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RESEARCH PAPERS

J. Appl. Mech. 1977;44(2):194-200. doi:10.1115/1.3424023.

Two-dimensional stability of leaward cylinder in the wake of fixed windward cylinder is studied within the framework of quasi-static aerodynamic theory at both subcritical and supercritical flow region. Routh-Hurwitz stability criterion is employed. Two important points are clarified: 1. The wake-induced flutter is symmetric with respect to the horizontal line if there is no xy (refer to Fig. 1) static coupling. When coupled, the wake symmetry preserves provided the sign of static coupling is changed. This finding is supported by recent experimental data [7] and is in contrary with previous results [4–6]. 2. For the uncoupled case, vertical and horizontal frequency coalescence does not necessarily imply no oscillation. This is in variance with previous studies [2, 3, 34]. The region of instability is related to four physical variables: vertical to horizontal natural frequency ratio κ = ωy /ωx = (Kyy /Kxx )1/2 , static coupling coefficient ε = Kxy /Kxx , cylinder spacing to diameter ratio d/c and flow characteristics. Some highlights of numerical results [1] are as follows: (a) The region of instability roughly lies between 0 < |ε| < 0.1 and 0.8 ≤ κ ≤ 1.2. (b) The region of instability enlarges as |ε| increases from zero to 0.8 when everything else is kept fixed. (c) For both subcritical and supercritical flow, the region of instability shrinks as d/c varies from 10–16 when keeping all other factors fixed. (d) The region of instability shrinks as the flow changes from subcritical to supercritical when everything else remains unchanged.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):201-206. doi:10.1115/1.3424024.

This paper examines the stability of a rectangular surface lying in isolation in an inviscid fluid in uniform subsonic motion when the surface, in its undeformed state, lies in a plane with its edges aligned parallel and perpendicular to the flow direction. The problem is formulated in the form of an integral equation which is solved approximately using the one-term Galerkin method so that expressions for the stability parameter are determined in the form of asymptotic series for the high and low aspect ratio limits. Surfaces supported on all edges as well as those whose edges are only partially supported are investigated. The results are compared with those for an infinite array of panels and an isolated panel replacing part of a rigid surface.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):207-212. doi:10.1115/1.3424025.

An analysis of flow-induced bending of rectangular plates simply supported on two sides and free on the leading and trailing edges, with viscous entry flows differing in flow rate on top and bottom, is presented. Viscous shear is shown to be important in modifying the plate deflection near the leading edge. The flow rate is maximized and deflection minimized by using relatively small length-to-width ratios. The results are directly applicable to stacked rectangular fuel-bearing plates in nuclear reactors.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):213-217. doi:10.1115/1.3424026.

This paper presents an analytical method for evaluating the hydrodynamic masses of a group of circular cylinders immersed in a fluid contained in a cylinder. The analysis is based on the two-dimensional potential flow theory. The fluid coupling effect among cylinders is taken into account; self and mutual-added masses for both inner and outer cylinders are evaluated. Based on the proposed method, the free vibration of two eccentric cylinders with a fluid-filled gap is analyzed as an example.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):218-221. doi:10.1115/1.3424027.

The concept of liquid-filled multiple concentric cylinders under compressive axial loading is investigated. An analytical model to predict the hydrostatic pressures in the liquid regions is formulated. It is found that upon loading a radially decreasing pressure gradient in the liquid layers is produced. The values of hydrostatic pressure from an experimental model comprising aluminum cylinders filled with hydraulic oil show good agreement with those predicted by the analytical model.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):222-226. doi:10.1115/1.3424028.

A bonded interface between two solids which have an appropriate mismatch in their mechanical properties can support Stoneley waves. The question investigated is whether an unbonded interface, which is unable to transmit tensile tractions, can sustain interface waves that involve localized separation. The answer is affirmative, and the following conclusions are reached: 1. The solids must be pressed together. 2. All combinations of materials can sustain interface waves involving separation. 3. The phase velocity of the interface waves is not fixed but lies within a range of values. For instance, in case of identical materials, the phase velocity may have any value falling between the velocities of Rayleigh and transverse waves (cR < c < cT ). 4. The interface waves do not involve a free amplitude, and the wave form is fixed. However, the length of the separation zones remains arbitrary, so that energy can still be transmitted at greatly different rates. 5. The solids move apart in the sense of an average displacement. 6. The gaps are symmetric about the centers of the separation zones, and the interface tractions are symmetric about the centers of the contact zones. 7. The interface waves involving separation exhibit features that are similar to those encountered in dynamic fracture. The interface tractions are square-root singular at both leading and trailing ends of the gaps. The two solids pull apart at the leading ends of the gaps with infinite discontinuities in particle velocities. The solids slam together at the trailing ends with exactly the opposite velocity discontinuities.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):227-230. doi:10.1115/1.3424029.

A Fourier synthesis of the steady-state vibrations of a rigid plate on an elastic half space is used to determine the deceleration and penetration of a rigid body impacting an elastic half space over a flat circular area. In order to obtain a satisfactory solution, it is necessary to integrate to a large value of the frequency factor. The theoretical values are compared with some simple experiments on lead and Neoprene.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):231-236. doi:10.1115/1.3424030.

Mathematical models of the cooling of large butt-welded plates are investigated. One thermoelastic infinite plate and one thermoelastic semi-infinite plate are considered. On the infinite plate two concentrated heat sources of constant power move with constant velocity along a straight line toward each other. They meet and are then immediately removed from the plate. On the semi-infinite plate one concentrated heat source of constant power moves with constant velocity along a straight line perpendicularly toward the edge and is removed as it reaches the plate edge. The straight plate boundary is thermally adiabatic and mechanically free. A previous investigation showed that transverse tensile stresses arise behind the two heat sources on the infinite plate when they approach each other and behind the single heat source on the semi-infinite plate when it approaches the plate boundry. Here it is shown that after removal of the heat source(s) such tensile stresses remain much longer in the semi-infinite plate than in the infinite plate. The transverse tensile stresses may explain the tendency of hot cracking in the end portion of a butt-weld.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):237-242. doi:10.1115/1.3424031.

The plane elastostatic problem of internal and edge cracks in an infinite orthotropic strip is considered. The problems for the material types I and II are formulated in terms of singular integral equations. For the symmetric case the stress-intensity factors are calculated and are compared with the isotropic results. The results show that because of the dependence of the Fredholm kernels on the elastic constants in the strip (unlike the crack problem for an infinite plane) the stress-intensity factors are dependent on the elastic constants and are generally different from the corresponding isotropic results.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):243-249. doi:10.1115/1.3424032.

Elastodynamic stress-intensity factors accompanying the three-dimensional steady-state elastodynamic response of an unbounded solid containing a semi-infinite crack, are investigated in this paper. Analytic solutions are obtained by application of the Fourier transform technique in conjunction with the Wiener-Hopf method. Two specific examples are worked out. For the diffraction of a plane longitudinal wave, which is incident under an arbitrary angle with the edge of the crack, explicit expressions are presented for the Modes I, II, and III stress-intensity factors. The variation of these quantities with the direction of the incident wave was worked out in detail, and the results are displayed in several figures. The second example deals with the elastodynamic field generated by the application of normal point loads of equal magnitude but opposite sense to the surfaces of the crack. For this case relatively simple approximate expressions are derived for the Mode I stress-intensity factor.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):250-254. doi:10.1115/1.3424033.

The elastostatic problem of a circumferential edge crack in a cylindrical cavity is investigated. The problem is formulated by means of integral transforms and reduced to a singular integral equation. The numerical scheme of Erdogan, Gupta, and Cook is used to obtain the relevant physical quantities and the stress-intensity factors, and crack opening displacements are computed for several values of crack length.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):255-258. doi:10.1115/1.3424034.

The problem of a semi-infinite work-hardening material with a finite length asymmetric edge crack subjected to uniform remote longitudinal shear is solved exactly by the use of hodograph transformation and the Wiener-Hopf technique. The material behavior is governed by a pure power-hardening stress-strain relation and for monotone loading the results are valid for both deformation and flow theories of plasticity. Numerical values are obtained for the path independent J integral for several values of both the angle of asymmetry and the power-hardening exponent.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):259-263. doi:10.1115/1.3424035.

The fracture patterns produced by localized impulsive loading on brittle beams and their dependence on the intensity and length of the load have been determined. Experiments were performed on effectively infinite beams loaded over a finite length with sheet explosive. The mechanisms, location, and time sequence of deformation and fracture were determined by posttest observation and by high-speed framing camera photographs. It was found experimentally that all fractures were initiated by bending stress and that the localized impulsive loading produced three different fracture patterns. The beam response was also predicted analytically by numerically integrating the characteristic equations of Timoshenko beam theory. It was found analytically that, depending on load length and intensity, a total of four fracture patterns, including the three observed experimentally, can be produced by localized impulsive loads.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):264-270. doi:10.1115/1.3424036.

The primary goal of this paper is to compute the stretching stress-intensity factor at the tip of a crack in a pressurized cylindrical shell. Shallow shell theory is used and the governing equations are reduced to singular integral equations along the crack, following earlier work by Folias and Copley and Sanders. The solution of the integral equations depends on a dimensionless parameter λ proportional to the crack length divided by the square root of the thickness times the midsurface radius of curvature. Series solutions are obtained for λ < 1 and numerical solutions for 0 ≤ λ ≤ 10. The major contribution of the paper is an asymptotic solution as λ → ∞. To avoid an intractable double Weiner-Hopf problem, the edge of the crack is assumed to be clamped in such a way that it can expand tangentially but cannot rotate or displace perpendicular to the midplane.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):271-278. doi:10.1115/1.3424037.

This paper presents a theoretical investigation into the continued quasi-static compression of a thin metal strip between two rigid, parallel rough dies. Three different constitutive postulates for the strip material are considered: (a) rigid isotropic hardening, (b) rigid-perfectly plastic with an anisotropic yield criterion, and (c) rigid-kinematic (anisotropic) hardening. An initially homogeneous such strip develops inhomogeneities through its thickness as it is compressed. This is due to the dependence of the yield locus on the rigid-body spin for an anisotropic material and on the strain-history for a hardening material. The length of the dies is supposed to be much greater than the current strip thickness. The solution is hence effectively independent of position along the length of the strip and can be found by integrating an ordinary differential equation.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):279-284. doi:10.1115/1.3424038.

The deflection of an infinite ice sheet by a submerged gas source, as would result from an undersea gas or oil well blowout is analysed utilizing an elastic thin plate model. The results show that fracture may occur either at the bubble center or just beyond the bubble edge, depending upon the bubble depth, the ice thickness, and the material properties assumed for the ice sheet. For ice one meter in thickness and a trapped gas depth greater than 100 mm, fracture at the bubble edge is probable. The critical bubble radius for failure varies rapidly with ice thickness, bubble depth, and the ice properties, which in view of the variability of the latter, makes the prediction of actual bubble radii to cause failure subject to a large degree of uncertainty.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):285-290. doi:10.1115/1.3424039.

A technique for determining the minimum mass design of continuous structural members is presented. The method involves formulating the minimum mass design problem as an optimal control problem, transforming the differential equations modeling the member into a penalty function, and then representing the state variables in terms of a Ritz-type expansion and discretizing to reduce the original optimal control problem to a parameter optimization problem. The technique is applied to determine the optimal design of a simply supported beam with fixed fundamental frequency of free vibration and a fixed-free column with specified Euler buckling load.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):291-298. doi:10.1115/1.3424040.

This paper serves as a further illustration of the concept of natural structural shapes, a concept in optimal structural design. Natural shapes occur as solutions of a multicriteria control problem with criteria “mass” and “stored energy” of the deformed structure. The corresponding optimality concept is that of Pareto-optimality. This general approach is applied to the calculation of optimal initial shapes of uniform shallow arches. The resultant problem is a so-called unbounded problem in multicriteria control theory; there are no state constraints. The solution consists of a family of optimal shapes. The subsequent specification of additional constraints such as the maximum allowable deflection, stress, mass, and the like, then yields a particular member of the family. The solutions to the minimum weight and the minimum of the maximum deflection problem appear as limiting cases.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):299-304. doi:10.1115/1.3424041.

Hamilton’s principle is used to derive equations of motion for a linear elastic three-layered ring. The theory includes the effects of shear deformation and rotatory inertia in each layer and radial strain effects in the middle layer. A convenient computational technique is developed for transient response evaluation. A companion experimental study was conducted using two different rings. Both rings had aluminum inner and outer layers, but each had a different low-modulus middle layer. Radial impulse loads distributed as a cosine over half the ring circumference, were applied to the outer ring surface, and the transient response was monitored with strain gages mounted on the aluminum layers. Measured strain-time histories were compared with theoretical calculations, and good agreement was obtained.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):305-310. doi:10.1115/1.3424042.

This paper extends the Moon-Pao theoretical treatment of the buckling of a rectangular beam of infinite length l and infinite width w to the case (a) l infinite, w finite, and the case (b) l finite, w infinite. Then an approximate formulation is used to obtain a lower bound to the critical buckling field for the case (c) l finite, w finite. It is concluded that finite specimen size alone cannot account for the discrepancy between the Moon-Pao theory and experiments.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):311-316. doi:10.1115/1.3424043.

The general lateral buckling equation is developed for a uniform, slender, simply supported beam fixed in torsion and with a load applied at the shear center of the midspan cross section. In this general equation, the effect of principal bending curvature (i.e., beam deflection prior to buckling) is completely accounted for. Therefore, a distinction is made between beams fixed in torsion about the deformed or undeformed elastic axis, and distinct boundary conditions are derived for each case. The equations for each of the two support conditions are then specialized to include only the first-order effect of principal bending curvature and these equations are compared with similar equations for cantilever beams and beams in pure bending. Finally, simplified buckling load formulas are derived and compared with numerical solutions of the general equations for each of the lateral buckling configurations. The comparison shows that the approximate formulas provide good estimates for the buckling load and that the classical buckling load formulas that neglect principal bending curvature are not always conservative for infinitely slender beams.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):317-321. doi:10.1115/1.3424044.

Discrete nonconservative elastic systems which lose stability by buckling (divergence) are considered. Simple (distinct) critical points were treated previously, and the case of coincident buckling loads is analyzed here. An asymptotic procedure in the neighborhood of the critical point is used to determine postbuckling behavior and imperfection-sensitivity. It is shown that the system may exhibit no bifurcation at all. In other cases postbuckling paths may be tangential to the fundamental path at the critical point. The sensitivity to imperfections is shown to be more severe than for systems with distinct buckling loads (e.g., one-third, one-fourth, and one-fifth power laws are obtained for certain cases).

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):322-328. doi:10.1115/1.3424045.

The steady-state whirl-spin relationships for the pendulously supported flywheel with bearing flexibilities, stiff sections of shaft and gyroscopic action are derived and experimentally verified. Stable and unstable operations of the system are experimentally demonstrated, and damping necessary to stabilize an inherently unstable system is theoretically derived for two modes of bearing displacements.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):329-332. doi:10.1115/1.3424046.

A recently developed theory is used to establish criteria for determining regions of possible motions in a reduced configuration space for a rigid body having one fixed point. Such regions are plotted for a numerical example and their qualitative features are examined.

Topics: Motion
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):333-336. doi:10.1115/1.3424047.

The critical excitation of a mechanical system, in the terminology of this paper, is one that drives the system to a larger response peak than any other in some class of allowed excitations. The critical excitation is of interest in questions related to the reliability and safety because the magnitude of the response peak is frequently an indicator of the survivability of the system. The problem of finding it has been solved for linear systems some time ago. This paper deals with the generalization of the problem to nonlinear systems. It is shown that its solution is in many ways analogous to its earlier counterpart.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Appl. Mech. 1977;44(2):337-338. doi:10.1115/1.3424048.

A counterexample involving a homogeneous, elastically isotropic beam of narrow rectangular cross section supports the assertion in the title. Specifically, a class of two-dimensional displacement fields is considered that represent exact plane stress solutions for a built-in cantilevered beam subject to “reasonable” loads. The one-dimensional vertical displacement V predicted by Timoshenko beam theory for these loads can be regarded as an approximation to either the exact vertical displacement v at the center line, or a weighted average of v over the cross section, or a quantity defined to make the virtual work of beam theory equal to that of plane stress theory. Regardless of the interpretation of V and despite the presence of an adjustable shear factor, Timoshenko beam theory for this class of problems is never more accurate than elementary beam theory.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):338-340. doi:10.1115/1.3424049.

The stability of fully developed, parallel flow in a rigid, concentric annulus to infinitesimal disturbances is analyzed. It is found that the annular flow is spatially stable to axisymmetric disturbances upto a modified Reynolds number of 10,000.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):340-342. doi:10.1115/1.3424050.
Abstract
Topics: Stress
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):342-343. doi:10.1115/1.3424051.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):343-344. doi:10.1115/1.3424052.

The time-varying expression of the momentum correction factor for the study of wave propagation in pulsatile blood flow is modified to take into account the temporary sign reversal of the velocity. A constant value for this factor is also proposed as a possible alternative to usually adopted values.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):344-345. doi:10.1115/1.3424053.

It is shown that the equations governing the pure bending of unsymmetrical prismatic beams can be written in a coordinate-free invariant form.

Topics: Equations
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):345-347. doi:10.1115/1.3424054.
Abstract
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):349-352. doi:10.1115/1.3424056.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):352-354. doi:10.1115/1.3424057.
Abstract
Topics: Elastodynamics
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):354-355. doi:10.1115/1.3424058.
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):355-356. doi:10.1115/1.3424059.
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. 1977;44(2):364. doi:10.1115/1.3424078.
FREE TO VIEW
Abstract
Topics: Physics
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):364-365. doi:10.1115/1.3424079.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):365-366. doi:10.1115/1.3424080.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):366. doi:10.1115/1.3424081.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):366. doi:10.1115/1.3424082.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):367. doi:10.1115/1.3424083.
FREE TO VIEW
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):367. doi:10.1115/1.3424084.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1977;44(2):367. doi:10.1115/1.3424085.
FREE TO VIEW
Abstract
Topics: Biophysics
Commentary by Dr. Valentin Fuster

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