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| Scattering of the SH wave by a crack in functionally graded one dimensional hexagonal piezoelectric quasicrystal |
| YANG Juan1,2,XU Yan1,3,SHI Jinhua2,DING Shenghu1 |
1.School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China;
2.School of Preparatory Education for Nationalities, Ningxia University, Yinchuan 750002, China;
3.Xinhua College, Ningxia University, Yinchuan 750002, China |
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Abstract Within the framework of quasicrystals linear dynamic theory, the dynamic fracture of a crack in a functionally graded one-dimensional hexagonal quasicrystals subjected to a time-harmonic elastic SH-wave was studied with integral transform technique. The material properties were assumed to vary continuously as an exponential function. Using the Fourier cosine transform, the boundary value problem of partial differential equation describing fracture problem was formulated to two pairs of dual integral equations, which were solved numerically with Copson method. The explicit expressions of phonon and phason elastic fields at crack face were determined and the dynamic stress intensity factors were obtained. Finally, numerical results showed the effects of gradient parameter, crack length , incident angle and normalized wave number on fracture characteristics of material. This study provides a theoretical basis for optimal design and nondestructive testing of quasicrystals.
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Received: 16 February 2022
Published: 28 June 2023
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