Vibration Analysis of Beams Traversed by a Moving Mass

Abstract

A detailed investigation into the analysis of beams with different boundary conditions. carrying either a moving mass or force is performed. Analytical and numerical techniques for determination of the dynamic behavior of beams due to a concentrated travelling force or mass are presented. The transformation of the familiar Euler-Bernoulli thin beam equation into a series of ordinary differential equations is demonstrated. These equations are solved numerically using fourth order Runge-Kutta and central difference expansion methods. It is observed that the results corresponding to either method of solution, with the assumption made (moving force or mass) are very close. Moreover, the moving force problem is solved using the finite element method. The inertial effect of the moving mass has been proven to be an important factor in the dynamic behavior of such structures. Finally. using the obtained dynamic deflection functions, values of maximum shear force and bending moment at each time step are calculated and variation of these parameters with time is demonstrated.