A feedback strategy, aiming at confining and suppressing simultaneously the vibratory motion in flexible structures, is proposed. It is assumed that the structure consists of parts that are sensitive to vibration. The proposed strategy makes use of control inputs whose number is less than or equal to that of the dimension of the discretized model. The design objective is to devise a feedback scheme that leads to transferring the vibrational energy from the sensitive parts to the remaining parts of the structure. In order to keep away from the build-up of transferred energy in the nonsensitive parts, the feedback scheme considers, along with the confinement, the suppression of vibration in both the sensitive and non-sensitive parts. The proposed strategy also accounts for the presence of persistent excitations. A finite element model of a cantilever beam is used to show the viability of the proposed strategy.