Analysis of high-speed rotating systems using Timoshenko beam theory in conjunction with the transfer matrix method

Higher operating speeds and increased sensitivity of modern electro-mechanical systems require improved methods for the computation of critical speeds and system response of flexible rotating shafts. Many high-speed systems generally contain disks with masses approaching the mass of the shaft. These observations emphasize the importance of including the effects of rotatory inertia and shear deformation of the shaft in the analysis. Traditional theory, which models a massless shaft, would be inaccurate for these systems. An analysis of flexible rotor systems has been performed using the Transfer Matrix Method. Although the method is well known, the present study utilizes Timoshenko Beam Theory in the construction of field matrices, which relate state vectors at adjacent nodes of the system. This approach takes into consideration the effects of transverse shear and rotatory inertia. Also included in the model are gyroscopic effects of the spinning disks. These effects are generally neglected in classical rotor dynamic theory. A general model was developed for the analysis of typical configurations in which the shaft is simply supported, and can carry an arbitrary number of disks. Numerical simulations were performed for comparision with classical results. These case studies show agreement with what is to be expected by introducing the greater flexibility of Timoshenko Beam Theory and the stiffening effects of gyroscopic couples