G.A.U.S., Mech. Eng. Dept., Univ. de Sherbrooke, Sherbrooke, PQ J1K 2R1, Canada
The purpose of the present work is the modeling of a beam actuated by a ceramic piezoelectric on the top with a PVDF piezoelectric on the opposite side acting as a sensor. The two piezoelectric are different in types, may be of arbitrary length and can be positioned independently along the beam. Since there is only one actuator, the asymmetric excitation induces transverse and axial displacement in the beam. This asymmetric actuation contrast with the symmetric actuation normally considered in the literature. Symmetric actuation implies no axial displacement. Here, both piezos are considered perfectly bonded to the beam and the Bernoulli--Euler hypothesis is used for the displacement field. The variational approach with Hamilton's principle is put to use in the theoretical model. Hamilton's principle states that the definite time integral of the Lagrangian shall be stationary. This formulation, which is energy based, allows one to consider any boundary conditions and to take into account the dynamic effects of both piezos on the beam response. The theoretical model gives the axial and transverse displacements, the strains, the mean quadratic velocity of the beam, and the voltage of the PVDF piezo sensor as a function of the voltage given to the actuating ceramic piezo. Experimental results are compared to the theoretical model for the case of the beam with free-ends boundary conditions.