Analysis and control of vibrations of honeycomb plates by parametric stiffness modulations

This paper addresses an active control of the resonant vibrations of a sandwich plate with the honeycomb composition of a core ply performed by a parametric stiffness modulation. The controlled vibrations are those of the dominantly flexural type excited by a transverse force acting at a low resonant frequency. The stiffness modulation is introduced by some fairly small changes in an orientation of plates composing cell elements of a core ply. It is performed at a comparatively high frequency identified by the resonance of a mode of the dominantly shear type. The method of direct partition of motions is used that predicts an existence of the modal interaction between the low-frequency and the high-frequency motions. It is shown that such a parametric control can provide a significant favourable shift of the first eigenfrequency of a controlled beam (the one subjected to the stiffness modulation) from its nominal value for an uncontrolled beam. Asymptotic results are checked by direct time-marching integration. The energy of the `micro-motions' is calculated and it is compared with the energies of flexural vibrations of a plate with and without control. Heavy fluid loading conditions are accounted for as well as material losses in a structure. It is demonstrated that although heavy fluid loading reduces the resonant frequencies of forced vibrations, the suggested mechanism of control remains valid in these cases.