The root-mean square (rms) surface error of a rectangular mesh (membrane) elememt subjected to isotropic tension in a faceted reflector surface is analyzed. The rectangular membrane element is assumed to be placed on any place of the reflector surface with an arbitrary angle between the side of the membrane and the direction of the principal curvature of the ideal reflector surface. The boundaries of the membrane are assumed to coincide with elliptic or hyperbolic paraboloidal surfaces. The deflection of the membrane is calculated based on a linear membrane equation. According to the constraints of parameters which determine the boundary deflections of the membrane element, different kinds of rms error optimizations are carried out and corresponding optimum membranes are obtained and compared. Effects of parameters, such as aspect ratio, boundary deflection, size, etc., upon the surface error of each optimum membrane are examined. The optimum membrane, which has minimum surface error among other optimum membranes, is found to give substantially lower errors than those of the best fit flat membrane. Comparison of the rms error of a rectangular membrane element with those of a circular and triangular membrane element of the same area is also made.
An application of a new method for experimental determination of aircraft inertia characteristics is shown in this paper. A measurement object is suspended by two pendulum arms and multidegrees-of-freedom oscillation is excited manually. The inertia characteristics given in the equation of motion of the oscillation system are identified from the measurement signals using the maximum likelihood estimation method. This method has an advantage over existing methods in that the center of gravity and the three dimensional inertia characteristics are simultaneously estimated. To apply the method to a relatively small object like a model ariplane, the dynamical equation of the oscillation system is derived in which the mass and the moment of inertia of the pendulum arms are taken into consideration. The two dimensional model is used to demonstrate the validity of the method and comments on the application to the complete three dimensional model are given.
Two dimensional viscous flows past a rotating circular cylinder are numerically calculated by the Vortex-in-Cell (VIC) method. The Random Walk method is used to simulate the diffusion of the vorticity. At a Reynolds number of 3×105, the reverse Magnus effect, is detected by introducing turbulent viscosity to an area of the deceleration side. The effect of the separation bubble for the reverse Magnus effect is also simulated. At low Reynolds numbers, results obtained by the VIC method agree well with those obtained by experiments and Oseen approximation. The validities of the VIC method and the Random Walk method are proved even in the low Reynolds number range.
This paper describes a Fuzzy-Bayesian analysis for deciding a proper inspection schedule to maintain aircraft structural integrity and compares it with the conventional Bayesian analysis developed in the preceding paper. Although subjective information is often given by inspection results because of fuzzy environment which arises from inspectors' judgement, it is difficult to make use of fuzzy information under conventional statistical theories. In the present study, an atempt is made for investigating fuzzy information expressed in terms of linguistic variable and considering a fuzzified Bayes' theorem in order to obtain posterior probability from the information. According to this approach, a priori uncertain parameters are estimated from data collected during in-service inspection. Numerical examples are presented to demonstrate the effectiveness of fuzzy information as well as that of objective one on continuing aircraft structural integrity.