In physics/engineering all systems, including molecular systems and particles, tend to vibrate at a natural frequency depending upon their structure. When an oscillating force is applied at the resonant frequency of the system, the amplitude of oscillation tends to infinitely   increase, what may result in system malfunction or worse to its collapse. Hence, in this work the application of active structures technology and its features for natural vibration control in slender geometrically non-linear beam-systems is discussed. The subject of interest covers a host beam member with top and bottom surface-bonded piezoelectric (PZT) layers. By precisely adjusting the voltage applied across PZT layers taking into account their poling direction and the direction of the electric field vector, it is possible to exert: tensile force in one PZT layer, compressive force in the other one or force both layers to behave in the same manner. In the studied case one induce equal residual force in terms of value and direction for each PZT layer, simultaneously applying compression or tension. Hence, having at both beam ends boundary conditions preventing longitudinal displacements, induced axial residual force creates non‑zero in‑plane stress along beam, what subsequently results in the adjustment of the eigenfrequency in regard to the non-actuated system.

One provides a mathematical formulation and derivation of motion equations using the Hamilton’s principle taking into account linear stress-strain relationship with electro mechanical coupling for the piezoelectric material. The influence of both structural parameters and piezoelectric actuation on fine-tuning of the oscillation frequency is investigated. Presented approximate numerical results reveal that the vibration frequency of the non-actuated system changes in a non-linear way together with the location of PZT layers bonding along the beam and their length. Moreover, as soon as the electric field is applied to the system it is exhibited that the piezoelectric actuation may be used as an efficient tool for alteration of system dynamic response far from the excitation band.