Control of mechanical energy pumping in the nonhomogeneous system of coupled oscillators

We describe nonlinear dynamics of essentially non-homogeneous system of coupled oscillators using the technique of multi-scale expansions. The resonant mechanism of passive energy transfer from a massive oscillator into a light auxiliary one provides essential reduction of energy of the massive oscillator. Proposed active control algorithm increases noticeably the efficiency of energy transfer in comparison with passive control. The important advantage of this algorithm is that it provides a small consumption of energy. It is expedient to use our algorithm in the certain limits of parameters determined in the paper. This algorithm provides a necessary level of reduction of oscillator amplitude in a wide range of external perturbations.