Centro Universitario de Paysandú, Universidad de la República, Ruta 3 km 363, Paysandú, Uruguay.
Engenharia Biomédica, Universidade Federal do ABC, Av. dos Estados 5001, Santo André, Brazil.
Ultrasonics. 2014 Aug;54(6):1631-41. doi: 10.1016/j.ultras.2014.03.006. Epub 2014 Mar 25.
Numerical simulations allow modeling piezoelectric devices and ultrasonic transducers. However, the accuracy in the results is limited by the precise knowledge of the elastic, dielectric and piezoelectric properties of the piezoelectric material. To introduce the energy losses, these properties can be represented by complex numbers, where the real part of the model essentially determines the resonance frequencies and the imaginary part determines the amplitude of each resonant mode. In this work, a method based on the Finite Element Method (FEM) is modified to obtain the imaginary material properties of piezoelectric disks. The material properties are determined from the electrical impedance curve of the disk, which is measured by an impedance analyzer. The method consists in obtaining the material properties that minimize the error between experimental and numerical impedance curves over a wide range of frequencies. The proposed methodology starts with a sensitivity analysis of each parameter, determining the influence of each parameter over a set of resonant modes. Sensitivity results are used to implement a preliminary algorithm approaching the solution in order to avoid the search to be trapped into a local minimum. The method is applied to determine the material properties of a Pz27 disk sample from Ferroperm. The obtained properties are used to calculate the electrical impedance curve of the disk with a Finite Element algorithm, which is compared with the experimental electrical impedance curve. Additionally, the results were validated by comparing the numerical displacement profile with the displacements measured by a laser Doppler vibrometer. The comparison between the numerical and experimental results shows excellent agreement for both electrical impedance curve and for the displacement profile over the disk surface. The agreement between numerical and experimental displacement profiles shows that, although only the electrical impedance curve is considered in the adjustment procedure, the obtained material properties allow simulating the displacement amplitude accurately.
数值模拟允许对压电设备和超声换能器进行建模。然而，结果的准确性受到对压电材料弹性、介电和压电特性的精确知识的限制。为了引入能量损耗，可以用复数来表示这些特性，其中模型的实部主要决定共振频率，虚部决定每个共振模式的幅度。在这项工作中，修改了基于有限元法（FEM）的方法，以获得压电圆盘的虚材料特性。通过阻抗分析仪测量圆盘的电阻抗曲线来确定材料特性。该方法包括获得在宽频率范围内使实验和数值阻抗曲线之间的误差最小化的材料特性。所提出的方法从每个参数的灵敏度分析开始，确定每个参数对一组共振模式的影响。灵敏度结果用于实现逼近解的初步算法，以避免搜索陷入局部最小值。该方法应用于确定 Ferroperm 的 Pz27 圆盘样品的材料特性。所获得的特性用于使用有限元算法计算圆盘的电阻抗曲线，并将其与实验电阻抗曲线进行比较。此外，还通过将数值位移分布与激光多普勒测振仪测量的位移进行比较来验证结果。数值和实验结果之间的比较表明，电阻抗曲线和圆盘表面上的位移分布的数值和实验结果之间具有极好的一致性。位移分布的数值和实验结果之间的一致性表明，尽管在调整过程中仅考虑了电阻抗曲线，但获得的材料特性允许准确地模拟位移幅度。
