Did S.P. Timoshenko and P. Ehrenfest Overestimate the Importance of the Fourth-Order Time Derivative in Their Theory of Beams?

In this study we investigate the importance of the fourth order time derivative that appears in the equations derived by Jacques Antoine Charles Bresse in 1859, as well as in equations that were derived by Stephen Prokofievich Timoshenko and Paul Ehrenfest during years 1912–1913 and reported by Timoshenko in the 1916 book on theory of elasticity in the Russian language and then in two papers dated 1920 and 1921, in English.