On the out-of-plane dynamic response of horizontally curved beams resting on elastic foundation traversed by a moving mass

摘要

In this paper, the dynamic behavior of Horizontally Curved Beams (HCBs) resting on an elastic foundation and subjected to a moving mass is investigated. The governing coupled non-linear differential equations of equilibrium are derived, where Coriolis acceleration, centrifugal force and rotary inertia are incorporated in the problem formulation. In the proposed analytical solution, by employing the transition matrix technique, the governing differential equations of motion are subsequently transformed into a new system of linear ordinary differential equations which can be solved using standard numerical procedures. The accuracy as well as the robustness of the solution is ascertained through a comparative study with the solutions previously reported in the literature. Extensive parametric study is then carried out in order to demonstrate the efficiency of the proposed semi-analytical approach. The design Dynamic Amplification Factor (DAF) spectra have been established in terms of influential parameters including radius and subtended angle of the curved beam, mass of the moving object and the number of dynamic modes. The significance of considering the inertial effect of the moving mass is also highlighted in the dynamic response of HCBs, especially in severely curved elements subjected to the excitation of a heavy mass traversing at high speeds. Moreover, the effect of higher dynamic modes in the response has been scrutinized. Thereafter, based on the multiple nonlinear regression analysis, simplified parametric expressions have been proposed for the calculation of DAFs, which can be used in practical and analytical applications. The paper is followed by the reformulation of the problem in order to examine the contribution of axial force on the out-of-plane responses of HCBs. The last two sections are devoted to the study of the influence of additional torsional stiffness due to fasteners as well as foundation vertical damping on the DAF response spectra. The results of this study suggest that the effect of additional inertial terms is crucial in a wide range of design parameters. Therefore, in comparison to the unsafe results originated from the moving force method, moving mass approach is a better and a more reliable representative of the real-world dynamic response of HCBs. As a general conclusion, with an increasing curvature of the HCB, the DAFs also increase. In a similar manner, the DAFs intensify due to an increase in the mass and ve-locity of the moving object. Moreover, it is shown that consideration of the axial force can attenuate the values of DAFs to a degree which mainly depends on the magnitude of the tensile force experienced by the HCB. The results also reveal that the inclusion of the foundation vertical damping leads to a reduction in the DAF spectra, which is shown to be more significant for sharply curved beams subjected to a high-speed heavy mass. However, by adopting the additional torsional stiffness, slightly smaller DAFs would be derived for all cases considered in this study. (C) 2020 Elsevier Ltd. All rights reserved.