Piezo-beam systems subjected to weak electric field: Experiments and modelling of non-linearities

Typical non-linear effects, e.g., dependence of the resonance frequency on the amplitude, superharmonics in spectra and a non-linear relationship between excitation voltage and vibration amplitude are observed in experiments with piezoceramics and in piezo-beam systems excited at resonance by weak electric fields. These non-linear effects can be observed for both the piezoelectric 31 and the 33-effect. In contrast to the well-known non-linear effects for piezo-ceramics in the presence of strong electric fields, our findings have not been described yet in detail in the literature. In this paper, a first description of these phenomena is given by formulating non-linear constitutive relations, in particular by introducing a non-constant Young's modulus E-c and piezo electric factor d(31) in the case of a piezo-beam system. The equations of motion for the system under consideration are derived via the Ritz method using Hamilton's principle. The non-linear parameters are determined and the numerical results are compared to those obtained experimentally. A finite element model is used for verification of the results obtained by the Ritz method. The effects described herein may have a significant influence whenever structures are excited close to resonance frequencies via piezoelectric elements. (C) 2002 Elsevier Science Ltd. All rights reserved.