Abstract: By the harmonically balancing method, the response computation of a kind of hysteretic vibration system composed of nonlinear dry frictionally damped shock absorber with the memory less part in which the cubic restoring force depending on the displacement ,x (t) only exists is studied. The conclution that due to the cubic restoring force the amplitude-frequency curve of system will appear the bending and jumping phenomena is proposed.

Key words: Hysteretic vibration system, Nonlinear, Response computation