Active control of bending waves in a periodic beam by the Timoshenko beam theory is concerned. A discussion about the possible wave solutions for periodic beams and their control by forces is presented. Wave propagation in a periodic beam is studied. The transfer matrix between two consecutive unit cells is obtained based on the continuity conditions. Wave amplitudes are derived by employing the Bloch-Floquet theorem and the transfer matrix. The influences of the propagating constant on the wave amplitudes are considered. It is shown that vibrations are still needed to be suppressed in the pass-band regions. Wave-suppression strategy described in this paper is employed to eliminate the propagating disturbance of an infinite periodic beam. A minimum wave-suppression strategy is compared with the classical wave-suppression strategy.
The wave propagation approach is presented to research the active vibration control of two-beam structures.Considering the continuity of the generalized displacement and the equilibrium of the generalized force at the discontinuity,the wave reflection and transmission coefficients are calculated.Wave control is applied somewhere upstream or downstream to two-beam structures.Vibrations of two coupled beams per unit disturbance are investigated.The results show that wave control is efficient,and the influence of the thickness ratio of two-beam structures on control location is discussed.
