Axial Force Influence on Transverse Displacement and Rotation Under Moving Load of Elastically Supported Damped Shear Beam

This research investigates the influence of axial force on the transverse displacement and rotation of a damped shear beam resting on an elastic foundation and subjected to moving load traveling at a constant velocity. The governing equations are coupled second-order partial differential equations. To simplify these equations, the finite Fourier series method was employed, transforming the coupled second-order partial differential equations into a set of coupled second-order ordinary differential equations. The simplified equations that describe the motion of the beam-load system were subsequently solved using Laplace transformation in conjunction with convolution theory to obtain the solutions. Comprehensive analyses are conducted to investigate the effects of axial force on the transverse displacement and rotation of damped shear beams of different length sizes when subjected to the moving load traversing the beam at different velocities respectively. Additionally, the study examines the effect of axial force on the critical velocities of the vibrating system. The findings reveal that the transverse displacement and rotation of the beam are noticeably reduced with increasing axial force. It is also found that as the value of axial force increases, the critical velocity increases indicating a safer dynamical system. From a practical perspective, this clearly indicates that axial force significantly enhances the dynamic stability of the beam when subjected to the moving load.