanism changes, with radius ratio, from centrifugal force to viscosity in the limiting plane Poiseuille flow case.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):551-554. doi:10.1115/1.3423928.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):555-558. doi:10.1115/1.3423929.

Analysis is made of a transient, fully developed, laminar flow of an incompressible fluid in a porous, parallel-plate channel. The crossflow through the plates is uniform, but is allowed to vary with time. In addition to a pressure gradient due to pumping, the flow is also under the inducement of the motion of one of the plates. Numerical results are obtained through the (final or nonfinal) use of the finite Fourier sine transform. Asymptotic flow patterns showing transient boundary layers are investigated. Finally, the formation of the flow from the start is described in physical terms.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):559-563. doi:10.1115/1.3423930.

Experimental measurements of the time scale τ(t ) of the burst phenomenon are reported for laminar-transitional turbulent, fully developed, pulsatile flow in a channel. Theoretical predictions for τ(t ) which are developed on the basis of a quasi-steady surface renewal formulation are shown to be in good agreement with the data.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):564-566. doi:10.1115/1.3423931.

The problem of describing the boundary layer existing inside a conical surface due to the presence of a swirling flow passing through the cone is considered. Approximate solutions based upon the Karman-Polhausen method are obtained for both the laminar and the turbulent cases. The results obtained are in close agreement with known solutions previously obtained in the limits of swirl with no throughflow and throughflow with no swirl. The present results appear to be valid over the entire range of swirl to throughflow ratios.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):567-570. doi:10.1115/1.3423932.

Turbulent boundary-layer behavior in the vicinity of a right-angle corner formed by intersecting flat plates is considered. Due to interference effects a secondary flow is induced. Numerical solutions are obtained for the main stream and secondary motion. Models with and without intermittency factors are considered. It is shown that the secondary motion is significantly different for laminar and turbulent conditions. Similar behavior has previously been observed experimentally.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):571-574. doi:10.1115/1.3423933.

An analysis of the inertial wave eigenfrequencies of a rapidly rotating liquid in a cylinder whose cross section is divided into four 90 deg sectors reveals that only if the cylinder height is less than the cylinder diameter can the fundamental frequencies be of the order of magnitude of the frequencies of spin-stablilized projectiles. Hence, sectoring the usual long cavities in liquid-filled, spin-stabilized projectiles will preclude the occurrence of a “Stewartson” resonance.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):575-578. doi:10.1115/1.3423934.

The creeping motion of an aerosol aggregate composed of two touching spheres is investigated. A continuum-slip theory, suitable for small values of Knudsen number, is developed. The drag on a pair of equal spheres moving along their line of centers is determined. For vanishing Knudsen number, this drag reduces to Faxén’s result. Theoretical results for the effect of small Knudsen number are compared with an approximate expression based on calculations for separated spheres.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):579-583. doi:10.1115/1.3423935.

A viscous fluid lies between two parallel plates which are being squeezed or separated. If the normal velocity is proportional to (1 − αt)−1/2 the unsteady Navier-Stokes equations admit similarity solutions. The resulting nonlinear ordinary differential equation is governed by a parameter S which characterizes unsteadiness. Asymptotic solutions for small S and for large positive S are found which compare well with those obtained by numerical integration. It is found that the resistance is proportional to (1 − αt)−2 but is not necessarily opposite to the direction of motion.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):584-588. doi:10.1115/1.3423936.

The method of multiple scales is used to derive two partial differential equations which describe the evolution of two-dimensional wave-packets on the interface of two semi-infinite, incompressible, inviscid fluids of arbitrary densities, taking into account the effect of the surface tension. These differential equations can be combined to yield two alternate nonlinear Schrödinger equations; one of them contains only first derivatives in time while the second contains first and second derivatives in time. The first equation is used to show that the stability of uniform wavetrains depends on the wave length, the surface tension, and the density ratio. The results show that gravity waves are unstable for all density ratios except unity, while capillary waves are stable unless the density ratio is below approximately 0.1716. Moreover, the presence of surface tension results in the stabilization of some waves which are otherwise unstable. Although the first equation is valid for a wide range of wave numbers, it is invalid near the cutoff wave number separating stable from unstable motions. It is shown that the second Schrödinger equation is valid near the cutoff wave number and thus it can be used to determine the dependence of the cutoff wave number on the amplitude, thereby avoiding the usual process of determining a new expansion that is only valid near the cutoff conditions.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):589-593. doi:10.1115/1.3423937.

Geometric optics, or the ray theory, is used to investigate the effect of pulse reflection and transmission at a curved fluid-solid interface. In particular, the problem of a plane pressure pulse, supported by an acoustic fluid, impinging on a plane symmetrical elastic body whose cross section is delineated by circular arcs is considered. The response of the solid is determined along its center line to reflection at the back interface with another fluid. Consideration of the special case in which the fluid densities are zero indicates that special care must be exercised in dealing with the in vacuo problem, and particularly in specifying the boundary conditions in that instance.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):594-598. doi:10.1115/1.3423938.

The time-dependent filtration of liquid through the wall of a soft, porous tube can be quite unlike that of a hard, porous tube. Under conditions described, the seepage is limited to thin layers near each surface, and in one of these layers, liquid seepage proceeds in a direction opposite to the sense of the applied pressure drop across the tube wall. This occurs because it is impossible to produce isotropic contact stress in the solid if kept at constant volume by the slowness of seepage. The liquid must then bear the entire isotropic stress.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):599-602. doi:10.1115/1.3423939.

One version of the surface integral method has been used to obtain the solutions of two-dimensional elasticity problems of the infinite strip with periodically spaced holes. Numerical results are presented and generalization to the case of a layered strip is obtained.

Topics: Strips , Elasticity
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):603-607. doi:10.1115/1.3423940.

The solution is obtained for both smooth and bonded contact between the strip and half plane of different elastic materials. First, the problems are reduced to singular integral equations of the second kind. Then the order of the stress singularity at the corners is extracted from the integral equations and numerical solutions are obtained. Interface normal and shearing stress are exhibited graphically for several material combinations.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):608-612. doi:10.1115/1.3423941.

The solution for a point force applied at the interior of an infinite transversely isotropic solid is obtained by introducing three potential functions which govern the displacements. Unlike previous publications where the solutions are expressed in different forms depending on the conditions satisfied by the elastic constants, the present paper provides a systematic approach to obtain a unified solution which is applicable for all stable transversely isotropic materials. The expression obtained does not have the deficiency suffered by previous solutions, namely, each individual term in the present expression does not tend to infinity on the z -axis. Thus accurate numerical evaluation of the Green’s function can be directly performed without the need to resolve the singularity algebraically.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):613-618. doi:10.1115/1.3423942.

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

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):619-624. doi:10.1115/1.3423943.

A new axisymmetric plasticity theory of fibrous composites which was developed by the authors is applied to problems involving large uniform thermal changes. The determination of loading surfaces and internal microstress fields is described. To verify the accuracy of the theory, a simulation of the T6 temper, followed by uniaxial extension of a W-Al composite has been made. The resulting microstresses show an excellent agreement with available experimental magnitudes measured in situ by an X-ray technique. In addition, there is a very satisfactory agreement with results obtained by the finite-element method.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):625-629. doi:10.1115/1.3423944.

In this paper we consider a problem of the response of an elastic half space subjected to an antiplane shear load. The load is suddenly applied and thereafter moves in an interval reciprocally as a trigonometric function of time. An analytical solution for the displacement is obtained in terms of single integration. It is shown that the discontinuity in the displacement occurs only for the case that the initial (maximum) speed of the load is greater than the speed of SH-wave. In this case the displacement has a finite jump on the leading wave front and a logarithmic discontinuity immediately behind the wave front which emanates from a point where the load speed comes up with SH-wave speed. Numerical calculations are carried out for several cases of the initial (maximum) speed of the load and are shown graphically.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):630-632. doi:10.1115/1.3423945.

Similarly to elasticity, it is useful to classify contacts between viscoelastic bodies by comparing the regions of contact in the loaded and load-free states. General properties are obtained for the class of contacts in which the contact region does not exceed the natural (load-free) contact. The displacements, strains, and stresses in such problems are proportional to the level of the loading history, but the scaling of load histories leaves the contact region unaltered. The results are valid within linear viscoelasticity, either quasi-static or dynamic. Additional properties are derived for plane contact problems in quasi-static viscoelasticity when the contact is monotonically receding.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):633-638. doi:10.1115/1.3423946.

The nonlinear problem of a spherical cavity surrounded by an infinite elasto-plastic medium, and subjected to uniform radial loads, is considered. The material is assumed to be incrementally elasto-plastic. No restriction on the magnitude of the deformation and stress is imposed. For the cases of internal or external pressure, the governing nonlinear differential equations are solved in terms of closed integrals. Numerical results obtained for some metals are also shown.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):639-644. doi:10.1115/1.3423947.

Rapid cycling solutions are presented for a simple two-bar structure subjected to variable temperature. Three constitutive relationships are considered, nonlinear viscous, strain-hardening and Bailey-Orowan models which describe differing aspects of the creep of metals. It is shown that the solutions for the viscous and strain-hardening relations are essentially similar and possess distinct reference stress histories over ranges of the governing parameters. The presence of recovery in the Bailey-Orowan model causes a distinctly different mode of behavior. Experimental results on a simulated two-bar structure are presented, under conditions where the strain-hardening hypothesis may be expected to be most relevant. Good agreement is obtained between theory and experiment although the presence of anelastic creep, with a short time scale, tends to reduce the effective thermoelastic stresses.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):645-651. doi:10.1115/1.3423948.

The notion of Plastic Internal Variables (PIV ) is used in reformulating, in a general form, the equations of rate-independent plasticity. The stress, temperature, and the PIV are the state variables for the present development. Loading-unloading is defined in terms of the usual loading function of classical plasticity. The concept of discrete memory parameters entering the constitutive equations for the PIV is introduced, in order to describe realistically the material behavior under cyclic loading. Within the framework of the general development, a simple model is constructed. By generalizing uniaxial experimental observations the concept of the “bounding surface” in stress space is introduced, defined in terms of appropriate PIV. This surface always encloses the yield surface, and their proximity in the course of their coupled translation and deformation in stress space during plastic loading determines an appropriate quantity function of the state variables and a corresponding discrete memory parameter on which the value of the plastic modulus depends. The model is compared with experimental results in a uniaxial case.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):652-656. doi:10.1115/1.3423949.

The problem of adhesively bonded sheets, one of which is cracked, is formulated by the utilization of integral transform methods. The objective of the investigation is to calculate the stress-intensity factor at the crack tip for the cracked sheets. Results are obtained when the cracked sheet has a single crack and an array of identical, equally spaced, coplanar cracks. Results tend to indicate that the growth of crack implies a reduction in the stress-intensity factor.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):657-662. doi:10.1115/1.3423950.

A pressurized, shallow, elastically isotropic shell containing a crack is considered. The crack is assumed to lie along a line of curvature of the midsurface. The equations governing the essentially equivalent residual problem, in which the only external load is a uniform normal stress along the faces of the crack, are reduced via Fourier transforms to two coupled singular integral equations. The solutions of these equations depend on three parameters: λ , a dimensionless crack length, κ, the dimensionless Gaussian curvature of the midsurface at the center of the crack, and ν, Poisson’s ratio. Perturbation solutions for small values of λ are obtained by expanding the kernels of the integral equations in series. Explicit formulas for stretching and bending stress-intensity factors are obtained. These represent the first-order corrections due to curvature effects of the well-known flat plate results. The connection with the work of Copley and Sanders for cylindrical shells and Folias for spherical and cylindrical shells is indicated.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):663-667. doi:10.1115/1.3423951.

This paper is concerned with obtaining stress estimates for the problem of axisymmetric torsion of thin elastic shells of revolution subject to self-equilibrated end loads. The results are obtained in the form of explicit pointwise stress bounds exhibiting an exponential decay with distance from the ends, thus supplying a quantitative characterization of Saint-Venant’s principle for this problem. In contrast to arguments using energy inequalities, here we apply a technique, recently developed by the authors, based on the maximum principle for second-order uniformly elliptic equations.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):668-670. doi:10.1115/1.3423952.

In the following a numerical solution is given for the vibration of an orthotropic layered cylindrical viscoelastic shell in an acoustic medium. The acoustic fluid is modeled through a finite-difference scheme. Numerical results for the elastic shell in an acoustic medium agree with previous solutions.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):671-674. doi:10.1115/1.3423953.

An additional solution is obtained for the vibrational behaviour of a uniform, simply supported Timoshenko beam. The characteristics of the mode are explained in physical terms.

Topics: Vibration , Deflection
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):675-680. doi:10.1115/1.3423954.

The response of a string to a mass particle undergoing a constant horizontal acceleration from rest has been calculated. The string deflection is expressed in terms of the transverse mass motion. A delay-differential equation is solved both numerically and asymptotically for the mass velocity. String profiles are presented at subsonic and supersonic speeds. Two oppositely traveling jumps in string displacement are found to appear as the mass is accelerated through the wave speed of the string.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):681-683. doi:10.1115/1.3423955.
Abstract
Topics: Cables
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):684-688. doi:10.1115/1.3423956.

The theory of Ritz is applied to the equation that Hamilton called the “Law of Varying Action.” Direct analytical solutions are obtained for the transient motion of beams, both conservative and nonconservative. The results achieved are compared to exact solutions obtained by the use of rigorously exact free-vibration modes in the differential equations of Lagrange and to an approximate solution obtained through the application of Gurtin’s principles for linear elastodynamics. A brief discussion of Hamilton’s law and Hamilton’s principle is followed by examples of results for both free-free and cantilever beams with various loadings.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Appl. Mech. 1976;43(4):689-690. doi:10.1115/1.3423957.
Abstract
Topics: Deformation
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):692-694. doi:10.1115/1.3423959.

The vibration of an elliptic ring clamped along two confocal ellipses was studied by McLachlan some time ago. Due to complexities in the computations of Mathieu functions, numerical results were not available. In this Note the fundamental frequencies of clamped ring membranes with a fixed area enclosed between two confocal ellipses of various eccentricities are computed. Results are presented in a tabulated form.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):694-695. doi:10.1115/1.3423960.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):695-697. doi:10.1115/1.3423961.
Abstract
Topics: Stress , Cylinders
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):697-698. doi:10.1115/1.3423962.
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):698-699. doi:10.1115/1.3423963.

The paper presents a definition of a finite rotation and a concise vector expression for the displacement vector associated with the rotation.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

BOOK REVIEWS

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):701-702. doi:10.1115/1.3423968.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1976;43(4):702. doi:10.1115/1.3423969.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster

ERRATA

Commentary by Dr. Valentin Fuster

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In