Critical comparison of exact solutions in random vibration of beams using three versions of Bresse-Timoshenko theory

In this study we deal with random vibrations of uniform Bresse-Timoshenko beams. In contrast with the original version of the Bresse-Timoshenkobeam theory, we utilize two truncated theories which do not contain the fourth order derivative with respect to time. It is shown that in some cases of damping, the mean square responses produced by these two theories coincide, whereas in other cases these quantities differ from each other. Different assumptions are made: