This work presents characteristic of the mechatronic system that describes relation between displacement of the free end of the beam and voltage supplied to the piezoelectric transducer bonded to the beam surface. The considered system was described by discrete - continuous mathematical model and approximate Galerkin method was used to analyse it. Work presents analysis of the flexural vibrating one-dimension machatronic system - the cantilever beam with piezoelectric actuator glued onto the surface of the beam. Taking into account the eccentric tension of the glue layer the considered system was modelled as the combined beam made up of the beam, glue layer and piezoelectric transducer. The substitute cross-section of the considered mechatronic system was introduced to unify material parameters. The area and moment of inertia of the substitute cross-section was calculated and using basic laws and dependences from theory of the strength of materials the stress on the substitute cross-section's surfaces was assigned. This work is connected with the previous authors' works concerned with the analysis of mechatronic systems with piezoelectric dampers of vibrations or piezoelectric actuators and it was done to improve the mathematical model of the considered system.