There are few papers where Fourier transform is used on formulating lifting-surface theories. Application of Fourier transform however has many merits over other methods, and is essential for some special problems. In supersonic flows, spanwise Fourier transform is applicable withoutdifficulties. In subsonic flows both spanwise and streamwise Fourier transforms are used, but disturbances infinitely upstream never vanish. This is a sort of paradox which must be circumvented. If the disturbances infinitely upstream are merely forced to vanish against mathematical logic, then the correct formulations have been attained for all cases investigated.
This paper is aimed to propose the practical method of estimation of the critical speed of the standing-wave phenomenon of tyre, although it is necessary to measure the fundamental physical quantities in advance by comparatively simple testings. It is explained that the square of the wave velocity of the tyre is the square sum of the velocity due to the stiffness tyre, of the velocity due to the internal pressure, and the velocity due to the centrifugal force of the rotating tyre. In addition, the amount of the reduction of the stiffness of the tyre due to the temperature rise in the rolling tyre is estimated. The practical empirical method is also proposed to take this reduction of the stiffness into account for the practical estimation of the critical speed.
A small-deflection theory is used in conjunction with a Galerkin technique to calculate the deflection under uniform pressure, first and second natural frequencies, and supersonic panel flutter characteristics of orthotropic elliptical plate with clamped-edge in the case where the direction of principal axis of orthotropy is arbitrary and direction of the supersonic flow is coincide with the axis of ellipse. The deflection is expressed in power series. A rigorous solution is obtained for deflection subjected to uniform pressure, and the form of rigorous solution is similar to that of the isotropic plate. The natural frequencies of elliptical plate are clarified. The critical value of supersonic panel flutter is obtained in six-modes approximation. Furthermore the simple formula of critical value is drived in two-modes approximation. The experimental results for deflections and natural frequencies are in fairly close agreement with theory.