On the frequency range of Timoshenko beam theory

This article concerns with the analysis of the frequency range within which Timoshenko’s model can be applied for the study of vibrating beams, possibly without incurring in large engineering approximations. Timoshenko's equations are solved in exact way for all classical boundary conditions; frequencies and modes are compared with exact or asymptotically exact solutions of the elasticity theory based on the plane stress assumptions. The analytical procedures, the comparisons and the related findings show that a threshold previously conjectured as cut-off frequency ωco= √KAG/pJ could be a useful indication, to a certain extent, but it does not seem generalizable; incidentally, the analytical procedure, naturally provides frequencies falling in what could be defined as a single spectrum of Timoshenko's beam theory.