Nonlinear vibrations of elastic beam with piezoelectric actuators

This paper presents theoretical and experimental investigations into nonlinear flexural vibrations of a structure composed of a host beam with piezoelectric ceramic actuators symmetrically bonded to its top and bottom surfaces. The composite beam is supported at its ends to completely restrain axial displacements or to impose the displacement of one or both ends. Applying voltage to piezoelectric actuators one creates prestress which can stabilize the structure when the external compressive force appears. The analytical model for describing flexural vibration of a beam under both the external load and piezoelectric actuation is based on the Euler-Bernoulli beam. The piezo material exhibits linear piezoelectricity with constitutive equations including electromechanical coupling. Due to geometrical nonlinearity, the solution to the problem has been obtained by using the Lindstedt-Poincare perturbation method. The main results concern the effect of the residual piezo force on the non-linear vibration frequency of the structure. In the experimental part of the study two laboratory stands have been designed and built for three and five segmented beams to find out and prove the effect of the electric field on the residual force and the natural frequency of both systems. Very good agreement between theoretical and experimental results has been observed.