Responses of a two degrees-of-freedom system with uncertain parameters in the vicinity of resonance 1:1

Abstract

We analyze the dynamics of a nonlinear mechanical system under the influence of an external harmonic force. The system consists of a linear oscillator (primary mass) and attached nonlinear dynamic absorber. It is supposed that the frequency of the external force is close to the natural frequency of the main mass. Assuming that the parameters of the system are uncertain, the stability conditions of the stationary regimes of the averaged equations are obtained analytically; these regimes correspond to the quasi-periodic motions of the original input system. An analytical approach to the problem of selecting the parameters of a dynamic absorber is proposed in order to reduce the amplitude of oscilla tions of the main system. The results obtained are compared with the results of the numerical integration of the equations of the motion with different initial conditions and parameter values