1-3 piezocomposites are first choice materials for integration in ultrasonic transducers due to their high electromechanical performance, particularly, in their thickness mode. The determination of a complete set of effective electroelastic parameters through a homogenization scheme is of primary importance for their consideration as homogeneous. This allows for the simplification of the transducer design using numerical methods. The method proposed is based on acoustic wave propagation through an infinite piezocomposite, which is considered to be homogeneous material. Christoffel tensor components for the 2 mm symmetry were expressed to deduce slowness curves in several planes. Simultaneously, slowness curves of a numerical phantom were obtained using a finite element method (FEM). Dispersive curves were initially calculated in the corresponding heterogeneous structure. The subsequent identification of the effective parameters was based on a fitting process between the two sets of slowness curves. Then, homogenized coefficients were compared with reference results from a numerical method based on a fast Fourier transform for heterogeneous periodic piezoelectric materials in the quasi-static regime. A relative error of less than 2% for a very large majority of effective coefficients was obtained. As the aim of this paper is to implement an experimental procedure based on the proposed homogenization scheme to determine the effective parameters of the material in operating conditions, it is shown that simplifications to the procedure can be performed and a careful selection of only seven slowness directions is sufficient to obtain the complete database for a piezocomposite containing square-shaped fibers. Finally, further considerations to adapt the present work to a 1-3 piezocomposite with a fixed thickness are also presented.

中文翻译：

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利用波传播对周期性1-3压电复合材料进行均质化：一种实验方法

1-3压电复合材料由于其较高的机电性能，特别是在其厚度模式下，是集成在超声换能器中的首选材料。通过均质化方案确定完整的有效电弹性参数集对于将其视为均质性至关重要。这允许使用数值方法简化换能器设计。提出的方法基于通过无限压电复合材料的声波传播，该复合材料被认为是均质材料。表达了2mm对称性的Christoffel张量分量，以推导几个平面上的慢度曲线。同时，使用有限元方法（FEM）获得了数字体模的慢度曲线。首先在相应的异构结构中计算色散曲线。随后确定有效参数的依据是两组慢度曲线之间的拟合过程。然后，将均质系数与基于快速傅立叶变换的数值方法的准结果进行比较，以用于准静态状态下的非均质周期性压电材料。对于非常大的有效系数，相对误差小于2％。本文旨在基于提出的均质方案实施实验程序，以确定材料在工作条件下的有效参数，结果表明，可以简化程序，仅仔细选择七个慢速方向就足以获得包含方形纤维的压电复合材料的完整数据库。最后，还提出了进一步的考虑，以使本发明适用于具有固定厚度的1-3压电复合材料。