单向纤维增强复合材料中剪切波多重散射问题的复变函数法

基于弹性波的多体散射理论和复变函数方法,利用波函数展开法和保角映射方法,研究了任意形纤维增强复合材料中剪切波的传播。根据相应的边界条件确定弹性波模式系数。给出了复合材料中基体区和纤维核区的波场。作为算例,分析了相同入射频率,不同纤维核的尺寸和形状的情况下,弹性波的传播特性。通过分析发现,低频长波区,弹性波以近似正弦函数的形式传播,纤维核的尺寸和形状对波场影响不明显;随着频率的增加,影响变得明显,大于一定的频率,纤维核的形状可明显地辨别出。最后对结果进行了分析讨论。

Complex Function Method for Solving Multiple Scattering of Shear Waves in Unidirectional Fiber-reinforced Composites

Based on the theory of multiple scattering,wave function expansion and conformal mapping are utilized to investigate the propagation of shear waves in arbitrary fiber-reinforced composites,and the expanded mode coefficients are determined according to the corresponding boundary conditions.As an example,the wave field in the matrix and fiber of the arbitrary fiber-reinforced composites are represented,and in the case of the same incident frequency and different size and shape of the fiber,the propagation behaviors of elastic waves in unidirectional fiber-reinforced composites are analyzed.It is revealed that the elastic waves with a sufficiently long wavelength propagate as a sinusoidal plane wave,and are insensitive to the fiber size and arrangement.As the frequency increases,the influence of the size and shape of fibers on the wave field gradually appears.When the frequency gets higher than a certain level,the shape of fibers can be distinguished clearly.