The transmission of plate flexural waves through a reinforcing beam is related to the coupling between the plate flexural waves and the flexural and torsional waves in the beam. The beam–plate coupling and the energy transmission through the beam can be described in terms of the trace wave matching of the flexural waves in the plate with the flexural and torsional waves in the beam. For a given incident flexural wave from the plate to the beam interface, the amount of trace matching is determined by the flexural and torsional wave numbers in the beam. It is shown in this paper that the reinforcing beam of an infinite beam–plate system serves as a good passive device in attenuating wave transmission except at two coincidences corresponding to the optimal wave trace-matching conditions. The maximum power flow across the beam at the optimal trace wave matching conditions can be reduced by a feedforward active control system using the information on the wave numbers at the coincidence conditions. In this paper, the coupling mechanisms involved with the wave transmission in a coupled beam–plate structure is used to explain the coincidence conditions of the wave transmission. The active control is applied to the reinforcing beam to attenuate the transmitted waves at the coincidences. Results demonstrate that it is possible to achieve a significant reduction of the transmitted energy by using an array of point forces and point moments, and the biologically inspired control strategy for the control actions.