正交各向异性板液/固界面的声反射与声透射

采用Legendre正交多项式法,对液/固界面声波反射和透射系数进行求解。利用Legendre正交多项式对正交各向异性板中的位移解进行展开,推导出板中的应力和波动控制方程。联立液/固界面的边界条件和波动控制方程,建立线性无关方程组,用以计算液/固界面的反射和透射系数及Legendre多项式的展开系数,计算所得铝板液/固界面的反射和透射系数与传递矩阵法的计算结果吻合良好。以单向纤维增强复合材料板为例,在不同的方位角下,分析了反射和透射系数随斜入射角度、入射波频率的变化关系,以及板中声场的位移分布。所取Legendre正交多项式截止阶数越大,可用来计算的频厚积范围越大。研究拓展了Legendre正交多项式法的适用范围,为材料力学性能的声学测量提供了理论基础。 

Acoustic reflection and transmission at the interface between orthotropic plate and liquid media

The Legendre Orthogonal Polynomial Method (LOPM) is proposed to calculate reflection and transmission coefficients of acoustic waves at liquid/solid interfaces.The displacement solutions of orthotropic plate are expanded by the Legendre polynomials.Combining the boundary conditions of liquid/solid interfaces and wave governing equations,the linear independent equations are established to calculate the reflection and transmission coefficients.The polynomials expansion coefficients obtained from these equations are used to derivate the displacement distribution.The reflection and transmission coefficients obtained by LOPM for aluminum plate are consistent with those results by Transfer Matrix Method (TMM).For the case of unidirectional fiber reinforced composite plate,the relationship between reflection/transmission coefficients,oblique incident angle or frequency under different azimuth angles are analyzed.The larger frequency-thickness product range can be compute accurately by improving the truncation of Legendre polynomials.This research widens the applicable range of LOPM,and provides useful guidance for the mechanical properties measurement of materials based on acoustic.