Sensitivity analysis of vibration response of timoshenko beam to mass ratio and velocity of moving mass and boundary conditions: Semi-analytical approach

In real-world physics phenomena, the boundary conditions of structural members in the structural beam systems affect the system response. Also, moving load or mass problems are used widely in many engineering fields, such as structural, transportation, mechanical engineering, etc. Therefore, it is necessary to study the effect of boundary conditions on beam vibrations. Hence, a semi-analytical approach for the Timoshenko beam with various boundary conditions under moving mass is presented in this paper. Dynamic Green Function is introduced for modeling the beam under moving mass. An accurate formulation is illustrated for modeling a Timoshenko beam under moving mass with different boundary conditions. Finally, some examples demonstrate to assess of the effect of different boundary conditions, the mass ratio of moving mass, and the speed of moving mass. The numerical results are shown the efficiency and simplicity of the present approach. Based on the results, it is found that the mass ratio affects the dynamic response shape. For moving mass, the delay of the maximum dynamic deflection with respect to the mass position, increases with the speed at the higher speeds. But for smaller values of the speed, the same results of the maximum dynamic deflection for the moving load model along with the moving mass model are obtained. On the other hand, the maximum dynamic deflection points of the curves move slightly towards the right end of the beam with an increasing mass ratio. Also, the location of the constraint in the asymmetric beams is more significant in dynamic response. It is found that the dynamic behavior of the beam under moving mass changes dramatically based on the type of boundary conditions. Furthermore, the displacement obtained for each boundary condition decreases with increasing mass speed.