Analytical vibration of spinning, elastic disk-spindle systems

This work;develops the dynamic equations of motion for a spinning disk-spin dle system and casts them in a structured formulation that reveals the clas sical gyroscopic nature of the system. The disk and spindle are modeled as elastic continua coupled by a rigid, three-dimensional clamp. The inherent structure of the system is clarified with the definition of extended operat ors that collect the component disk, spindle, and clamp equations of motion into a compact analytical form. The extended operators are easily identifi ed as the inertia, elastic bending stiffness, gyroscopic, and rotational st iffness operators, and they possess the symmetry and definiteness character istics that define gyroscopic continua. Consequently, well-known analytical methods Sor gyroscopic systems are readily applied to disk-spindle systems , Qualitative eigensolution properties, an exact, closed-form response anal ysis, and the Galerkin discretization that follow naturally from the struct ured formulation are discussed. A free and forced vibration example is pres ented.