Further Insights Into the Timoshenko–Ehrenfest Beam Theory

Abstract

In this paper, the theory of a Timoshenko–Ehrenfest beam is revisited and given a new perspective with particular emphasis on the relative significances of the parameters underlying the theory. The investigation is intended to broaden the scope and applicability of the theory. It has been shown that the two parameters that characterize the Timoshenko–Ehrenfest beam theory, namely the rotary inertia and the shear deformation, can be related, and hence, they can be combined into one parameter when predicting the beam’s free vibration behavior. It is explained why the effect of the shear deformation on the free vibration behavior of a Timoshenko–Ehrenfest beam for any boundary condition will be always more pronounced than that of the rotary inertia. The range of applicability of the Timoshenko–Ehrenfest beam theory for realistic problems is demonstrated by a set of new curves, which provide considerable insights into the theory.