| Citation: | HE Cunfu, REN Zhewen, LYU Yan, et al. Reflection/transmission characteristics based on Legendre orthogonal polynomial method[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(7): 1258-1266. doi: 10.13700/j.bh.1001-5965.2019.0434(in Chinese)
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Study on acoustic testing method for mechanical properties of thin layer materials.Based on Legendre orthogonal polynomial method, linear independent equations are constructed and the reflection/transmission coefficient of acoustic waves at the interfaces is calculated using liquid/solid boundary conditions and wave control equations. The method analyzes the influence of the cut-off order on the solution result, and finds the critical value of the order under different frequency and thickness products, then calculate the reflection/transmission coefficient based on the cut-off order. The calculation results obtained by the Legendre orthogonal polynomial method are compared with those obtained by the transfer matrix method, and the accuracy of the theoretical model is verified. Ultrasonic waves' oblique incidence into a thin-layer material forms a Lamb wave. The dispersion characteristics at the steady state are intrinsically linked to the reflection features. According to Snell's law, the three-dimensional surface of the frequency-velocity-reflection coefficients is calculated using the Legendre orthogonal polynomial method. This result is compared with the dispersion curves simulated by Disperse. It is proved that the solving result is consistent with the Lamb wave dispersion characteristics. The influence of attenuation on the experimental results during the propagation of the acoustic wave is reduced by collecting the reference signal which is the directly obtained wave without a sample. A reflection and transmission experimental system was built to measure the frequency spectrum of reflection and transmission coefficients at different incident angles. The experimental results are compared with the theoretical results, and the accuracy of the results obtained by the theory is verified. A solving methodology without root-finding algorithm for acoustic reflection/transmission coefficients is realized. This method provides a theoretical basis and experimental guidance for the non-destructive testing of the mechanical properties of thin-layer materials.
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