Hysteresis elements such as elasto-plastic dampers are important elements for mechanical structures, especially for earthquake-proof structures. When such nonlinear supports are utilized for piping systems, the nonlinearities of the hysteresis elements and the geometrical complexity of the piping systems lead to complicated seismic responses, and thus further studies are required in order to enhance the reliability of the earthquake-proof design. In the seismic response analysis, the method of time history response analysis is widely used. In this paper, a method of nonlinear seismic response analysis for a piping systems using a combination of the FEM and the Differential Algebraic Equations (DAE) is proposed. As it is well known, the DAE is suitable for numerical analysis of time history responses for mechanical structures and machinery elements. According to the advantage of the DAE, the numerical modeling and simulation of a complex piping systems supported by the hysteresis elements can be easily carried out by using the proposed method. In order to verify the usefulness of the method, the time history responses of piping systems supported by a elasto-plastic damper is examined for seismic excitation by using the proposed method. The damper is modeled as a bilinear model. The effects of the second stiffness and the stiffness associated with the plastic deformation of the damper on the seismic responses are investigated using an actually recorded earthquake motion.

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