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Just as it is indubitably accepted that the piezoelectric actuators do not behave in a linear fashion when subjected to strong electric fields, it was also believed that they behaved in a linear manner at weak electric fields excitations. But this notion was shattered by the experimental evidence offered by researchers in recent years, where it was observed that the piezo-actuators behaved non-linearly even when actuated at voltages which resulted in weak electric fields in the piezoelectric actuator. Most of the experiments, however, were conducted on the piezoelectric patches, and consequently most of the studies were aimed at establishing the non-linear relationship in the “31” electromechanical coupling, and the nonlinear elastic relation of the material along the longitudinal axis. Though this may be expected due to the widespread usage of the patches, the “33” coupling needs to be investigated too —as stack actuators are the preferred ones for the actuation of large structures. This study aims at characterizing the nonlinear behavior both in the patches and the stacks; thereby establishing the nonlinear constitutive equations for both the “31” and “33” coupling. To achieve this, a two-step experimental procedure was followed, wherein, firstly, the mechanical domain was isolated and studied to establish the non-linear elastic behavior. Later, equipped with the nonlinear stress-strain relation, experiments were conducted to identify the nature of the nonlinearity in the electromechanical coupling. Unlike the two-step experimental procedure, which facilitates a separate investigation into the mechanical domain and the electromechanical coupling, the experimental procedures employed in the previous studies yield data which mixes the contributions from both the mechanical domain and the electromechanical coupling. The experiments were conducted to obtain a family of displacement frequency response curves of the bending modes of a piezoelectric-beam and a piezostack-beam. The information from the displacement frequency response curves, and the profile of the backbone curves, obtained from both steps of experimentation, were used to determine the exact nonlinear terms required to represent the observed phenomenon. Eventually the nonlinear constitutive equations were constructed with these terms.
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