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RESEARCH PAPERS

J. Appl. Mech. 1961;28(4):481-490. doi:10.1115/1.3641772.

The simple linearized transonic flow theory as originally proposed by Oswatitsch and Keune [1] and by the present authors [2] is improved by considering and partially correcting its error. In this manner a theory which is easy to apply and which should be valid for a great number of smooth bodies is obtained. This improved theory predicts shock waves in the lower transonic regions. It is applied to a number of significant body and airfoil shapes and its predictions are compared with experiments and results of other theoretical investigations.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):491-496. doi:10.1115/1.3641773.

The free oscillations of a fluid in a rotating, axially symmetric container are investigated under the assumption that the equilibrium motion of the fluid be a rigid-body rotation. Gravitational forces are neglected. The resulting boundary-value problem leads to an elliptic or hyperbolic partial differential equation, depending on the frequency/angular velocity ratio. The problem is solved for a cylindrical container and discussed exhaustively. Due to the Coriolis force, there exist modes with the radial velocity component vanishing inside the fluid (“nodal cylinders”), besides the usual nodes in axial and azimuthal direction. The oscillations in the neighborhood of critical container dimensions are analyzed. Numerical results are presented in graphs.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):497-506. doi:10.1115/1.3641774.

By assuming oil viscosity constant, Reynolds’ equation for journal bearings has been solved in a manner similar to Hill’s method. Two approximate solutions using E. O. Waters’ method and Ritz’s method have been added. Numerical computations have been carried out for a centrally supported 120-deg bearing with a unity slenderness ratio. Isobarriers have been determined from the pressure distributions. In order to show a justification for assuming the viscosity constant, the Reynolds equation was solved for the infinitely long bearing with variable viscosity, and the solution compared with that of Sommerfeld.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):507-510. doi:10.1115/1.3641775.

Previously, solutions of the problem of the Rayleigh-type bearing with a step which is not straight have involved the use of the electrolytic tank or the use of relaxation methods, both of which are somewhat inconvenient as compared with the approximate analytical method described in this paper. The solution of the derived differential equation is in the form of a convergent infinite series, but for rapid computation it is shown that an economized series (the τ method for the solution of linear differential equations) yields results of high accuracy.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):511-518. doi:10.1115/1.3641776.

The present study deals with torque and cavitation characteristics of idealized two-dimensional and axially symmetrical butterfly valves. Theoretical results obtained for the two-dimensional case are compared with the ones obtained experimentally and by a relaxation technique. Based on the results of the two-dimensional case, an approximate solution is presented for the more general and practical case of three-dimensional butterfly valves. The results are in good agreement with the actual flow tests.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):519-528. doi:10.1115/1.3641777.

A steel bullet in the form of a right circular cylinder which strikes a 10-mil-thick plane lead target at 45 deg incidence and at 2700 fps acquires on its front surface a series of corrugations, or waves, approximately 10 mils in amplitude and 40 mils in wave length. This phenomenon is investigated from a hydrodynamic point of view and it is found that similar waves develop at much lower velocities with materials which are viscous liquids under ordinary conditions. A mechanism of wave formation based on a hydrodynamic instability is presented.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):529-534. doi:10.1115/1.3641778.

Elastic-plastic design permits the most effective use of the strength of the rectangular tube section. The condition of failure for a tube of perfectly elastic-plastic material is analyzed, and a formula is derived from which the limit load can be computed directly, A procedure is developed for determining by the area-moment method the wall deflection at any load from a bending-moment diagram modified to account for reduced rigidity. The total deflections thus found are plotted against the various loads. This theoretical load-deflection curve then becomes the basis for design.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):535-543. doi:10.1115/1.3641779.

This paper presents numerical solutions of the Reynolds equation for finite length, gas-lubricated cylindrical journal bearings under static loading (this corresponds to a load of constant magnitude and direction with respect to the bearing). It is shown that the incompressible results are but only limiting cases to the more general compressible solutions. The results of the two solutions are dovetailed together through the use of two dimensionless parameters: the inverse of the Sommerfeld number and the compressibility number. Comparisons of the iterative solutions and the first-order perturbation and the “linearized ph” methods are made. The advantages and disadvantages of these methods of analysis are discussed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):544-550. doi:10.1115/1.3641780.

Knowledge of stress concentration is very important for engineers in many practical cases. But the stress-concentration factors for Hooke’s law often cannot be used because most technical materials have stress-strain laws deviating from Hooke’s law. In the second edition of his book “Kerbspannungslehre” the author gave a calculation method for a special nonlinear deformation law. In the present paper a general theory for arbitrary stress-strain laws is established which leads to a calculation method for the real values of the concentrated stresses in the material.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):551-556. doi:10.1115/1.3641781.

A class of systems of coupled Hill’s equations is studied. It is shown that for systems of equations in this class, completely decoupled Hill’s equations may be obtained and the stability of the solutions may be studied in a very much simpler manner. Several physically significant problems are treated to demonstrate the nature of the method.

Topics: Equations , Stability
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):557-562. doi:10.1115/1.3641782.

A numerical solution is obtained for the nonlinear equations for clamped, shallow spherical shells under external pressure. Results are presented in the postbuckling range which have not been computed previously. The upper and lower buckling pressures are compared with the experimental data of Kaplan and Fung.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):563-566. doi:10.1115/1.3641783.

This paper analyzes the transient response of a simple harmonic oscillator to a stationary random input having an arbitrary power spectrum. The application of the results of this analysis to the response of structures to strong-motion earthquakes is discussed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):567-570. doi:10.1115/1.3641784.

The stability of uniform rotation of a rigid body about a principal axis of inertia is analyzed for the case where there is a diametral inertia inequality and there is an elastic restoring mechanism with a diametral stiffness inequality which rotates with the body. This model is an idealization for systems such as a two-bladed propeller rotating on a flexible shaft whose stiffness characteristics are not rotationally symmetric. It is found that many such systems possess unstable speed ranges. The instability may be due to either type of asymmetry alone or due to the interaction of the two. Quantitative analytical results are obtained which relate the unstable speed range to the gyroscopic coupling, the inertia inequality, the stiffness inequality, and the relative orientation of the principal axes of inertia with respect to the principal axes of stiffness. Three-dimensional stability surfaces are plotted to give a qualitative overview of the interplay of the various parameters.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):571-573. doi:10.1115/1.3641785.

Torsional-vibration modes are uncoupled from the bending and extensional modes in thin shells of revolution. The solution for the uncoupled torsional modes then depends upon a linear second-order differential equation. The governing equation is subsequently solved for the frequencies of a conical shell. A tabulation of the first five frequencies for varying ratios of the terminal radii is presented. These frequencies are identical to those of an annular plate which has the same supports as the conical shell.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):574-578. doi:10.1115/1.3641786.

A general method for obtaining the differential equations governing motions of a class of nonholonomic systems is presented. Several supplementary theorems are stated, and the use of the method is illustrated by means of two examples.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):579-584. doi:10.1115/1.3641787.

New frequency and normal mode equations for flexural vibrations of six common types of simple, finite beams are presented. The derivation includes the effect of rotatory inertia and transverse-shear deformation. A specific example is given.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):585-590. doi:10.1115/1.3641788.

A method is presented for calculating the lateral vibration characteristics of rotating systems and establishes improved criteria for design. The method is also applicable to the vibration analysis of interconnected beam systems which are nonrotating and lying in a single plane. This first part restricts itself to the development of the method of analysis. A companion paper describes the experiences related to the computer program and to some of the applications of the method since 1957.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):591-600. doi:10.1115/1.3641789.

A description is given of computer programs based on Part 1 of this paper, and some of the results of using those programs are presented.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):601-607. doi:10.1115/1.3641790.

The method of birefringent coatings for the determination of elastic and plastic surface strains of opaque bodies like metals assumes perfect elasticity of the coating material. In reality the coating, assumed much softer than the metal, presents the problem of a general viscoelastic layer under prescribed boundary displacements (at the metal-plastic interface). As already shown, this problem is greatly simplified for isotropic linear viscoelastic coatings, for small strains, for a linear law of strain birefringence, and for interface displacements expressed as a product of a function of space co-ordinates by a time function. The obviously advantageous stress-strain-optical linearity was experimentally verified in pure and in plasticized epoxy resins which make the best coatings. Tests were carried out in uniaxial loading and in shear, in creep, as well as in relaxation. The main conclusion is that the pure epoxy resins show negligible inelasticity, and the plasticized have a linear photo-viscoelastic behavior. Explicit laws were fitted to the creep and relaxation curves. Tests were also carried out with deeply notched coated steel bars deformed in the plastic range. The variation of fringe pattern with time was found to be negligible for the pure epoxy resins and to diminish slightly and proportionally with time throughout the model for the plasticized resins.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):608-610. doi:10.1115/1.3641791.

When a load, for instance a heavy roller, moves slowly along the surface of a solid mass of soft material, a “hump” deformation is often observed to precede it. The process of formation from an initially level surface, and the final form of hump established, are investigated analytically for a purely viscous material, in two-dimensional motion. It becomes evident that a material showing nonlinear creep, or a viscoelastic material, would show qualitatively similar behavior, the simple viscous model being adequate to exhibit the essential qualitative features.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):611-617. doi:10.1115/1.3641792.

The problem of a rigid cylinder rolling on the surface of a viscoelastic solid is solved in an approximation in which inertial forces are neglected. With the introduction of viscoelastic effects, the symmetry associated with the corresponding elastic problem is destroyed, and in particular the cylinder motion is impeded by a resistive force. For a standard linear solid, the resulting coefficient of friction, a function of the rolling velocity V, tends to zero for small and large values of V, and attains a single maximum at an intermediate value.

Commentary by Dr. Valentin Fuster

DESIGN DATA AND METHODS

J. Appl. Mech. 1961;28(4):618-623. doi:10.1115/1.3641793.

This paper deals with the determination of the stress distribution at the fillet of a flange attached internally to a hollow cylinder. A load parallel to the axis of the cylinder and of variable eccentricity acts on a bearing plate which rests on the flange. The strains are measured by means of electrical resistance wire strain gages. The ratios of the mean cylinder diameter to the cylinder wall thickness and of the mean cylinder diameter to the flange thickness are varied. The principal stresses at the fillet are given as functions of these parameters. The experimental results are compared with the stresses calculated on the basis of an approximate theoretical solution for both an axial and an eccentric load.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Appl. Mech. 1961;28(4):624-627. doi:10.1115/1.3641794.
Abstract
Topics: Vibration
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):628-631. doi:10.1115/1.3641795.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):631. doi:10.1115/1.3641796.
Abstract
Topics: Disks
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):633. doi:10.1115/1.3641797.
Abstract
Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):636. doi:10.1115/1.3641802.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster

BOOK REVIEWS

J. Appl. Mech. 1961;28(4):637. doi:10.1115/1.3641804.
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Abstract
Topics: Motion
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):638. doi:10.1115/1.3641805.
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Abstract
Topics: Feedback
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):638. doi:10.1115/1.3641806.
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Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):638-639. doi:10.1115/1.3641807.
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Abstract
Topics: Space flight
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):639. doi:10.1115/1.3641808.
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Abstract
Topics: Solids
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):639. doi:10.1115/1.3641809.
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Abstract
Topics: Kinematics , Linkages , Design
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):639-640. doi:10.1115/1.3641810.
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Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):640. doi:10.1115/1.3641811.
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Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):640. doi:10.1115/1.3641812.
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Abstract
Topics: Fluid dynamics
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1961;28(4):640. doi:10.1115/1.3641813.
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Abstract
Topics: Boundary layers
Commentary by Dr. Valentin Fuster

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