On the role of nonlinear piezoelectric constitutive parameters in the dynamic response of clamped–clamped axially loaded beams

Abstract

In this paper the influence of nonlinear constitutive piezoelectric parameters in the electromechanical coupled response for a clamped–clamped axially loaded energy harvester is studied. Due to the high slenderness ratio of the device, a three section beam according to Bernoulli–Euler theory, is proposed. The second section corresponds to the MFC 2814 bonded piezoelectric sheet. The complete partial differential equations that govern the axial–flexional–electric coupled problem are derived by using the Hamilton's principle. A reduced version of these expressions are obtained by assuming the axial displacement is quite smaller than transverse. The discretization of the equations is made according to the Galerkin method. An approximated solution for the single mode representation is obtained by the Method of Multiple Scales (MMS) and compared with the direct numerical integration of the equations showing excellent results. A prototype device is built, and experimentally tested to be compared with the proposed model. The numerical solutions and experimental results confirmed the need to consider nonlinear piezoelectric relationships for the proposed configuration to correctly predict the generated voltage.