Abstract: The invention concerns the design methodology for high speed rotating shafts based on the wave spectrum analysis of the vibrational modes of elastic circular rods and shells. In accord with the invention, a shaft is designed by (1) selecting the material of the shaft; (2) determining dilational wave speed of the material as a function of frequency; (3) determining shear wave speed of the material as a function of frequency; (4) solving for critical frequencies of the shaft by solving a three-dimensional characteristic frequency equation for the shaft, the equation being defined by the dilational wave speed, the shear wave speed, and the inner and outer radius of the shell, the critical frequencies defining functions that depend upon physical dimensions of the inner and outer radius; and (5) specifying the inner and outer radius of the shell by minimizing cross-over of critical frequencies over operational rotational speeds of the shaft.

Abstract: A set of three geometric anagles is initiated to track the trajectories of moving objects. The objects to be tracked include but not limit to: satellites, space shuttles, airplanes, missiles moving in aerospace; submarines, ships, fish groups and other moving objects in hydrospace; cars, trucks, trains, human-beings and anmals moving on lands; planet motions in the solar system; particle motions in a controlled experiment in our national labories; contaminants, and hazardous materials in a variety of environmental conditions. All these objects can be detected and monitored by means of various sensing technologies which include seismic, acoustic, electro-magnetic, thermal, chemical, electro-optical and infrared. Mapping and monitoring systems could be deployed in unattended arrays or aboard ground, air, or maritime vehicles.