In this paper, an analytical method of the beam with springs and dampers fixed at the ends was proposed based on equivalent single degree of freedom (SDOF) system and secondary Lagrange’s dynamic equations, in order to develop a new effective method to enhance the aseismic capability of underground structures. The dynamic response of elastically supported and damply supported beams subjected to both seismic loading and static axial loading was analyzed by the proposed analytical procedure. The theoretical results were validated by the numerical simulation. In order to further investigate the effects of springs and dampers fixed at the ends of the columns in nonlinear response situation, the 3D nonlinear seismic responses of the Dakai metro station structure with and without the isolators were analyzed by ABAQUS respectively. It is demonstrated that: (1) the proposed analytical procedure can predict the dynamic response of beams with elastic and damper supports subjected to both seismic loading and axial loading. (2) Setting isolators at the supports of the column could enhance the aseismic capability of the structure effectively. (3) The axial static loading induced by the gravity of the soil and structure provide the constraint on the column, and therefore could not be neglected in the structural dynamic analysis.
On interpolation to an analytic function in equidistant points: problem $\beta$
