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.

This paper is focused on an optimal design of two degree of freedom (2-DOF) dynamic vibration absorber (DVA) for the simply supported damped beam subject to a harmonic force excitation. In order to achieve this aim, we first show how to define the objective function of optimal design problem for 2-DOF DVA. Second, we apply the cyclic topology-based particle swarm optimization (PSO) to find the optimal design parameters of 2-DOF　DVA. Finally, some numerical results are compared with those of conventional researches, which demonstrates a reliability of the proposed design method

From comparing the impact dynamic absorber with the impact damper in the auxiliary vibration system with the conventional dynamic absorber, the following conclusions are obtained as follows ; 1. Recognizing that the amplitude restraining effect of the impact dynamic absorber become resonable in a comparison of conventional one development of an improved dynamic absorber may be probable. 2. With increasing the frequency ratio, the 1st resonance peak is higher but the 2nd one gets lower. In addition, the frequency ratio is peak located at the same resonance. 3. The optimum impact clearance is smaller and the vibration constraining effect becomes better with and increase in the mass of impact ball. And it is recognizable that the optimum tuning frequency ratio and impact clearance in an accordance with the mass ratio are varied. 4. The optimum tuning condition becomes gradually lower than the case of r=1 and maximum amplitude becomes lower with an increment in the mass ratio. However, the impulse clearance is larger and the working range of restraining vibration amplitude become smaller with a decrement in the mass of impact ball.