Apresentam-se as bases teóricas do Método de Elementos Finitos (MEF) piezoelétrico, e a sua aplicação na modelagem de transdutores de ultra-som piezoelétricos, que consiste na determinação das características vibracionais (frequências de ressonância e anti-ressonância, modos de vibrar e coeficiente de acoplamento eletromecânico), obtenção da curva de admitancia, análise transiente da estrutura piezoelétrica sujeita a uma excitação pulsada e análise da influência da variação das constantes piezoelétricas do transdutor com o raio. Utilizando-se o MEF aplicado a acústica obteve-se o campo acústico gerado pelo transdutor operando em onda contínua, bem como iniciou-se o estudo da propagação de ondas num líquido, analisando-se as ondas geradas pela excitação pulsada de um pistão plano em contato com o fluido. Os modos de vibrar e os valores de frequências de ressonância obtidos para um transdutor, foram comparados com os resultados experimentais.

The theoretical basis of piezoelectric finite element method (FEM), and its application in piezoelectric ultrasonic transducer modelling is presented. Among these applications we have the calculation of resonance and antiresonance frequencies, vibration modes, piezoelectric coupling coefficient, admittance curve and transient analysis of piezoelectric structure excited by a short pulse. By means of piezoelectric FEM the influence of variation of piezoelectric constant with radius is analysed. It is discussed three kind of functions (linear, cosinoidal and Gaussian). This technique is called apodization. The acoustic filed generated by the transducer operating in continuous wave (CW) was calculated by using FEM applied to acoustic, considering the fluid-structure coupling. The study of wave propagation in liquids is started by using FEM, analyzing the waves generated by a plane piston in contact with the fluid, excited by a short pulse. For each case discussed above, all boundary conditions and hypothesis assumed in the construction of finite element models are discussed. Although the models considered are circular transducers, the concepts acquired can be expanded to other geometries. The vibrational modes were visualized by means of a laser interferometry technique (ESPI), and the admittance curves were measured by using an impedometer. These results were compared with the FEM results, and the models precision was discussed.