Showing papers in "Journal of Applied Mechanics in 1963"

Crack point stress singularities at a bi-material interface

Abstract: A continuing study of plane stress singularities at corners and cracks has been extended to the case of a crack in. a hard (soft) material ending normal to a continuous interface with a soft (hard) material. The increase (decrease) in stress singularity over the homogeneous material case. which is of the characteristic inverse square root of distance from the crack point, is given for all relative rigidities between zero and infinity. Associated changes in the principal stress and distortion strain energy density distribution are also discussed, along with indications of application to such situations as microcrack growth near grain boundaries and earth faults in layered strata.

Unsymmetrical Buckling of Thin Shallow Spherical Shells

Abstract: : A theoretical study of buckling of clamped shallow spherical shells under uniform external pressure is presented. For sufficiently large deflection, deformations of such shells are not proportional to the applied pressure. The shell deforms axisymmetrically under sufficiently low pressure. The problem of axisymmetrical snapping has been solved by different numerical methods and the results agree with each other. The buck ling pressures obtained in such a manner are too high as compared with experimental results ob tained in References. Initial imperfections of the shell and unsymmetrical buckling are presumed to be the sources of this discrepancy between axisymmetrical buckling theory and experiment.

Turbulent Wakes in Pressure Gradients

Abstract: The application of moderate pressure gradients can exercise a large influence on the decay of wakes produced by obstructions in a flow field. In fact, a positive pressure gradient may arrest completely the decay process and cause the relative wake size to grow rapidly. This phenomenon could exist in any diffusing passage whose entrance flow has a wake-type distortion. Such a nonuniformity, due to a blade or a strut or other cause of stagnation-pressure variation in the stream, could lead to diffuser stall, as has been demonstrated experimentally. An analytical study of the problem has been made on the basis of measurements made in the M.I.T. Gas Turbine Laboratory. Theoretical considerations have led to a very convenient calculation formula which shows quite acceptable agreement with experimental data. The methods employ momentum integral equations and an “eddy viscosity” which is uniform across the wake and proportional to the product of the local free-stream velocity and the momentum thickness.

Breathing vibrations of a partially filled cylindrical tank - linear theory.

Abstract: Hydrodynamic theory for breathing vibrations of a partially filled, cylindrical tank, giving natural frequencies of liquid sloshing as well as pressure distribution

Impact on an Elastically Connected Double-Beam System

Abstract: : Differential equations of motion of an elastically connected double beam system subjected to an impulsive load are discussed mathematically. 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.

Gravity-Gradient Excitation of a Rotating Cable-Counterweight Space Station in Orbit

Abstract: : The gravity gradient excitation of a whirling cable-counterweight space station in orbit is investigated. The Lagrange's equations of motion for transverse oscillations of the system are derived and shown to be of the Mathieu type. A few representative cases are solved on an IBM 7090 computer for the cable's natural frequencies, which are required in the stability criteria derived. The stability criteria for the axial vibrations are derived in an appendix and shown to be of the same kind as those for the transverse vibrations of the cable. Damping is included in the analyses and found to be effective and essential for prevention of parametric excitation instability of the system.