Non-linear longitudinal vibrations of piezoceramics excited by weak electric fields

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 as well as jump phenomena are observed in experiments with piezoceramics 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 exhibited by piezoceramics in the presence of strong electric fields, these effects are not described in detail in the literature. In this paper, we attempt to model these phenomena using an electric enthalpy density to capture the cubic-like effects observed in the experiments. The equations of motion for the system under consideration are derived via the Ritz method using Hamilton's principle. The ‘non-linear’ parameters are identified and the numerical results are compared to those obtained experimentally. The effects described herein may have a significant influence in structures excited close to resonance frequencies via piezoelectric elements.