A straight wing lying on a diameter of a circular closed tunnel is studied, where minimum induced drag is assumed. Exact expressions of spanwise lift distribution and induced drag are obtained from the TREFFETZ plane. When the ratio of wing-span to tunnel-diameter increases, lift distribution changes gradually from elliptic to uniform distributions, and induced drag gradually decreases until it becomes zero in the limiting case when the ratio reaches unity.
The stress distribution around a circular or elliptical cutout, or two circular ones in a thin cylindrical shell is investigated under axial load, torsion or internal pressure. The analysis is based on the shallow shell theory. General solutions of the Donnell-type equations are superposed, and then the boundary condition on the free edge and the single-valued displacement condition are satisfied by a collocation procedure. The result covers wider ranges of curvature parameterβand distance between two cutouts than previous researches. Systematical investigation is done on the influence of parameter variation on stress concentration.
This paper treats mainly the theoretical analysis about the wave motion of the tyre tread assuming the tread is a beam with a bending stiffness, which is subject to a tension due tothe internal pressure and the centrifugal force, and the side walls have the effect of an elastic foundation on the tread. The analysis is performed under the assumption that the standingwave phenomenon of tyres appears when the running velocity of the tyre reaches the wave velocity in the circumferential direction of the tyre. It is theoretically explained that the wave velocity of the tread is a function of the wave length and the minimum wave velocity with respect to the wave length corresponds to the critical standing-wave velocity, and the wave length corresponding to the minimum velocity can be determined by both the bending stiffness and the spring conatant of the elastic foundation and, however, it is independent of the circumferetial tension of the tread. It is also shown that the assumed bending stiffness and the assumed elastic spring constant of elastic foundation in this analysis can be experimentally determined by the measurement of the displacement of the tyre tread due to the statical concentrated load at a point on the tread and consequently the length of the standingwave can be predicted by the displacement curve of this statical test. It is also explained that the wave motions produced by the impact load at a point of the tread can be considered as the compound waves of many single harmonic waves of different wave length and, in the case of damped wave motion, the damping of the single wave with the distance from the impact point depends on its wave length.