Characterization of elastic and electromechanical nonlinearities in piezoceramic plate actuators from vibrations of a piezoelectric-beam

Piezoceramic actuators have been observed to exhibit nonlinear behaviour even when subjected to weak electric fields. The experimental observations necessitate the need for a nonlinear constitutive equation, to aptly describe the behaviour of the piezoelectric actuators. The nonlinear response could have been effected due to a nonlinear behaviour in the mechanical domain (nonlinear elastic behaviour), or due to a nonlinear electromechanical coupling, or due to a combination of both the nonlinear elastic behaviour and nonlinear electromechanical coupling. To locate the source of nonlinearity and to identify the nature of the nonlinearity, a two-step experimental procedure is proposed in this article, wherein experiments were conducted on a cantilever duralumin beam with a pair of surface bonded PZT-5H piezoelectric patches. The source of the nonlinearity in the piezoelectric actuators (as to whether it is from the mechanical domain, or in the electromechanical coupling) can be directly identified from the experimental results obtained from this procedure. The nature of the contribution of each domain, to the overall nonlinear behaviour, can be deduced from the backbone curves obtained from the piezoelectric-beam vibrations. The first-step of the experimental procedure was aimed at investigating only the mechanical domain of the piezoelectric actuator. This was achieved by short circuiting the PZT-5H patches and obtaining the displacement frequency response curves of the piezoelectric-beam by base excitation. The second-step of experiments were aimed to investigate the presence of nonlinearity in the electromechanical coupling. Here, the piezoelectric-beam was excited by the PZT-5H actuator to get a similar set of displacement frequency response curves for the first, second and third modes. The nonlinear constitutive equation was established from the profile of the backbone curves of the displacement frequency response plots obtained from the experiments. It was observed that, apart from the linear terms, both quadratic and cubic strain terms were required to represent the stress in the piezoelectric material. The electromechanical coupling too required a nonlinear representation whereby, aside from the linear relation the stress was equal to the product of cubic strain and the electric field.