A new kind of composite structures has been developed, called intelligent or smart structures. They appear most often in the form of beams, rods, plates or shells which are additionally equipped with distributed sensors, actuators, control elements and even supply systems. The problems of free vibration damping, selection of control systems, glue interactions between a structure and piezoelements and frequency influence are widely discussed in the works by Crawley and de Luis, Jie Pan, Hansen and Snyder and Tzou. The application of piezoelements for damping the parametric vibration of a rod under a harmonically varying axial force was the subject of a study by Tylikowski. Active vibration control can also be achieved by utilizing so-called electrorheological fluids filling special channels inside a structure. Electrorheological fluids are characterized by a strong dependence of their viscosity on the externally applied electric field.