This study deals with the vibration transmissibility of a vibration isolation device, which is composed of frictional damping and nonlinear softening springs, when its base is harmonically excited. The SCAP method, a type of averaging method, is employed to obtain steady-state responses. The vibration characteristics due to excitation of the base are investigated through the analysis of displacement transmissibility in the steady-state response. In this process, displacement transmissibility for design parameters is analyzed, and the stability of the response is also investigated. The vibration isolation effect due to frictional damping is found to be more effective in the case of the softening spring than in the case of the hardening spring. Additionally, the pattern of the jump phenomenon observed during frequency sweeping, both upward and downward, has been identified.

In this paper, the effect of a dynamic vibration absorber to suppress the response of a base excitation vibration system composed of a cubic nonlinear spring and a friction damper is investigated. And the dynamic absorber consists of a linear spring and a viscose damper. The mathematical models of these systems are governed by second order nonlinear ordinary differential equations. The response characteristics of the system are analyzed using the slowly changing phase and amplitude(SCPA) method, which is one of the averaging methods. As a function of the friction force ratio, It was obtained the locking frequency at which the relative motion starts was obtained, and the regions where the locking occurred. The displacement transmissibility was investigated according to the change of the design parameter, and the optimal design parameters could be found to minimize the displacement transmissibility.