Transverse vibrations of short beams: Finite element models obtained by a condensation method

This paper is concerned with the dynamic behaviour of Timoshenko beams. A new method for simply and systematically constructing finite beam elements is then proposed. The continuous model, which takes into account both rotary inertia and transverse shear deformation, is presented as a tutorial review. It allows certain vibratory phenomena characteristic of short beams to be demonstrated. A method is proposed for constructing a two-node finite element based on Guyan condensation that leads to the results of classical formulations, but in a simple and systematic manner. This element is verified with numerical and experimental tests. The proposed method is then generalized in order to obtain new improved three-node finite elements. (C) 1997 Academic Press Limited.