Effect of Flexural Rigidity on Dynamic Response to Moving Load of Damped Shear Beam Resting on Vlasov Foundation

This research investigates the effect of flexural rigidity on dynamic response to moving load of damped shear beam resting on an Vlasov foundation when subjected to moving load traveling at a constant velocity. The governing equations are coupled second-order partial differential equations. The finite Fourier series method was employed to transform the coupled second-order partial differential equations into a set of coupled second-order ordinary differential equations. The resulting simplified equations that characterize the motion of the beam-load system were then solved using Laplace transformation alongside the convolution theory to derive the solutions. Extensive analyses were performed to assess the impact of flexural rigidity on the transverse displacement and rotation of damped shear beams of different lengths when subjected to the moving load traversing at a constant velocity. Furthermore, the research investigates how flexural rigidity affects the critical velocities of the vibrating system. The results indicate that both the transverse displacement and rotation of the beam significantly decrease as flexural rigidity increases. Additionally, it was observed that an increase in flexural rigidity correlates with a rise in critical velocity, suggesting a more stable dynamic system. From a practical standpoint, these findings clearly demonstrate that flexural rigidity plays a crucial role in enhancing the dynamic stability of the beam under the influence of the moving load.