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RESEARCH PAPERS

J. Appl. Mech. 1964;31(4):577-584. doi:10.1115/1.3629717.

The flow generated by the rotation of a flexible disk next to a wall is analyzed for small Reynolds numbers. A nonlinear differential equation for the radial variation of the pressure and the gap width is solved simultaneously with the equation governing the deflection of a spinning circular membrane under axial pressure load. Optical methods are used to measure the gap width experimentally. The theory agrees well with the measurements.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):585-593. doi:10.1115/1.3629718.

The stability of Couette flow and flow due to an azimuthal pressure gradient between arbitrarily spaced concentric cylindrical surfaces is investigated. The stability problems are solved by using the Galerkin method in conjunction with a simple set of polynomial expansion functions. Results are given for a wide range of spacings. For Couette flow, in the case that the cylinders rotate in the same direction, a simple formula for predicting the critical speed is derived. The effect of a radial temperature gradient on the stability of Couette flow is also considered. It is found that positive and negative temperature gradients are destabilizing and stabilizing, respectively.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):594-596. doi:10.1115/1.3629719.

An analysis is presented for the laminar radial flow of an incompressible fluid between two closely spaced parallel plates. A solution is obtained by perturbing the creeping-flow solution and an expansion is carried out in terms of the downstream coordinate. The solution is found to agree well with experimental measurements except near the channel entrance.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):597-604. doi:10.1115/1.3629720.

The authors consider the problem of an ellipsoid performing simple-harmonic swaying or yawing oscillations of small amplitude in the free surface of an ideal incompressible fluid, with gravity. The problem is examined in the limit of low frequency. The first nonzero term in the radiation pattern, which is a dipole term, and the damping coefficient, are found for sway. In the case of yaw the first nonzero term in the radiation pattern is a quadrupole term, and involves a higher power of frequency. Hence, the damping coefficient for yaw is of smaller order than the damping coefficient for sway, at low frequency. The strip-theory prediction of the sway damping coefficient is compared with the exact value and is shown to be too large by a factor of order K.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):605-610. doi:10.1115/1.3629721.

The stability of a rod loaded by an axial force and moment and gravity forces is considered by energy methods. The displacements are restricted in such a way that the rod must remain in contact with a rigid circular cylinder. The configuration is found to be stable for all loads unless the additional restriction is made that the cross-sectional elements of the rod do not rotate as they move around in contact with the cylinder. For these restricted displacements it is found that axial moment is not important in determining the stability of the configuration.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):611-620. doi:10.1115/1.3629722.

Impact is considered on a rod of finite length whose material exhibits viscoplastic behavior described by a power-law relation between strain rate and dynamic overstress. Strain-hardening and elastic strains are neglected. Solutions previously obtained for the linear case are supplemented by deriving upper and lower bounds for the final strain. The general solution for the nonlinear case, with strain and stress assumed uniform along the rod, is derived and compared with results of the complete solution. The general solution for uniform strain is also compared and contrasted with results of the simplest rigid-plastic (rate independent) theory involving plastic wave propagation.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):621-626. doi:10.1115/1.3629723.

The paper presents the development and solution of the differential equations of motion of an elastically connected double-beam system subjected to an impulsive load. In addition to the theory there is presented a description of impact experiments on double beams. Theoretically and experimentally determined strains as functions of time are compared in the form of curves. The agreement is remarkably good for the type of load used.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):627-634. doi:10.1115/1.3629724.

The problem treated is that of an infinite free plate with a circular cylindrical cavity subjected to a step normal displacement. The linear equations of elasticity are employed and the formal solution is obtained using a multi-integral transform technique, necessitating the introduction of extended Hankel transforms, and residue theory. Some properties of the Rayleigh-Lamb frequency equation, pertinent to the inversion process, are derived. Numerical information for the far field, showing the effect of the hole radius on the displacements, is obtained using the stationary phase method and, in the case of the radial displacement, the solution is compared with the corresponding slab solution. The results show that at a given station the plate-cavity solution approaches that for the slab, as the hole radius decreases. The head of the pulse and stationary-phase approximations to the corresponding horizontal slab displacement are also compared, and some discrepancies between the two are found in the vicinity of the wave-front arrival time.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):635-646. doi:10.1115/1.3629725.

The quasi-static and dynamic indentation of a hard steel sphere into a massive lead block, considered to represent a rigid perfectly-plastic half-space, has been investigated experimentally. The technique of visioplasticity was employed to calculate the stress pattern from which an empirical relation delineating the variation of hydrostatic pressure with depth of indentation was constructed. This expression was utilized in conjunction with a model of the surface-deformation process to describe the growth of the crater analytically. The force-indentation relation obtained in this manner agrees with that determined by direct observation to within 6 percent, while the predicted permanent crater depth was found to be 10.8 percent lower than that measured under dynamic conditions. The results of the present investigation have also been compared with solutions based upon the Haar-Karman criterion of yielding and upon the hypothesis of a constant flow pressure.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):647-653. doi:10.1115/1.3629726.

After stating a variational theorem which is a further generalization of known variational theorems and which has as its Euler equations all of the field equations and the boundary conditions of classical linear three-dimensional elasticity, the remainder of the paper deals with its application to shell theory. A new characterization of the basic system of field equations and the boundary conditions of the linear theory of elastic shells is derived which includes the effect of transverse shear deformation and involves only symmetric resultants and symmetric shell-strain measures. These results are of special significance in relation to those of a number of recent investigations in shell theory under the Kirchhoff-Love hypothesis in which the boundary-value problem of shell theory is recast in terms of symmetric (but not necessarily the same) variables.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):654-658. doi:10.1115/1.3629727.

The viscoplastic flow of a long thick-walled tube is investigated. The tube is subjected to internal pressure and has its ends restrained from motion in the axial direction. The material of the tube is rigid-viscoplastic and incompressible. The pressure required to produce a specified expansion of the tube is calculated for two examples. In the former the effect of different viscosity coefficients is observed. In the latter example a comparison is made of the effects of perfect plasticity, viscosity, and inertia.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):659-666. doi:10.1115/1.3629728.

The elastic contact of a plate with two axisymmetric bodies, generally of dissimilar elastic properties and curvatures, is considered. The solution of the resulting two integral equations is given as a truncated series of Legendre polynomials of even order whose coefficients may be determined from a system of linear algebraic equations. The relationships between the total load, radii of curvature of the bodies, contact radii, approach, radial displacements, maximum contact stress, and the plate thickness can then be computed in terms of these coefficients. Numerical computations have been carried out for the contact of a plate with two identical spheres.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):667-675. doi:10.1115/1.3629729.

A long circular cylindrical shell is to be pierced with a circular cutout, and it is desired to design a plane annular reinforcing ring which will restore the shell to its initial strength. Upper and lower bounds on the design of the reinforcement are obtained. Although these bounds are far a part, it is conjectured that the upper bound, in addition to being safe, is reasonably close to the minimum weight design. Some suggestions for further work on the problem are advanced.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):676-682. doi:10.1115/1.3629730.

Experiments have been carried out on thin tubular specimens of alpha brass subjected to various combinations of torque and transverse tension, after initial overstrain in torsion. The loading paths were based upon a yield function expressing one degree of anisotropy which had been found previously to give good correlation of initial radial loading paths. The primary definition of yield used was the “Taylor-Quinney, Lode”; however, “Limit of Proportionality” and “Initial Loading Slope Tangent” definitions have also been investigated. The derived yield surface (Taylor-Quinney) shows strong positive cross effect, rotation, and a Bauschinger effect extending over the whole reversed quadrant to initial loading. No indication of the formation of a corner on the yield surface was found.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):683-693. doi:10.1115/1.3629731.

A unified treatment is presented of certain portions of Burmester theory by including finite as well as infinitesimal displacements. Theorems of R. Mueller concerning collinearity, order of contact, symmetry, and location of the Burmester points associated with infinitesimal, coplanar displacements of a plane, are extended to the more general case of arbitrary, coplanar displacements. Additional extensions relate to a recent study of infinitesimal displacements by G. R. Veldkamp [27] and, in some instances, are not related to earlier studies. The results of the present investigation are summarized in Table 2.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):694-699. doi:10.1115/1.3629732.

One of the basic theories of kinematic synthesis, namely, Burmester’s classical centerpoint-circlepoint theory, is shown to be one of several special cases of a broader, more general new theory, involving points of the moving plane whose several corresponding positions lie on cycloidal curves. These curves may be generated by “cycloidal cranks.” Such “cycloidpoints,” centers of their generating circles (“circlepoints”) and base circles (“centerpoints”) are proposed to be called “Burmester point trios” (BPT’s). In case of 6 prescribed arbitrary positions, such BPT’s appear to lie, respectively, on three higher plane curves proposed to be called “cycloidpoint,” “circlepoint” and “centerpoint curves,” or, collectively, “generalized Burmester curves.” In the case of hypocycloidal cranks with “Cardanic” proportions, the hypocycloids become ellipses. For 7 prescribed positions, the number of BPT’s is finite. Application to linkage synthesis for motion generation with prescribed order and timing is presented and cognate-motion generator linkages, based on multiple generation of cycloidal curves, are shown to exist. Analytical derivations are outlined for the equations of the “generalized Burmester curves,” and possible further specializations and generalizations are indicated.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):703-704. doi:10.1115/1.3629735.
Abstract
Topics: Stress
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):704-705. doi:10.1115/1.3629736.
Abstract
Topics: Equations
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):706-707. doi:10.1115/1.3629737.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):707-708. doi:10.1115/1.3629738.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):708-710. doi:10.1115/1.3629739.

In this Note the deflection of a linear viscoelastic plate due to a concentrated impulsive load, applied at a point on the plate, has been discussed. The material considered is of the Voigt type and the plate is a rectangular one.

Topics: Stress , Deflection
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):710-711. doi:10.1115/1.3629740.
Abstract
Topics: Cylinders
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):711-713. doi:10.1115/1.3629741.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):714-716. doi:10.1115/1.3629742.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):716-717. doi:10.1115/1.3629743.
Abstract
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):719-722. doi:10.1115/1.3629745.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):722-723. doi:10.1115/1.3629746.
Abstract
Topics: Vibration
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):724-726. doi:10.1115/1.3629748.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):726-728. doi:10.1115/1.3629749.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):728-729. doi:10.1115/1.3629750.
Abstract
Commentary by Dr. Valentin Fuster

ERRATA

Commentary by Dr. Valentin Fuster

DISCUSSIONS

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

BOOK REVIEWS

J. Appl. Mech. 1964;31(4):735. doi:10.1115/1.3629762.
FREE TO VIEW
Abstract
Topics: Errors
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):735. doi:10.1115/1.3629763.
FREE TO VIEW
Abstract
Topics: Navigation
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):735-736. doi:10.1115/1.3629765.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):736. doi:10.1115/1.3629766.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1964;31(4):736. doi:10.1115/1.3629767.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster

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