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RESEARCH PAPERS

J. Appl. Mech. 1965;32(2):241-257. doi:10.1115/1.3625792.

Turbulent flows, even when stationary on the average, are time-dependent. The study of such flows must take into account their statistical properties, not only spatial but temporal as well. A review is given of the main results of space-time measurements pertaining to: (a) In incompressible flows, double and triple velocity correlations, double correlations of wall pressure and of wall pressure and velocity of the main flow; (b) in compressible flows, double correlations of pressure at the wall and outside supersonic boundary layers, and autocorrelations of velocity in a supersonic wake. The space-time correlations give evidence to the heredity and (a) the convection velocities of the vorticity and entropy modes, as compared to the mean material convection velocity, and (b) the propagation of the acoustical mode.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):258-262. doi:10.1115/1.3625793.

A simple closed-form solution has been obtained for an axisymmetrical turbulent swirling jet issuing from a circular source into a semi-infinite motionless ambient fluid by introducing the assumptions of similar axial and swirling velocity profiles and lateral entrainment of ambient fluid into the integrated governing equations. Results for the decays of the axial and swirling velocities and the spray of the jet agree closely with the existing experimental findings on the velocity fields of a swirling round turbulent jet of air generated by flow issuing from a rotating pipe into a reservoir of motionless air.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):263-270. doi:10.1115/1.3625794.

An analysis of the lift augmentation properties of a vertical solid two-dimensional subsonic jet due to the presence of the ground is presented. The jet efflux is assumed to behave as an ideal, inviscid fluid, and familiar potential flow techniques are used to solve the resultant problems. The factors controlling the phenomenon are height from the ground, nozzle wall angle, and compressibility. The results in the form of curves of lift augmentation against height from ground show that, whereas the effects of compressibility are very small, the effect of nozzle wall angle is important and can be a useful design-control parameter.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):271-276. doi:10.1115/1.3625795.

This paper is addressed to the problem of determining the subsonic flow field that exists between the shock and the associated blunt body at small angles of attack. An inverse perturbation procedure is used whereby the shock itself is caused to rotate and the body that supports the perturbed shock is determined. It is found that the perturbed body does not possess a rigid-body-rotation relation relative to the primary flow body. Curves and tables are presented which represent the results of the numerical computations.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):277-284. doi:10.1115/1.3625796.

The problem of predicting pressures and flow rates for extruders with geometrical parameters arbitrarily variable along the axis is considered for isothermal, Newtonian conditions. A graphical method is applied to an actual case of a truncated, cone-shaped extruder. Experimental results are reported. The same general procedure, but with further simplified formulas, is applied subsequently to cases of extruders having diameter, pitch, and thread depth linearly variable along the axis.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):285-289. doi:10.1115/1.3625797.

Inherent friction compensation can be obtained by grooving one of the bearing surfaces in such a way that the through-flow of lubricant (oil or gas) exerts viscous forces in the direction of motion. In this study, theoretical and experimental data have been presented and many applications suggested. An experiment concerning an application as a continuous viscometer has been successful.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):290-294. doi:10.1115/1.3625798.

A study is made of the problem of transient elastic wave propagation when a load is applied to one end of an infinitely long rod of arbitrary cross section. Fourier and Laplace transforms aid in developing a general solution in the form of a sum over all modes of harmonic wave propagation and integrals over all wavelengths. An expansion at long wavelength reveals two types of modes of propagation which are called longitudinal and radial shear modes. For a suddenly applied pressure, the long-distance, long-time response is found to be an integral of the Airy integral.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):295-302. doi:10.1115/1.3625799.

A new formulation is presented for the deformation of a rigid, ideally plastic cantilever beam with an attached tip mass under impact loading at its tip. The effects due to arbitrarily large displacements are rigorously taken into account. The results are compared with Parkes’ solution2 in which the geometry changes are neglected. Comparisons with experiments3, 4 show that neglect of the geometry changes is responsible for part of the discrepancies between Parkes’ theory and the experiments.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):303-314. doi:10.1115/1.3625800.

A solution method using realistic (broad-band) viscoelastic response characteristics covering approximately ten decades of logarithmic time is presented for wave propagation in two-dimensional geometries. A Dirichlet series representation of the viscoelastic mechanical properties and a numerical collocation inversion procedure overcome many of the computational difficulties associated with the Laplace-transform approach to dynamic linear viscoelasticity and also afford a complete time solution. Stress distributions are given for two complementary cases, (a) the viscoelastic half-space subjected on the upper surface to the steady motion of a step pressure load moving supersonically relative to any wave speed in the material, and (b) the semi-infinite thin plate similarly loaded on its edge.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):315-322. doi:10.1115/1.3625801.

Experiments are presented which demonstrate the statistical nature of the buckling of thin strips under very high axial compression. Probability distributions of wavelengths determined theoretically from assumed “white-noise” perturbations in initial shape are compared favorably with the experimental distributions. In other experiments, a new optical-lever method of recording lateral motions is used to observe bending waves and buckling in an impacted strip. From these and experiments on large-strain buckling of rubber strips it is concluded that effects of axial-wave propagation do not significantly influence the wavelengths at which the buckles form.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):323-330. doi:10.1115/1.3625802.

For a viscoelastic clamped shallow spherical shell, the vertical deflection due to uniformly distributed external pressure is a function of time. When time reaches a critical value, the shell may snap through suddenly. This critical time depends on the magnitude of the applied pressure as well as the shell geometry. The governing equations for large deformations of viscoelastic shells can be derived by applying the correspondence principle to the equivalent equations in the elastic case. The critical times for various shells under different pressures are evaluated numerically. If the deflection volume of the shell is a constant throughout the deformation process, the external pressure decreases due to relaxation of stresses in the viscoelastic shell. This decreasing external pressure is also calculated in this paper.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):331-336. doi:10.1115/1.3625803.

A long cylindrical shell without end loads or restraints is considered to be loaded uniformly by external pressure applied as a rectangular-shaped pulse in time. It is assumed that the shell material is elastic and perfectly plastic, that the material points in the shell are displaced only in the radial direction, and that all points on the middle surface of the shell have the same motion in time. This paper investigates the total impulse which must be delivered to the shell in order to bring the inward radial displacement to a prescribed maximum value. The impulse needed to cause the prescribed displacement is calculated as a function of pulse-duration time and compared with the impulse for zero-pulse-duration time, which is calculated using the Dirac delta function. The ratio, a function of maximum displacement and pulse-duration time, always increases with increasing pulse-duration time, but the rate of increase is relatively less severe for more ductile materials. The duration of the plastic regime is also calculated, since this affects the growth of buckling displacements according to the analysis of Abrahamson and Goodier.2 It is found that, for a given total impulse, the plastic-regime duration time decreases with increasing pulse-duration time. Thus, buckling would be most severe for the shortest pulse-duration time.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):337-345. doi:10.1115/1.3625804.

In this paper, the problem of determining the stresses and deformations in a thin, homogeneous, orthotropic shell of revolution under the action of axisymmetric loads is reduced to the solution of a single inhomogeneous second-order linear differential equation with a complex dependent variable. Asymptotic solutions are obtained which are uniformly valid in both the steep and shallow regions of the dome-shaped shell. The complementary, or “edge-effect,” solutions are expressed in terms of Thomson’s functions of a noninteger order. The order depends both on the shape of the meridian curve at the apex of the shell and on the ratio of the elastic moduli. The particular solution is found in terms of an appropriate linear combination of the Lommel’s function and Thomson’s functions. This particular solution is equivalent to the well-known “membrane” solution in the steep portion of the shell but in the shallow portion gives significant bending stresses. The particular and complementary solutions are used to investigate the behavior of orthotropic pressure vessels with rigid rings clamped to the edges.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):346-350. doi:10.1115/1.3625805.

A solution is presented for a semi-infinite cylindrical (Timoshenko type) shell subjected to dynamic loading at one end using the method characteristics. Explicit results are obtained for the propagation of discontinuities. These results are combined with a simple numerical procedure to obtain the solution in all regions. Numerical examples are given for an elastic and a viscoelastic material and comparisons are made to previous results concerning wave propagation in shells.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):351-358. doi:10.1115/1.3625806.

Wave solutions are obtained by the Laplace-transform method for a semi-infinite beam subjected to a concentrated load moving at a velocity which may be supersonic, intersonic, or subsonic with respect to the bending and shear-wave velocities of the beam. Curves are drawn showing the velocity distribution behind a load moving supersonically.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):359-364. doi:10.1115/1.3625807.

The coupled nonlinear oscillating systems studied do not possess linear normal modes. The nonlinearly related modes of

m11 + k = 1n akx1k +    k = 1n Ak(x1 − x2)k = 0m22 + k = 1n bkx2k −    k = 1n Ak(x1 − x2)k = 0  (1)
with k = 1, 3, 5, . . . . . .
are expressed as superpositions of the linear normal modes of each of the homogeneous systems of the form
m11 + akx1k +    Ak(x1 − x2)k = 0m22 + bkx2k −    Ak(x1 − x2)k = 0  (2)
whose force fields are superimposed to yield the force field of equations (1).

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):365-372. doi:10.1115/1.3625808.

In this paper a Lyapunov type of approach is used to obtain sufficient conditions guaranteeing the almost sure stability of linear dynamic systems with stochastic coefficients. The results are generalized to include a certain class of nonlinear system and also to guarantee the almost sure boundedness of the forced oscillations of linear dynamic systems with stochastic coefficients.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):373-377. doi:10.1115/1.3625809.

A dynamic system having multiple degrees of freedom and being under parametric excitation has been studied in an earlier paper [2]. However, the analysis given there necessitates certain restrictions on the distribution of the natural frequencies of the system. In this paper those restrictions are removed. The analysis presented here shows how to obtain a constant matrix whose eigenvalues determine the stability or instability of a system of ordinary differential equations with periodic coefficients at a given excitation frequency. The constant matrix is expressed entirely in terms of the given system parameters and the excitation frequency.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):378-382. doi:10.1115/1.3625810.

Analytical solutions of three problems in coupled thermoelasticity are presented for the case when the material coupling parameter equals unity. The problems considered are: (a) Danilovskaya’s problem of a step function in temperature at the surface; (b) a step function in surface strain; and (c) constant velocity impact. Solutions are presented for the case of thin bars (one-dimensional stress) and are obtained by the Laplace-transform technique. There is great simplification in the equations when the material coupling parameter equals unity which permits the straightforward inversion of the transformed solutions. The results demonstrate significant deviations from the corresponding uncoupled solutions.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):383-388. doi:10.1115/1.3625811.

Many problems in mechanics are formulated as nonlinear boundary-value problems. A practical method of solving such problems is to extend Newton’s method for calculating roots of algebraic equations. Three problems are treated in this paper to illustrate the use of this method and compare it with other methods.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):389-399. doi:10.1115/1.3625812.

The governing equations of coupled thermoelasticity are investigated with the aim of obtaining solutions by means of a perturbation series in the coupling parameter. The perturbation technique is applied to the equations and a simpler set of perturbation equations is obtained. The convergence of the series solution is established, and it is shown that the result is a form of the exact solution to the governing equation for a suitable range of values of the coupling parameter. Numerical results are obtained for a typical problem using only the first two terms of the series solution. A second perturbation technique, well suited to the thermoelasticity problem and based on the method of Krylov and Bogoliuboff, also is presented in this paper. The technique is applied to two problems and the results are compared with the exact solutions.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):400-402. doi:10.1115/1.3625813.

The two-dimensional problem of a crack opened under constant pressure between two dissimilar materials is examined. It is found that an apparent solution to the problem does not satisfy a necessary physical condition.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):403-410. doi:10.1115/1.3625814.

The problem of two bonded dissimilar semi-infinite planes containing cracks along the bond is reconsidered. The external loads considered include the tractions on the crack surfaces, in-plane moments, residual stresses due to temperature changes, concentrated load and couple acting at an arbitrary location in the plane, and one-sided wedge loading of the crack. The stresses along the bonds are calculated and shown in graphs. In the example of wedge loading, the stress state and displacements in the vicinity of the crack tip are more closely studied; and the bonding stress σ and the relative displacement v1 − v2 along the crack are plotted as functions of log(r/a). It was found that, even though the stresses and displacements oscillate as r approaches zero, for the example of glass-steel bond the first zero of σ occurs around (r/a) = 10−10.63 , and at a distance (r/a) = 10−10 the stress-concentration factor has already exceeded 104 . Similarly, the region within which relative displacements oscillate is 0 < (r/a) < 10−7 , and the maximum value of interference becomes v2 − v1 = P10−9.7 , P (lb/in.) being the wedge load. It was concluded that, considering the magnitudes of distances and stresses involved, in practical applications the phenomenon of stress oscillation, which seems to be a peculiar characteristic of mixed-boundary-value problems of linear infinitesimal elastostatics, may be ignored.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):411-417. doi:10.1115/1.3625815.

Solutions are presented, within the scope of classical elastostatics, for a class of asymmetric mixed boundary-value problems of the elastic half-space. The boundary conditions considered are prescribed interior and exterior to a circle and are mixed with respect to shears and tangential displacements. Using an established integral-solution form, the problem is reduced to two pairs of simultaneous dual integral equations for which the solution is known. Two illustrative examples, motivated by problems in fracture mechanics, are presented; the resulting stress and displacement fields are given in closed form.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):418-423. doi:10.1115/1.3625816.

The in-plane extension of two dissimilar materials with cracks or fault lines along their common interface is considered. A method is offered for solving such problems by the application of complex variables integrated with the eigenfunction-expansion technique presented in an earlier paper. The solution to any problem is resolved to finding a single complex potential resulting in a marked economy of effort as contrasted with the more laborious conventional methods which have not yielded satisfactory results. Boundary problems are formulated and solutions are given in closed form. The results of these evaluations also give stress-intensity factors (which determine the onset of rapid fracture in the theory of Griffith-Irwin) for plane problems.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):424-428. doi:10.1115/1.3625817.

This investigation is concerned with the effects of couple stresses on the elastic behavior of a composite body, formed by the presence of a cylindrical inclusion within an infinite exterior region. The exterior region is assumed to be subjected to uniaxial tension at infinity. The inclusion and the exterior are assumed to have different elastic constants G1 , ν1 and G2 , ν2 respectively, as well as distinct characteristic lengths l1 and l2 . These characteristic lengths provide a measure of the granular or crystalline substructure of the materials and introduce the effect of couple stress. Particular attention is focused on the stress-concentration factor at the interface between the inclusion and the exterior region. The results are evaluated for various ratios of G1 :G2 and l1 :l2 . They are shown to depend on those ratios as well as on the dimensions of the inclusion.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):431-432. doi:10.1115/1.3625819.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):432-434. doi:10.1115/1.3625820.
Abstract
Topics: Membranes
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):434-437. doi:10.1115/1.3625821.
Abstract
Topics: Vibration
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):439-440. doi:10.1115/1.3625823.
Abstract
Topics: Vibration , Equations
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):441-442. doi:10.1115/1.3625824.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):442-443. doi:10.1115/1.3625825.
Abstract
Topics: String
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):444-445. doi:10.1115/1.3625827.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):445-447. doi:10.1115/1.3625828.
Abstract
Topics: Free vibrations
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):447-448. doi:10.1115/1.3625829.
Abstract
Topics: Vibration , Shells
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):448-449. doi:10.1115/1.3625830.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):449-451. doi:10.1115/1.3625831.
Abstract
Topics: Shells
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):451-453. doi:10.1115/1.3625832.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):453-454. doi:10.1115/1.3625833.

The dynamic response of two lumped-parameter models for an elastic beam is considered. It is shown that, as compared to the beam with continuous properties, the model of lumped flexibility yields response that is too high, and the model of lumped mass yields response that is too low.

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):456-458. doi:10.1115/1.3625835.

This Note presents an exact solution for the stresses in a semi-infinite strip subjected to a symmetrically placed concentrated load. The solution is constructed by method of images. The resulting system of equations, which consists partly of integral equations and partly of algebraic equations, is solved by method of successive approximations. Convergence of the method is proved.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):458-459. doi:10.1115/1.3625836.

The problem of the thick elastic plate with a symmetric circular pressure loading is considered. The normal stress distribution on the midplane and for two positions off the midplane is obtained by a numerical integration of the solutions. A comparison of the stress distribution on the midplane is made with previous results.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):459-461. doi:10.1115/1.3625837.
Commentary by Dr. Valentin Fuster

DESIGN DATA AND METHODS

J. Appl. Mech. 1965;32(2):462-463. doi:10.1115/1.3625838.
Abstract
Commentary by Dr. Valentin Fuster

DISCUSSIONS

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

BOOK REVIEWS

J. Appl. Mech. 1965;32(2):477. doi:10.1115/1.3625858.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):477. doi:10.1115/1.3625859.
FREE TO VIEW
Abstract
Topics: Elasticity
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):477. doi:10.1115/1.3625860.
FREE TO VIEW
Abstract
Topics: Linkages
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):477. doi:10.1115/1.3625861.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):477-478. doi:10.1115/1.3625862.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):478. doi:10.1115/1.3625863.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):478. doi:10.1115/1.3625864.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):478-479. doi:10.1115/1.3625865.
FREE TO VIEW
Abstract
Topics: Solid mechanics
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):479. doi:10.1115/1.3625866.
FREE TO VIEW
Abstract
Topics: Gasdynamics
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1965;32(2):479. doi:10.1115/1.3625867.
FREE TO VIEW
Abstract
Topics: Plasma physics
Commentary by Dr. Valentin Fuster

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