Axial force contribution to the out-of-plane response of horizontally curved beams under a moving mass excitation

Abstract

Horizontally curved beams subjected to a moving mass do experience a time-varying axial force due to the in-plane centrifugal action of the inertial accelerations. The current study aims at investigating the contribution of the induced axial force to the out-of-plane dynamics of horizontally curved beams under the excitation of a moving mass. The governing differential equations of motion are established to account for the action of the axial force, and also the effect of mass inertia, Coriolis and centrifugal forces introduced by a moving object. In the course of dealing with the semi-analytical approach, a new system of ordinary differential equations is distilled utilizing the transition matrix method in order to be amenable for numerical computations. The veracity of the solution has been corroborated through comparison with the results attained by the previous studies addressed in the literature. Moreover, the efficiency of the proposed solution is demonstrated through conducting an extensive parametric study. In that regard, the dynamic impact factor spectra have been obtained for various design parameters including the geometrical and dynamic properties of the system. The findings reveal that, in general, the dynamic impact factor is highly affected by the mass and velocity of the moving object. Furthermore, the results indicate that the inclusion of the axial force can result in a reduction in the dynamic impact factor spectra, which is shown to be more substantial for the response evaluation of short-span horizontally curved beams excited by a high-velocity heavy mass. In this particular situation, the mitigating effect of the axial force becomes comparable to that of the foundation damping. This paper concludes with an investigation on the influence of the axial force on the time-history patterns, which is demonstrated to attenuate the response amplitudes at both the forced and free vibration phases.