The goal of this research is to numerically look for a proper feature for functionally graded materials mechanical property distribution function evaluation based on through transmitted ultrasonic bulk wave amplitude variation. A numerical approximation called homogenous layers approximation is introduced and employed for wave propagation formulation in functionally graded plate, followed by finite element utilization for verification. As the amplitude of the propagated ultrasonic wave is affected by acoustic impedance and wave divergence angle variation in the functionally graded material plate thickness, while neglecting the attenuation phenomenon, numerical investigation has been performed in order to quantify the contribution of each mechanism on the wave amplitude behavior. One-dimensional investigations, using homogenous layers approximation and finite element method, show that the final value of the wave amplitude is the same for all functionally graded material property distribution function power index, while two-dimensional results, obtained from finite element method, provide a suitable amplitude variation manner based on the wave divergence angle variation in functionally graded material thickness direction. The final results shows that it is possible to calibrate the received wave amplitude distribution on the receiving side of the plate, in a through transmission test, for the material property distribution function power index evaluation. Moreover, the concept of functionally graded material ultrasonic shoe is introduced, suitable for beam focusing applications instead of expensive phased array systems.

中文翻译：

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功能梯度板中超声波体波传播特性的数值研究

本研究的目的是在数值上寻找基于透射超声波体波振幅变化的功能梯度材料力学性能分布函数评估的适当特征。引入了称为同质层近似的数值近似，并将其用于功能梯度板中的波传播公式，然后利用有限元进行验证。由于传播的超声波的幅度受功能梯度材料板厚度的声阻抗和波发散角变化的影响，同时忽略了衰减现象，为了量化每种机制对波幅的贡献，已经进行了数值研究行为。一维调查，使用同质层近似和有限元方法，表明对于所有功能梯度材料特性分布函数功率指数，波幅的最终值是相同的，而由有限元法获得的二维结果提供了合适的幅值变化方式基于功能梯度材料厚度方向的波发散角变化。最终结果表明，在直通传输测试中，可以对板接收侧的接收波幅值分布进行标定，用于材料特性分布函数功率指数评估。此外，引入了功能梯度材料超声鞋的概念，适用于波束聚焦应用，而不是昂贵的相控阵系统。表明对于所有功能梯度材料特性分布函数功率指数，波幅的最终值是相同的，而从有限元方法获得的二维结果，提供了一种基于功能上波发散角变化的合适的幅值变化方式。分级材料厚度方向。最终结果表明，在直通传输测试中，可以对板接收侧的接收波幅值分布进行标定，用于材料特性分布函数功率指数评估。此外，引入了功能梯度材料超声鞋的概念，适用于波束聚焦应用，而不是昂贵的相控阵系统。表明对于所有功能梯度材料特性分布函数功率指数，波幅的最终值是相同的，而从有限元方法获得的二维结果，提供了一种基于功能上波发散角变化的合适的幅值变化方式。分级材料厚度方向。最终结果表明，在直通传输测试中，可以对板接收侧的接收波幅值分布进行标定，用于材料特性分布函数功率指数评估。此外，引入了功能梯度材料超声鞋的概念，适用于波束聚焦应用，而不是昂贵的相控阵系统。