The field of tensions of a rotating anisotropic disc of a variable thickness loaded with undistracted forces on the outer contour

The work gives a solution of the plane elasticity problem for rotating polar-orthotropic annular disks of a variable thickness. The disk is loaded with a system of equal focused forces on the outer contour applied evenly along the rim and symmetric concerning the diameter. The disk is seated with an interference fit on the flexible shaft so that a constant contact pressure acts on the interior contour. The stresses and deformations arising in such a rotating anisotropic annular disk will be non-axisymmetric. A conclusion of a fourth-order partial differential equation for the effort function is drawn. Its general solution is searched out in the form of a Fourier series of cosines with even numbers. As a result, an infinite system of ordinary differential equations is solved for the coefficients of the series. These differential equations correspond to the linear Volterra integral equations of the 2 nd kind, which are solved using resolvents. Constants of integration are determined from the border conditions. Expressions for the stress components are written through the effort function by the well-known formulas. We find the components of the displacement vector in the disk by the integration of the Hooke’s law equations for the polar-orthotropic plate. We calculate the deformation components in a ring anisotropic disk by Cauchy differential relations if we know the displacements. The solved formulas for stresses, deformations and displacements completely describe the stress-deformed state in a rotating polar-orthotropic disc of variable thickness with a system of focused forces on the outer contour. The results of the work can be used in the design of working disks of turbomachines and turbo compressors, as well as rotors of centrifugal stands.

Color display of the localized spectrum

This paper develops a new display technique for seismic cross‐sections, called spectral color. The need to visualize frequency information in seismic data is recognized uniformly and often is accomplished through the color display of instantaneous frequency. The spectral content of a reflected event can carry information about the reflecting horizon’s characteristics which will not be resolved in the instantaneous state of the record. Spectral color is devised to overcome the problem of displaying an entire localized spectrum at each time sample and offset of a seismic section. The localized spectrum is calculated with a relatively new time‐frequency representation called the S-transform, which combines a Fourier technique with adaptive windowing in the frequency domain. A color (RGB triplet) based on the localized spectral content is calculated and the pixel is displayed at the appropriate position in the seismic section. As a result, the seismic cross‐section is displayed in an intuitive manner that is much the way we see the world around us. Strongly reflecting or well‐lit objects appear to us as bright, and the color tells us about the frequency content of the reflected energy. Spectral color is applied to ultrasonic laboratory data acquired over a thin anisotropic disk. It reveals a change in color (spectral content) with azimuth where no significant amplitude variation with azimuth was observed. Spectral color is illustrated further by application to a 3-D field data set and is compared to other, more standard, color displays.

Thermal Effect on the Transverse Vibration of High-Speed Rotating Anisotropic Disk

An attempt has been made to consider the thermal effect on the transverse vibration of a high-speed rotating disk in a steady-state heat conduction. The material of the disk, in this case, is assumed to be thermomechanically anisotropic. The present attempt is made with an objective to provide some theoretical studies on the problem that may serve as a base from which more detailed investigations with regard to the usage of composite material may be attempted to gain new and needed design information regarding turbine disks and thereby to reduce the chances of turbine failure. In this connection a new critical speed of disk rotation has been obtained and consequently this critical speed is found to depend on central temperature, thermomechanical anisotropy, and so forth.

Thermal stresses in a rotating, nonhomogeneous, anisotropic disk of varying thickness and density

Closed form solution is obtained for stresses in a rotationally symmetric, nonhomogeneous, anisotropic, annular disk of varying thickness and density, subjected to thermal loading. Analysis is presented for a particular type of anisotropy, namely Polar Orthotropy, in which axes of anisotropy coincide with the principal axes of stresses at each point in the disk. The variations of homogenity, density and thickness are assumed to be hyperbolic. Numerical results in the form of graphs presented show the effect of nonhomogenity, density and degree of orthotropy on the stress distribution in a disk subjected to constant and varying temperature gradients. Homogeneous, varying density anisotropic rotating disk of varying thickness forms a special case of the analysis.