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RESEARCH PAPERS

J. Appl. Mech. 1960;27(4):603-608. doi:10.1115/1.3644067.

A method is described for solving certain problems of subsonic aerodynamic design where flow boundaries in the physical plane are required to have specific dynamic characteristics. The method is tested on two type-problems with known exact solutions: the two-dimensional gas jet and the flow in the neighborhood of stagnation points. It has been found to give the solution with a degree of accuracy acceptable for practical design.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):609-612. doi:10.1115/1.3644068.

An analytical study of the compressibility effects on the characteristics of two-dimensional slider bearings is made. By the variational method, it is shown that, for a given bearing length, no optimal film shape of the bearing can be found to yield a maximum total load. Analysis of the numerical results carried out for stepped films with a compressible lubricant under isothermal compression or expansion indicates that this anomaly is due to the nonlinear nature of the compressible problem. By considering a modified variational problem, it is further shown that stepped-film bearings with isothermal lubricant still yield the maximum total load for a given mass flow rate passing through the bearings, but the exact shape of the optimal stepped film is found to depend on the value of the maximum pressure.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):613-616. doi:10.1115/1.3644069.

A simple analytical expression is derived which predicts the effect of mass transfer on countercurrent heat transfer to a vaporizing body. In this theory, the fluid stream is assumed to be inviscid and of constant thermal conductivity. The inviscid theory correlates well with heat-transfer data without mass transfer and is believed to predict heat-transfer rates fairly accurately at high mass-transfer rates.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):617-622. doi:10.1115/1.3644070.

This paper presents a theoretical solution for transient heat conduction in a rod of finite length with variable thermal properties. A numerical procedure is developed and the results of one example are presented and compared with the corresponding solution for the case of constant properties. Application to the problem of determination of thermophysical properties is discussed briefly.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):623-628. doi:10.1115/1.3644072.

Transient temperatures in a coaxially moving tube and a stationary rod resulting from a step change in the rate of energy generation within the rod are obtained. For the small values of time, the use of finite Hankel transforms reduces the problem to the solution of an integrodifferential equation. In the solution of this equation, Laplace transforms have been used considering the convolutive property of the kernel involved. For the large values of time, this method is not convenient, and the asymptotic behavior of the temperature functions is given by means of the classical approach which requires the use of Laplace transforms. For a given time, it is found that the interface temperature gradient is inversely proportional to the axial distance.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):629-634. doi:10.1115/1.3644073.

In this paper, a method is presented for obtaining the transient thermal-stress distribution and the residual stresses in a spherical body where the time-dependent temperature distribution is symmetrical with respect to the center of the sphere. The material is assumed to be elastoplastic, while in the plastic range it work-hardens isotropically. The von Mises yield condition is used. The thermal and mechanical properties of the material are assumed to be temperature independent. The problem is reduced to a single nonlinear differential equation which is solved numerically on the NCR 304 digital computer. Several sets of numerical data representing various degrees of work-hardening in the spherical bodies during a cooling process are presented.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):635-639. doi:10.1115/1.3644074.

The linear thermoelastic problem is solved for a uniform heat flow disturbed by a hole of ovaloid form, which includes the ellipse and circle as special cases. Results for stress and displacement are found in closed form, by reducing the problem to one of boundary loading solvable by a method of Muskhelishvili.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):640-643. doi:10.1115/1.3644075.

Many physical systems exhibit hysteresis which may be adequately described by a bilinear hysteresis model. This paper considers the response of such a system to sinusoidal excitation. It is shown that the system exhibits a soft-type resonance with stable, single-valued response curves. For such a system it is shown that there exists a critical value of the excitation, above which unbounded resonance occurs.

Topics: Resonance
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):644-648. doi:10.1115/1.3644076.

A first-order nonlinear solution is presented for the problem of forced sinusoidal oscillations of a semi-infinite bar exhibiting weak bilinear hysteresis.

Topics: Oscillations
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):649-652. doi:10.1115/1.3644077.

An analysis is made of the response of a system with bilinear hysteresis to random excitation. It is shown that for moderately large inputs, the additional damping created by the bilinear hysteresis decreases the mean squared deflection compared with that for a linear system with the same viscous damping. However, for large inputs, the decrease in the stiffness of the system due to the bilinear hysteresis causes the mean squared deflection to increase over that for the equivalent linear system.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):653-662. doi:10.1115/1.3644078.

Previous treatment of vibration of elastic sandwich plates [1–6] is extended in this paper to the vibration study of sandwich cylindrical shells. General theory is developed. Simplified equations are applied to the investigation of axially symmetric and torsional vibrations.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):663-668. doi:10.1115/1.3644079.

Making use of the field equations of elasticity, the frequency equation is derived for the free, transverse vibrations of a solid elastic mass contained by an infinitely long, rigid, circular-cylindrical tank. This frequency equation relates the natural circular frequencies and Poisson’s ratio. This relationship is plotted revealing a very interesting steplike variation of the natural frequency with Poisson’s ratio. Displacement fields are plotted for two natural frequencies in each of the first three modes.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):669-676. doi:10.1115/1.3644080.

The determination of the natural frequencies and normal modes of vibration for continuous panels, representing more or less typical fuselage skin-panel construction for modern airplanes, is discussed in this paper. The time-dependent boundary conditions at the supporting stringers are considered. A numerical example is presented, and analytical results for a particular structural configuration agree favorably with available experimental measurements.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):677-680. doi:10.1115/1.3644081.

The validity of the classical treatment of problems involving axisymmetric plates, partially constrained from deflection by the presence of a smooth, rigid, plane surface, is re-examined, and both the practical and conceptual advantages of carrying the analysis within the scope of the E. Reissner plate theory are illustrated by means of an example.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):681-689. doi:10.1115/1.3644082.

The problem solved is that of an infinite plate subjected to a suddenly applied concentrated transverse shear load. The solution is derived from a plate theory that incorporates, in addition to bending, the effect of shear force and rotatory inertia on the deflection. These added effects give the present theory true wave character along with greater accuracy in the waves predicted. Numerical evaluation of the solution brings out the effects of dispersion and distortion on the moment and shear-force response of the plate. A criterion is developed for judging the accuracy of this response. It is based on a comparison, employing the stationary phase method, of the present approximate and exact (three-dimensional) theories.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):690-695. doi:10.1115/1.3644083.

This investigation is concerned with the propagation of axisymmetric stress waves in unlimited thin shallow elastic spherical shells. In particular, a solution is obtained for an unlimited shallow spherical shell subjected to a harmonically oscillating concentrated load at the apex. This solution, exact within the scope of the linear theory of shallow shells, has an outward propagating wave character in the entire range of forcing frequency. Appropriate expressions for the mechanical impedance and the energy input are derived, and numerical results are obtained for the axial displacement corresponding to various forcing frequencies.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):696-700. doi:10.1115/1.3644085.

A right circular conical shell of edge angle α is subjected to a concentrated load Q directed along the axis. The collapse load is found to be Q = 2πM0 cos2 α, independently of the size or support conditions of the shell. Some solutions are also obtained for the case where the load is distributed over a finite area. Bounds are found on the collapse load of a general rotationally symmetric shell under a concentrated load.

Topics: Shells , Stress , Collapse
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):701-709. doi:10.1115/1.3644086.

First and second-order moments of the stress tensor are obtained for the elastostatic problem concerning the half-plane subjected to random boundary tractions. The cases treated include the following types of applied surface tractions: (a) A purely random Gaussian load (white noise); (b) concentrated loads of random magnitudes separated by equal intervals; (c) a concentrated load acting at a random location; and (d) concentrated loads of equal magnitudes separated by random intervals.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):710-716. doi:10.1115/1.3644087.

A formal integral transform solution is obtained for the response of an elastic half-space to a radially symmetric pressure signature of variable pressure and variable velocity. An asymptotic approximation to this solution is developed and expressed in terms of the known solution for the response of a half-space to a two-dimensional pulse moving with constant velocity plus a correction that is important only if the blast-wave speed directly above the point of observation is close to the Rayleigh-wave speed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):717-725. doi:10.1115/1.3644088.

An experimental investigation was undertaken to determine the force-indentation relations governing the contact of hard-steel balls and plane surfaces of various metals both under static and dynamic conditions, the latter involving the Hopkinson-bar technique, with maximum elastic strain rates of 500 sec−1 . Excellent correlation was obtained between the measured permanent crater diameter at the contact point and that calculated from strain-gage data by means of an equation treating the bar as a one-dimensional member. A comparison also was effected between the static and dynamic force-indentation curves, the Hertz law of contact, and a relation based upon the concept of a constant flow pressure in the plastic regime.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):726-732. doi:10.1115/1.3644089.

Boussinesq-Papkovich potentials are used in conjunction with the bispherical co-ordinate system to analyze three problems in the classical theory of linear elasticity: (a) The extension of the Boussinesq point-load problem to that in which the half-space contains a spherical cavity; (b) the determination of the stress distribution in an eccentric spherical shell under uniform internal pressure; (c) the determination of the stress distribution in a half-space containing a uniformly pressurized spherical cavity. Numerical results are presented for representative configurations and load distributions in each case.

Commentary by Dr. Valentin Fuster

DESIGN DATA AND METHODS

J. Appl. Mech. 1960;27(4):733-734. doi:10.1115/1.3644090.
Abstract
Topics: Thickness
Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Appl. Mech. 1960;27(4):735-737. doi:10.1115/1.3644091.
Abstract
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):739-740. doi:10.1115/1.3644093.
Abstract
Topics: Vibration
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):740-743. doi:10.1115/1.3644094.
Abstract
Topics: Aluminum , Absorption , Tubing
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):743-744. doi:10.1115/1.3644095.
Abstract
Topics: Vibration , Shells
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):744-746. doi:10.1115/1.3644096.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):747-748. doi:10.1115/1.3644097.

An approximate solution is derived for the pressure ratio in high-speed subsonic flow through constant-cross-section circular tubes with friction and heating. The results are compared with those obtained from an accurate numerical calculation. The gas used is air. A wide range of variables such as temperature ratio, exit Mach number (up to 0.90), tube length-to-diameter ratio, and shape of the power distribution function is examined. The derived expression is found to be quite accurate in all cases.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):749-750. doi:10.1115/1.3644098.

A simple boundary-layer approximation formula is derived for the temperature distribution in liquid metal which flows past a porous flat plate at zero incidence at velocity U and is sucked into it at velocity V.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

BOOK REVIEWS

J. Appl. Mech. 1960;27(4):759. doi:10.1115/1.3644121.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):759-760. doi:10.1115/1.3644122.
FREE TO VIEW
Abstract
Topics: Evaporation
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1960;27(4):760. doi:10.1115/1.3644123.
FREE TO VIEW
Abstract
Topics: Aerodynamics
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

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