Large deformation of pressurized shallow spherical membranes including flat membranes, is analyzed via the Ritz method based on potential energy minimization. The material of the membrane is assumed to obey Hooke's law and the deformation is assumed not to be very large. A function which expresses the change of the deflection profile of the membrane effectively with a few unknown parameters is used as a trial function for the potential energy functional. The deflections and stresses calculated by this method agreed fairly well with other analytical solutions. This energy method is applied also to the case of one-dimensional membranes. The energy method presented in this paper is shown to give a symplified and rather accurate solution for a pressurized shallow spherical membrane and a one-dimensional membrane.
In coming new space age, we will have frequent trips between the ground and mission orbits by large rockets to realize the large projects such as space stations and solar power satellite systems. In such cases a great deal of rocket effluents should be released in the atomosphere. But, its effects on our environment is still unknown, and therefore various studies on these problems are expected. About such environmental problems, some studies were performed which motivated by so called “ionospheric hole” observed when Skylab-I was launched, May 14, 1973. It was certified by later scientific studies that the phenomenon was caused by the chemical reaction between rocket effluents and ionized particles in the ionosphere, by which the electron density of the ionosphere suddenly decreased to about a half values of that in its normal state in the range of about 1, 000km in radius centering about rocket trajectory and it took about 4 hours to recover. In this study, the results of these fundamental studies are applied to the engineering problem, that is, the numerical simulation of the change in electron density in the ionosphere is carried out in consideration of the diffusion of rocket effluents released along arbitrary trajectory in upper atomosphere and their chemical reactions with the ionospheric constituents.
Three-dimensional boundary layers include a velocity component normal to outside potential flows and thereby become unstable much earlier than two-dimensional cases. There are two causes contributing the cross-flow in boundary layers along a swept wing, one of which is the pressure gradient in the direction normal to wing leading edge and the other the pressure gradient along the leading edge. The latter does not appear in the case of infinite sheared wings, but exists in a usual swept wing with finite span, in particular when it is tapered, and is surely expected to affect stability characteristics of the boundary layer. Thus a simple and approximate procedure of boundary-layer calculations and stability calculations is presented for a purely three-dimensional flow around a slightly tapered wing. Then the method is applied to the boundary layer along a yawed cylinder to show important effects of sweep angle and taper ratio on the diagram of critical Reynolds numbers.
This paper describes an on-board shape control technique for large mesh antenna reflectors that compensates the surface errors caused by thermal deformation. Shape control is carried out by displacing the stand-offs to which the cable network is attached. The displacement values are calculated so as to regain the designed parabolic surface. The experimental system consists of a 4m∅ mesh antenna reflector, two theodolites for position measurements and actuators for displacing the stand-offs. The surface error caused by thermal deformation in orbit is assumed and the proposed surface control is applied to compensate this error. The validity of the control method is confirmed by the good agreement of calculated and experimental results. Finally, the antenna patterns are calculated by using experimental data. The effectiveness of the proposed method is confirmed by the restoration of antenna gain.
To substantiate the validity and usefulness of the mathematical model proposed in Part 1 of this paper, dynamic wind tunnel tests to measure hub vertical load response of a rotor in forward flight are conducted using one bladed model rotor. Following brief descriptions concerning design features of the testing apparatus, comparisons between numerical and experimental results are made. Physical requirements and resolution accuracy imposed on multiple sinusoidal blade pitch control for reducing hub vertical loads are clarified. Numerical results showed quite well agreement with experimental ones at low speed range, however, further improvements of wake modeling are anticipated for the speed ranges where such dynamic effects as the blade-tip vortex interaction are dominated.