Analytical Investigation of Vibration Characteristic about Spinning Cantilever Beam

Spinning structure is one of important types of classical gyroscopic continua, and many interesting phenomena of the gyroscopic continua have been found due to the gyroscopic effect. In this paper, the vibration characteristic analysis of the spinning cantilever beam is studied. The two linear partial differential equations governing two transverse vibrations are derived by the extended Hamilton principle. The ordinary differential dynamic equations are obtained by using the modal expansion of Galerkin method. The natural frequencies, complex modes, and stability of the spinning cantilever beam are investigated by solving the standard eigenvalue problems of the linearized system directly. Some novel interesting phenomena have been obtained numerically and important conclusions have been drawn for this special spinning system.