Critical Velocities for Beams Subjected to Moving Constant Loads

摘要

This paper calculates the special speeds (resonances) of a beam when the constant moving loads go after each other on it. By this way, the deflection of the beam may increase infinitely. A new load was assumed to enter the beam domain from the left as soon as the old one exited the beam from the right and this process being repeated. First, a theoretical formulation is developed for simply supported beam and several examples are solved to verify the formulation and also to show the effect of various parameters on modal properties of the beam. It has been shown that for simply supported beam when each moving load reaches the right hand side of it, the deflection of all points on the beam is zero. In addition, at such instants, all points on the beam have the same velocity direction with monotonic increase in their magnitudes. Then, a numerical method called discrete element technique (DET) is developed and the results obtained from analytical method are compared with numerical conclusions. Finally, having obtained the good agreement between the results of two methods and complicated analytical formulation for beams with other boundary conditions, the special speeds for these types of beams are obtained using DET.