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 Youngʹs modulus Ec and piezo electric factor d31 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.