Flexural Vibration of Timoshenko Beams, Using Distributed Lumped Modeling Technique

This paper focuses on the development of a complete model of the Timoshenko beam, based on considering the effects of shear deformation. A method based on distributed-lumped modeling approach is proposed to solve the governing equations. Natural frequencies obtained by this method are compared and verified with Chebyshev pseudospectral method. The effects of shear deformation on natural frequency of pinned and clamped beams are discussed for various diameters. In addition, the effects of lumped mass and its position are investigated for clamped and pinned rotors with different diameters. It is shown that, while the new method leads to highly accurate results, its simplicity and accuracy makes it appropriate for application on industrial systems.