An elasto-plastic damper is one of the vibration absorbers in which energy is absorbed by elasto-plastic deformation of the hysteretic type damper. It is used for the piping system. The piping system is continuous system. Since it is difficult to find the analytical solution of the equation of motion for the system with elasto-plastic damper, the equation of motion is treated by various approximate methods in which the system is usually considered as a single- or a multiple-degree-of-freedom system, but not as a continuous system. In order to analyze the response of a nonlinear continuous system, however, it is necessary to consider the system as a continuous system. In this paper, the nonlinear steady-state response of the piping system with elasto-plastic damper is undertaken by approximate solutions, which are easily obtained by a simple procedure and are more practical than the exact solutions. As a continuous model of the piping system, a beam simply supported or clamped at one end, with elasto-plastic damper at the other end is used. The restoring force is modeled as hysteresis loop characteristics in order to consider the energy loss in the damper. In the analysis, the restoring force is expanded into the Fourier series, and only fundamental terms are considered. The resonance curves and mode shapes of the beam are obtained from the approximate solution. And effect of elasto-plastic damper on the forced response of continuous system is examined.

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