Asymmetric actuation and sensing of a beam using piezoelectric materials

This paper presents the development of a theoretical model and an experimental study for the response of a beam actuated by a ceramic piezoelectric on one side with a PVDF piezoelectric on the opposite side acting as a sensor. The two piezoelectric are of different types, may be of arbitrary length, and are positioned independently along the beam. Since the actuation is done by a single piezo on one side of the beam, an asymmetric excitation is applied to the beam that causes simultaneously extensional and flexural displacements. Both piezoelectric elements are considered perfectly bonded to the beam. The variational approach with Hamilton’s principle is used to develop the theoretical model. This formulation, which is energy based, allows one to consider any boundary conditions at the ends of the beam and to take into account the dynamic effects (mass loading and stiffness) of both piezos on the beam response ignored in existing models. Experimental results are presented for the free–free boundary conditions. Those results show good agreement with the theoretical model and prove that the piezo’s modify the mode shapes and natural frequencies of the beam. The changes in the mode shapes can be of vital importance in some applications.