Abstract: Much attention has been paid to the properties of materials and the shapes of crosssections of beams in order to increase the resistance of seismic loading structures. The seismic resistance of beams could be also increased effectively by setting some special constrained condition at the supports. The dynamic response of beams is investigated with flexible supports condition which show the elastic and damping feature. A simplified equivalent DOF analytical method of the beam with springs and dampers was established on basis of secondary Lagrange's dynamic equations. The dynamic response (relative displacement of the midspan, the absolute displacement of the supports, the influences of the stiffness and damping coefficient and etc.) of beams is analyzed, the theoretical results are validated by ABAQUS numerical simulation method, Which shows that the equivalent DOF analytical method could precisely describe the dynamic response of beams with flexible supports subjected to seismic loading, and setting springs and dampers at the supports could reduced the displacement of the midspan relative to the supports effectively, but it may increased the absolute displacements at the supports.

Key words: seismic load, elastic support, damping support, dynamic response