Analysis of Transverse Displacement and Rotation Under Moving Load of Prestressed Damped Shear Beam Resting on Vlasov Foundation

This study examines the transverse displacement and rotation of a prestressed damped shear beam supported by a Vlasov foundation when subjected to a moving load traveling at a constant velocity. The governing equations are expressed as 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 sequence of coupled second-order ordinary differential equations. Subsequently, the simplified equations that describe the motion of the beam-load system were solved using Laplace transformation in conjunction with convolution theory to obtain the solutions. The effects of some pertinent structural parameters on the transverse displacement and rotation of a prestressed shear beam when under the moving load were illustrated in graphs. Notably, the graphs indicate that an increase in these pertinent structural parameters reduces the transverse displacement and rotation of a prestressed shear beam when subjected to the moving load. From a practical standpoint, increase in the values of these structural parameters significantly enhances the stability of the beam and increases the critical speed of the dynamic system, thereby minimizing the risk of resonance and ensuring the safety of the structure's occupants.