A simple spinning laminated composite shaft model

A simple spinning composite shaft model is presented in this paper. The composite shaft contains discrete isotropic rigid disks and is supported by bearings that are modeled as springs and viscous dampers. Based on a first-order shear deformable beam theory, the strain energy of the shaft are found by adopting the three-dimensional constitutive relations of material with the help of the coordinates transformation, while the kinetic energy of the shaft system is obtained via utilizing the moving rotating coordinate systems adhered to the cross-sections of shaft. The extended Hamilton’s principle is employed to derive the governing equations. In the model the transverse shear deformation, rotary inertia and gyroscopic effects, as well as the coupling effect due to the lamination of composite layers have been incorporated. To verify the present model, the critical speeds of composite shaft systems are compared with those available in the literature. A numerical example is also given to illustrate the frequencies, mode shapes, and transient response of a particular composite shaft system.