The vibrational power input to flexible beam- or plate-like machinery supporting structures at a single connection point subjected to simultaneously acting sinusoidal force and moment excitations is investigated. The vibrational power components due to the direct force, moment and the coupling between translational and rotational motions are compared. The study shows that because of the presence of coupling mobility functions for a multi-excitation system, the resultant vibrational power input to the supporting structures, at certain frequencies, may be smaller than the vibrational power input resulting from the force when it acts alone. Various vibrational control schemes, both active and passive approaches, based on minimisation of the resultant vibrational power input to the supporting structures are proposed and evaluated.