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FOREWORD

J. Appl. Mech. 1968;35(1):i. doi:10.1115/1.3601181.
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Abstract
Commentary by Dr. Valentin Fuster

RESEARCH PAPERS

J. Appl. Mech. 1968;35(1):1-6. doi:10.1115/1.3601165.

The problem considered is that of an infinitely long elastic beam subject to a moving concentrated force whose position is a stochastic function of time, X(t). The expected deflection and expected bending moment are analyzed, with special attention being given to the case of a stationary process X(t) and to the case in which X(t) is a Wiener process.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):7-12. doi:10.1115/1.3601177.

A theorem and two corollaries for the almost sure stability of linear nonautonomous random systems are presented. These results are applied to the study of the stability properties of some often encountered second-order equations and the obtained stability conditions are compared to previously known criteria.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):13-19. doi:10.1115/1.3601128.

A study is made on the parametric torsional stability of an elastic cantilever of rectangular cross section under dynamic axial loading. The coupling between the longitudinal and torsional motions exists due to the “shortening effect.” The problem is so formulated that the stability of torsional vibrations is represented by a Mathieu equation, the stability of which is well known. The effect of longitudinal vibrations on the torsional stability is investigated. The steady-state torsional-vibrational response curves are given analytically, and the effect of longitudinal damping on the boundary of stability and the steady-state response curves is also determined.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):20-24. doi:10.1115/1.3601168.

For the analysis of relative motion, classical vector mathematics is limited to the use of one moving reference frame when taking vector derivatives. However, many dynamical systems consist of a number of rigid bodies in motion relative to one another. The classical procedure requires the specification of the position of each body relative to a single “main body.” The use of relative coordinates allows a natural specification of the position of one moving body relative to another moving body in network fashion. To use relative coordinates in dynamic and kinematic analyses, it is necessary to use relative vector derivatives involving more than one moving reference frame. This paper presents general expressions for the kth-order derivative of a relative position and angular velocity vector measured in any moving reference frame in a system of m reference frames with multiple relative motion. These expressions are used to develop a procedure which generates the differential equations of motion for the system by routine substitution of the relative coordinates and their scalar derivatives. This procedure offers promise as an algorithm for machine generation of the system equations and eliminates the possibility of neglecting subtle accelerations due to relative motion. The use of the procedure is demonstrated by generating the equations of motion of an offset unsymmetrical gyroscope.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):25-30. doi:10.1115/1.3601169.

The theory of Part 1 is applied to a flexible rotor in which bearing forces are taken as linear functions of journal displacement. The balancing problem is viewed as the optimization (by digital computer) of the angular orientations of all disk masses at rotor assembly, after a rough balance of each mass is achieved and the location of its mass center experimentally established. A “disk sensitivity” criterion is suggested for determining which disk locations show the greatest effect of balance change on rotor performance. Finally, an example of the predicted difference in bearing force for a typical rotor with arbitrary disk orientation, and with improved orientation, is presented.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):31-39. doi:10.1115/1.3601170.

The dynamic stability of simply supported, shallow arches subjected to timewise step loads is studied in this paper. Presented is a general method which allows us to treat arches of arbitrary shape and load of arbitrary spatial distribution. Specific problems investigated are sinusoidal arches under sinusoidal loads, the effects of the second harmonics in the arch shape and in the load distribution, and sinusoidal arches subjected to uniform loads or concentrated and eccentric loads. The results are expressed in the form of sufficiency conditions for stability and sufficiency conditions for instability. The criteria given in this paper are reliable because the analysis does not involve truncating the solutions to a small number of modes.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):40-46. doi:10.1115/1.3601171.

The basic concepts of a general method of kinematic synthesis of space mechanisms are developed by means of vectors and quaternion operators applicable to path, function, and motion generation (body guidance) for finite and infinitesimal displacements (point, order, and combined point-order approximations). For writing the position equations, space mechanisms are represented by one or more loops of a general kinematic chain of ball-jointed bar-slideball members. Appropriate mathematical constraints on the relative freedom of these members render the general chain equivalent to the represented mechanism. The method leads to a system of equations of canonical simplicity, uniform for all tasks of finite spatial synthesis, often yielding closed-form linear solutions for small numbers of precision conditions. The same system of equations is then used to refine the solution for greater precision by numerical methods. Typical applications are indicated, some involving the use of a spatial finite circlepoint-center point theory, which includes classical planar Burmester theory as one of its special cases. An earlier general complex-number method of planar synthesis is shown to be a special case of the general spatial method introduced here.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):47-52. doi:10.1115/1.3601172.

Approximate solutions are given for the nonlinear bending response of thin plates of rectangular and circular geometry subjected to various boundary conditions such as simply supported and clamped-in edges. The investigation of the response of the plates has been restricted to two particular pulses, the step function and the exponentially decaying pulse, of which the latter can be used for an adequate description of a blast load on the plate. Proper transformation of the dependent time function, such that the additional transforming function will be a solution of the linear system disturbed by the same pulse function, will bring the time differential equation into a form so that Lighthill’s extension of Poincaré’s perturbation method can be employed for the solution of the problem.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):53-58. doi:10.1115/1.3601173.

The instability of a column under axial load is well known. A similar phenomenon is discussed in this paper for a beam-plate in a transverse magnetic field. Experiments show that the beam may buckle (in the sense of an Euler column) when the uniform magnetic field strength reaches a critical value. A mathematical model is proposed with distributed magnetic torques along the plate. A nontrivial adjacent equilibrium configuration satisfying the magnetostatic field equations is shown to exist for characteristic values of the external magnetic field. Results as predicted from this model compare favorably with experiments.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):59-65. doi:10.1115/1.3601174.

It is clear from a survey of literature on the dynamic deformation of rigid-plastic plates that most work has been focused on plates in which either membrane forces or bending moments alone are considered important, while the combined effect of membrane forces and bending moments on the behavior of plates under static loads and beams under dynamic loads is fairly well established. This paper, therefore, is concerned with the behavior of circular plates loaded dynamically and with deflections in the range where both bending moments and membrane forces are important. A general theoretical procedure is developed from the equations for large deflections of plates and a simplified yield condition due to Hodge. The results obtained when solving the governing equations for the particular case of a simply supported circular plate loaded with a uniform impulsive velocity are found to compare favorably with the corresponding experimental values recorded by Florence.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):66-72. doi:10.1115/1.3601175.

Buckling and initial postbuckling behavior is determined for thin, elastic cylindrical shells of elliptical cross section. This study complements the buckling and advanced postbuckling calculations reported by Kempner and Chen on a similar class of shells. The initial postbuckling analysis indicates that, like compressed circular cylinders, the oval cylinders will be highly sensitive to small geometrical imperfections and may buckle at loads well below the predictions for the perfect shell. On the other hand, buckling will not necessarily result in complete collapse. A series of simple tests has been performed which provide qualitative verification of the major features of the theory.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):73-79. doi:10.1115/1.3601176.

Axisymmetric plastic buckling of axially compressed cylindrical shells is studied for semi-infinite shells and shells of finite length subject to free-edge boundary conditions. It is shown that the length of the cylinder has a negligible effect on the buckling load. Reductions in buckling stresses from the classical simple-support value are significant, with the amount of reduction dependent on the details of the variation of tangent modulus with stress. Numerical results are presented for cylinders composed of 2024-T4 aluminum and 3003-0 aluminum.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):80-86. doi:10.1115/1.3601178.

A theory is postulated to explain the dynamic plastic buckling of cylindrical shells in sustained axial compressive flow. Tube impact experiments are described in which uniform axisymmetric waves were produced. Predicted and experimental wavelengths are in satisfactory agreement. According to the theory presented, wavelengths do not depend strongly on strain-hardening modulus and, based on results for two aluminum alloys, neither do experimental wavelengths. This result is shown to apply also to slow plastic buckling.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):87-94. doi:10.1115/1.3601179.

A general three-dimensional plasticity theory is presented for describing the plastic flow of homogeneous, isotropic rock. Normality of the deformation-rate vector to the yield surface is incorporated into the stress-deformation rate law used in the theory. The rock is assumed to be perfectly plastic or nonwork-hardening with a dependence of the yield strength on the hydrostatic component of stress. A particular type of yield surface, which is representative of the behavior of rock, is assumed in an application of the theory. The specific problem considered is the solution for the incipient plane flow under a flat lubricated punch.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):95-101. doi:10.1115/1.3601180.

Solutions are presented for the plane-strain plastic flow of rock under a pointed punch for two cases. In the first problem the indentation of a half space by a pointed punch is considered, and in the second the influence of a previous indentation on the formation of the next indentation is evaluated. The plasticity theory used in this analysis was developed by the authors earlier for rock mechanics applications. This theory incorporates a yield surface which is dependent on the mean normal stress and normality of the deformation rate vector to the yield surface. Work-hardening and elastic strains are neglected in the theory. These solutions furnish the analytical basis for some elementary experiments which may help to evaluate the theory.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):102-106. doi:10.1115/1.3601120.

The paper presents a uniform method of treating a variety of problems of optimal design of sandwich structures. The design procedure consists of two steps: The integration of an optimality condition, which is a differential equation for the optimal displacement field that does not involve any design parameters, and the subsequent determination of the optimal distribution of elastic stiffness or plastic resistance from the usual differential equations of the structure. Optimal elastic design for maximum stiffness, maximum fundamental frequency, or maximum buckling load, and optimal plastic design for maximum safety are treated as examples.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):107-110. doi:10.1115/1.3601121.

A structure made of a rigid perfectly plastic material and subjected to more than one independent load is considered. A mode vector is defined for any plastic mechanism and shown to have the same properties relative to the yield-point load interaction surface that the strain-rate vector has to the material yield surface. An application to a circular plate under two independent loads leads to close bounds on the interaction curve.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):111-116. doi:10.1115/1.3601122.

Hill’s extremum principle for a strain-hardening plastic material is applied to determine the displacement distribution and the strains at the center and at the roots of rounded V-grooves in a bar in tension. This analysis is used to present the shear strain at fracture as a function of triaxial tension for 7075-T6 aluminum, as compared to the more usual tension and torsion tests.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):117-122. doi:10.1115/1.3601123.

A perturbation technique is described which may be used for obtaining approximate solutions in plasticity when the field equations are hyperbolic. The characteristic parameters of the exact equations are employed as independent variables. The technique has been used to a limited extent in supersonic fluid mechanics, but not fully exploited. It apparently has not been used before in plasticity. As an example, an upper-bound solution is obtained to an axisymmetric problem: Expansion of a circular hole in a finite flat plate. The accuracy of the technique is illustrated by comparing the stresses with those obtained by a well-known finite-difference method. The advantages of the technique over an earlier perturbation method based on approximate characteristics are demonstrated by a comparison with a solution to the same problem obtained by that method.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):123-128. doi:10.1115/1.3601124.

Equations are derived for the load/deflection relations, the energy dissipation per cycle, and the instantaneous rate of dissipation. The energy dissipation per cycle is only valid for steady-state cyclic loading, whereas the load/deflection equations and instantaneous dissipation rate are valid for arbitrary loading and take into account the previous loading history. The difference between the instantaneous dissipation rate in a lap joint and the equivalent linear system is illustrated for cases of sinusoidal loading and triangular loading.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):129-133. doi:10.1115/1.3601125.

A derivation is given of a particular form of the isothermal nonlinear stress constitutive relation for materials with fading memory. This particular derivation results in a form for the constitutive relations that is well suited for application in solving boundary-value problems. The resulting forms are applied to obtain the exact quasi-static solution for the torsion of a right circular isotropic viscoelastic cylinder. Several effects due to the nonlinearity of the problem are discussed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):134-138. doi:10.1115/1.3601126.

A rigid, circular cylinder embedded in an elastic medium is subjected to a plane stress wave whose front is parallel to the axis of the cylinder. Expressions for the displacement, velocity, and acceleration of the cylinder are derived, and numerical results are presented for an incident stress wave with a step distribution in time. Formulas for the response of the cylinder produced by an acoustic wave are also presented, and it is shown that the responses from the elastic and acoustic waves are identical when the cylinder density is equal to the medium density. These results can be used as influence functions to determine the response of the cylinder produced by a plane wave with arbitrary time dependence.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):139-147. doi:10.1115/1.3601127.

This work is concerned with the transient dynamic response of a periodically ring-reinforced, infinitely long, circular cylindrical shell to a uniform pressure suddenly applied through the surrounding acoustic medium. The incident particle velocity is zero, and the rings are assumed to be slightly flexible. A classical theory of the Donnell type is used to analyze the shell while the fluid is described by the linear acoustic field equation. The solution is obtained by assuming a power series expansion in the ring stiffness parameter and utilizing a technique which reduces the transient dynamic problem to an equivalent steady-state formulation. Numerical results are presented for a steel shell immersed in salt water for different ring spacings. For the case of rigid rings, a cylindrical and plane wave approximation was also used to represent the fluid field. It is shown that the cylindrical wave approximation yields reasonably accurate results. Flexible ring results, although limited, indicate that undamped or nonradiating components of the shell vibration are activated.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):148-154. doi:10.1115/1.3601129.

The problem of subharmonic liquid response in a container subjected to vertical (axial) excitation has been solved to the first approximation by the method of perturbation, employing characteristic functions. In principle, the tank can be arbitrary. However, the computational effort required to construct the characteristic functions and their derivatives may limit the application to tanks of relatively simple geometry such as a compartmented axisymmetric tank. As a check of the theoretical result, the simplest example for a rectangular tank is given, and the results are in good agreement with experiments and a third-order theory by Yarymovych.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):155-159. doi:10.1115/1.3601130.

Laminar flow is considered between parallel rotating disks having a circular exhaust hole at an inner radius and supplied with fluid at the outer radius with pressure higher than the available sink pressure. The problem statement for asymptotic (fully developed) flow is formulated. A procedure for perturbing a creeping flow solution and an iteration scheme are developed to produce a solution for higher Reynolds numbers. The solution depends on two parameters, a Reynolds number and a mass flow parameter, and is asymptotic in the sense that a third parameter would be necessary for a solution with an arbitrary tangential velocity component specified at the outer radius of the disks and/or an arbitrary distribution of the radial velocity component between the disks. From computations conducted by digital computer, the region having uninflected radial velocity profiles is delineated. Typical results are presented for the velocity components as functions of Reynolds number, the average radial component of velocity at the entrance, and the inner radius of the disks.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Appl. Mech. 1968;35(1):160-162. doi:10.1115/1.3601132.

The intent of this note is to point out the role of initial displacements (due to manufacturing errors) in the analysis of toroidal shells by linear bending theory. It is shown that the stresses and displacement are very sensitive to small variations of the meridional curvature in the case of uniform pressure. On the other hand, the analysis is comparatively immune to these imperfections when the loading consists of forces or moments applied to the edges of the shell. These conclusions are drawn from the toroidal shell equations of Novozhilov and Zienova, which have been modified such as to include highest-order terms in initial displacements. No solution of the equations is attempted.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):162-164. doi:10.1115/1.3601133.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):164-166. doi:10.1115/1.3601134.
Abstract
Topics: Fluids , Motion
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):167-168. doi:10.1115/1.3601135.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):169-170. doi:10.1115/1.3601137.

The differential equation governing the symmetric deformations of circular cylindrical elastic shells of exponentially varying thickness is solved in terms of Kelvin functions. An application of the solution to the calculation of the edge displacement and rotation for a semi-infinite shell is also presented.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):171-172. doi:10.1115/1.3601138.

Stability boundaries for an axially moving string are presented in chart form similar to those of an Ince-Strutt diagram.

Topics: String , Stability
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):172-173. doi:10.1115/1.3601139.

A simple method is proposed to obtain the roots of Flügge’s equation when the eigenfunction has a trigonometric expression in the longitudinal direction. The significance of the solution is discussed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):176-177. doi:10.1115/1.3601141.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):177-178. doi:10.1115/1.3601142.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):178-181. doi:10.1115/1.3601143.
Abstract
Topics: Pipes , Vibration
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):183-184. doi:10.1115/1.3601145.
Abstract
Topics: Laminar flow
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):184-186. doi:10.1115/1.3601146.

In a recent paper, Das [1] considered the slow steady flow of a viscous fluid in an annulus with uniform, small, but arbitrary, injection and suction velocities along the walls. The purpose of this Note is to show how to obtain the general fully developed solution for a permeable annulus. It is shown how this solution reduces, when the injection or suction is small, to that given by Das and a few comments are made on Das’ paper.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):186-187. doi:10.1115/1.3601147.

There has been much recent interest in the possibility of hardening an underground structure by means of an elastic plate placed on the ground above the structure. To obtain a simple expression for the interaction pressure between the ground and the plate, the present analysis treats the problem of a plate on top of an acoustic medium subjected to a uniformly moving pressure pulse. It is found that an approximate equation suggested by S. B. Baldorf is quite valid in the superseismic range of load speed. The specific problem of a step function loading traveling with uniform velocity, superseismic to the foundation, is treated. The extension of this problem to an actual elastic foundation is straightforward and is not treated.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):188-190. doi:10.1115/1.3601148.

A doubly symmetric hole having parts of three intersecting circles as its boundary is suitable as a stress concentrator in the investigations of the fatigue properties of materials. Using Homalite 100 as the model material, a series of photoelastic experiments was made to determine the stress concentration factors at such hole in finite strips under tension. The results were compared with those calculated from a semiempirical equation suggested by Mitchell and other experimental results.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):190-192. doi:10.1115/1.3601149.
Abstract
Commentary by Dr. Valentin Fuster
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. 1968;35(1):200. doi:10.1115/1.3601166.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1968;35(1):200. doi:10.1115/1.3601167.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster

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