In order to study the dynamic response of continuous beams with arbitrary boundary conditions

a mechanical model of intermediate elastic supported beams with arbitrary constraints at both ends was established

and the method of solving its vibration frequency was given. The theoretical solution to the dynamic response of the beam under moving load was derived by means of mode superposition method. A MATLAB program was written to solve the equation

and the results obtained by the proposed method were compared with the values obtained by the finite element method through calculation example

which verified the correctness

precision

and application scope of the proposed method. The influence of the boundary conditions on the vibration response of the structure was analyzed. Results show that the higher order modes of the continuous beam with intermediate elastic support under arbitrary constraints at both ends were obviously different from those of the continuous beam with simple or fixed supports at both ends. The amplitude at the boundary of the higher order mode curve was larger because of the elastic boundary condition. Under the action of moving load

the maximum downward displacement of the beam appeared in the middle of the span

while the maximum upward displacement appeared in the ends of the beam. Positive bending moment and negative bending moment alternately appeared in each section of the beam body

and the positive bending moment in the middle of the span and the negative bending moment at the end points were the most significant. The fluctuation period of the mid-span displacement became longer when the moving velocity of the load increased. Compared with different boundary conditions

the variation amplitude of mid-span deflection of elastic support at both ends was between fixed support at both ends and simple support at both ends. The stiffness of rotational spring at both ends affected the vibration amplitude of the structure

while the stiffness of rotational spring had a more obvious effect on the maximum vibration displacement of the structure.