Transverse Vibration Analysis of Uniform Beams under Various Ends Restraints

The beam analysis, based on the assumptions of the Bernoulli-Euler theory, in free vibration has been largely investigated. Many researches focused on the transverse vibrations study, under the application of different boundary constraints where different theories were applied. The considered stiffness and mass matrices are those obtained by assembling the elementary ones resulting from the FEM use The Jacobi method allowed the solution of the eigenvalue problem. These well known concepts were applied to the study of beams with constant geometrical and mechanical characteristics having one to two overhangs with variable lengths. Murphy studied, by an algebraic solving approach, a simply supported beam with two overhangs of arbitrary length, which allows an experimental determination of the E elastic modulus.The advantage of our paper offers a possibility of extending this approach to many interesting problems formed by beams vibrating transversally with various ends restraints.