全局矩阵法及其在层状各向异性复合板中Lamb波传播特性研究中的应用

纤维增强复合材料中兰姆波的传播因其在无损评价中的应用而成为广泛研究的课题。一般采用传递矩阵法对各向异性多层媒质进行建模。虽然这种方法较为方便,但在大频厚积时会出现数值不稳定。本文作者对Nafeh的传递矩阵方法进行改进,所得到的全局矩阵方法具有较好的稳定性,其程序能有效地产生兰姆波的频散曲线。纤维增强复合材料中兰姆波的传播受多种因素的影响,层数的影响是其中之一。给出了不同层数复合板中兰姆波的相速度频散曲线以及两个基本模式a₀和s₀沿板厚方向的应力分布。这些数值示例为层状各向异性复合材料板的无损评价提供了理论依据。 

GLOBAL MATRIX AND ITS APPLICATION TO STUDY ON LAMB WAVE PROPAGATION IN LAYERED ANISOTROPIC COMPOSITE PLATES

Lamb wave propagation through fiber-reinforced composites has become a subject of intensive study due to its application to nondestructive evaluation. The anisotropic multilayered media are now usually studied by the transfer matrix formalism. Though this formalism is very convenient, it leads to numerical instabilities at high frequency-thickness products. The method developed in this paper using the global matrix is an improved version of Nayfeh's matrix method. The program using the global matrix has preferable stability, which can effectively create dispersion curves for Lamb wave propagation in anisotropic multilayered composites. Characteristics of Lamb wave propagation in fiber-reinforced composites are influenced by many factors and one of them is the number of layers. The calculated dispersion curves for different layered structures are presented together with plots of the through-thickness particle stress component amplitudes for two fundamental modes a_0 and s_0. These numerical examples provide a powerful tool for nondestructive evaluation of anisotropic layered plates.