In-plane vibration analysis of horizontally curved beams resting on visco-elastic foundation subjected to a moving mass

This paper deals with the in-plane dynamics of Horizontally Curved Beams (HCBs) supported by a visco-elastic foundation under the excitation induced by a moving mass. What has been included as worthy of detailed exposition is the inevitable contribution of the inertial actions of the mass object into the problem formulation. By taking into account the effect of Coriolis acceleration, centrifugal force and rotary inertia, the governing coupled non-linear differential equations of equilibrium for a simply supported HCB are derived.In the proposed solution, a new system of linear ordinary differential equations is distilled from the governing differential equations of motion, which can be solved utilizing standard numerical techniques. The capability as well as the reliability of the proposed semi-analytical solution is also examined through an extensive parametric study.On that account, non-dimensional parameters are defined to advantage as input data in response calculations and to better interpret the outcomes. To this aim, the Dynamic Amplification Factor (DAF) spectra are introduced with particular attention to the influential parameters such as subtended (central) angle and radius of the HCB, mass and speed of the moving object along with the number of contributing modes.The significance of allowing for the contribution of moving mass inertia is demonstrated in the dynamic response of HCBs, focusing on highly curved elements under the action of a heavy mass at high speeds.It is shown that, in a wide range of design parameters, the simplified moving-force solution would not work to satisfaction if utilized in the analysis of HCB-moving mass dynamics. However, the moving mass framework takes care of all the essential effects induced due to a moving object running on an HCB.In addition, on the basis of the multiple nonlinear regression analysis, simplified expressions have been established which are advantageous in that they supply a means to predict the DAFs in a more practical manner. The findings of the present investigation imply that the influence of additional inertial terms is of fundamental importance in a wide range of design parameters. Therefore, emphasis is placed on implementing the moving mass method, as a more rigorous and reliable representative of the real-world dynamic response of HCBs in comparison with the unsafe results obtained from the moving force approach.Attention is also accorded to the influence of cross-ties in conjunction with the torsional stiffness of rail-tie connection on the in-plane dynamics of HCBs. Also, the results indicate that sharply-curved HCBs, especially at high velocities, are apt to higher DAFs under the action of an in-plane moving inertial load.