In this work, the nonlinear behavior of the piezoelectric actuators are investigated from the experimental analysis of a piezoelectric-beam. A sequential experimental procedure is followed to study the elastic domain and the electromechanical coupling. Though this was done before, this time emphasis is also placed on other factors that may influence the experimental results. Experimental investigations are conducted to check (i) whether the way in which the fixed boundary condition is implemented induces any nonlinear behavior in the structure’s response, (ii) whether the air drag plays a role in the observed nonlinear effect and (iii) whether the dip in the input force and voltage levels, around the resonance, lead to the observed displaying the nonlinear effect. The results of these additional studies, along with the findings from the sequential experimental procedure, suggest a linear elastic behavior and a nonlinear electromechanical coupling in the piezoelectric actuators.
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.
In this work, the notion of using surface bondable piezoelectric actuators, which directly use the “33” electromechanical coupling, for actuating large structures is investigated. This concept was a result of the attempt to control the vibrations of a steel marine platform with piezoelectric actuators. Piezoelectric actuators find applications both in the excitations of membrane-like structures, wherein thin patches are bonded to the surface of the substructure to, and in the excitation of large structures, where piezoelectric stack actuators are conventionally employed akin to an electrodynamic exciter with stringer —to provide transverse loading. For the case of the actuation of the marine platform, the use of the piezoelectric stack actuators in a conventional manner could not be suggested for implementation on the actual structure due to its associated drawbacks. As an alternative, the concept of the surface bondable piezoelectric stack actuators was proposed. This design allows the stack actuators to be bonded to the surface of the structure (like a patch), and just like the patches, on the application of an external electric field would generate axial forces on the surface of the structure. In this study, the design of such an actuator is elaborated; following which, an analytical model is derived for beams with surface-bonded stack actuators. The analytical model is derived for the bending vibrations of the structure, and is used to investigate the necessity of the design and the actuation capability of the surface-bondable stacks. The actuation capability of the surface bondable stacks are compared with the actuation capability of other stack implementations, and with similar sized piezoelectric patches. Finally, experimental evidence is provided to demonstrate the practicality of the design.
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