RESUMO
Lead magnesium niobate ceramics (PMN) are promising materials for application in the field of high power transducers. The advantage of PMN materials are the large strains generated under moderate electric field and the low hysteresis. The electrostrictive effect is non-linear, the corresponding physical constants depend on temperature and frequency and a DC electrical bias is required. These difficulties must be considered at the design stage. A finite element model has been developed and validated in the ATILA code for non-linear static and time-domain analyses. These numerical modelings are used to design and test two Langevin-type electrostrictive transducers. The first transducer is made of PMN-PT-La (90-10-1%) ceramics (TRS Ceramics), the second one of ESCI ceramics (Morgan Matroc). For given static mechanical prestresses, resonance frequencies and effective coupling coefficients are measured at different DC electric fields and temperatures.
RESUMO
A finite-element model is proposed for the time-domain analysis of electrostrictive materials. Hom's material model, developed for lead magnesium niobate (PMN) ceramics, is used. It includes the quadratic dependence of strain with polarization, the saturation of polarization, assumes constant temperature, and excludes hysteresis. The theoretical formulation is justified by the principle of virtual works. The numerical model is obtained after discretization in space and time. The validation is performed by comparing numerical results with semianalytical results for an electrostrictive spherical shell subjected to a step in voltage or in charge. From these results, a method to compute the coupling coefficient of electrostrictive materials, based on Ikeda's definition, is proposed and applied to a bar with parallel electric field.