Dynamics of beams travelled by equally spaced forces via transfer matrix approach

Abstract

Abstract This work addresses the dynamic behavior of slender elastic structures travelled by a train of equally spaced transverse forces. Assuming the structures are representable via an Euler-Bernoulli beam, the velocity of the train of forces is constant, and the distance between adjacent forces is equal to an integer submultiple of the beam length, the problem is solved analytically. The analytical solution is based on a linear map, which transforms the system state (positions and velocities of the beam points) at the time instant at which one of the travelling forces leaves the beam from one of its ends, to the system state at the time instant at which the subsequent travelling force in the train leaves the beam from the same end. The reiteration of the linear map provides the time response of the beam. The proposed solution enables the analytical study of the dynamic behavior of the structure and highlights the presence of critical velocities at which divergence phenomena by response accretion may occur. Comparisons with the results of numerical methods confirm the accuracy of the analytical solution.