Analysis and Prediction of the Dynamic Antiplane Characteristics of an Elastic Wedge-Shaped Quarter-Space Containing a Circular Hole

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Advances in Mathematical Physics Pub Date : 2023-03-30 DOI:10.1155/2023/9951245

Shenling Liu, Jie Yang, Yue Liu, Q. Liu

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Abstract

Based on the wave function expansion method, the dynamic antiplane characteristics of a wedge-shaped quarter-space containing a circular hole are studied in a complex coordinate system. The wedge-shaped medium is decomposed into two subregions along the virtual boundary using the virtual region decomposition method. The scattering wave field in subregion I is constructed by the mirror method, and the standing wave field in region II is constructed by the fractional Bessel function. According to the continuity conditions at the virtual boundary and the stress-free boundary of the circular hole, the unknown coefficients of the wave fields are obtained by the Fourier integral transform, and the analytical solution of the dynamic stress concentration factor (DSCF) of the circular hole is then obtained. Through parametric analysis, the effects of incident wave frequency, geometry of the wedge, and corner slope on the DSCF of the circular hole are discussed. The results show that when the SH-wave is horizontally incidence at high frequencies, the DSCF of the circular hole can be significantly changed by introducing the corner slope. Moreover, when the corner slope is high, the maximum DSCF can be amplified about 1.2 times. Finally, the back propagation (BP) neural network prediction model of DSCF is established, and the coefficient of regression is found to reach more than 0.99.

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含圆孔的弹性楔形四分之一空间的动力反平面特性分析与预测

基于波函数展开法，研究了在复杂坐标系下含圆孔的楔形四分之一空间的动态反平面特性。采用虚拟区域分解方法，沿虚拟边界将楔形介质分解为两个子区域。子区域I的散射波场采用镜像法构造，子区域II的驻波场采用分数阶贝塞尔函数构造。根据圆孔的虚边界和无应力边界的连续性条件，通过傅里叶积分变换得到了波场的未知系数，从而得到了圆孔的动应力集中系数的解析解。通过参数分析，讨论了入射波频率、楔形几何形状和角斜率对圆孔离散场的影响。结果表明:当sh波在高频率下水平入射时，引入转角斜率可以显著改变圆孔的离散场密度;当坡角坡度较大时，最大DSCF可放大约1.2倍。最后，建立了DSCF的BP神经网络预测模型，发现回归系数大于0.99。

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来源期刊

Advances in Mathematical Physics 数学-应用数学

CiteScore

2.40

自引率

8.30%

发文量

151

审稿时长

>12 weeks

期刊介绍： Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike. As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.