Vibration of spinning beam based on transfer matrix method of linear multibody systems

The analysis of natural vibration characteristics has become an important step of the manufacture and dynamic design in different engineering branches and industries. In order to solve the vibration behavior of spinning Euler- Bernoulli beam, a transfer matrix method for multibody systems is developed. The components of the transfer matrix are all functions of the system's natural frequency. However, overall transfer equation only involves boundary state vectors; whereas the state vectors at all other connection points do not appear. The state vectors at the boundary are composed of displacements, rotation angles, internal bending moments and internal shear forces, which are partly known and partly unknown. In addition, the overall transfer matrix is independent of the degrees of the freedom. For validation, the proposed approach will be demonstrated for example taken from the literature.