正交各向异性空心圆柱体中的纵向导波

LONGITUDINAL GUIDED WAVES IN ORTHOTROPIC HOLLOW CYLINDERS

基于三维线弹性理论,采用勒让德正交多项式展开法,推导了正交各向异性材料中纵向导波的耦合波动方程,并对耦合波动方程进行了数值求解。首先,为确定方法的适用性和准确性,利用Disperse软件求解各向同性空心圆柱体中纵向导波的频散曲线,并将其与勒让德正交多项式展开法求解结果相对比,二者结果完全一致。然后,讨论了勒让德正交多项式截止值对轴对称导波频散曲线收敛性的影响,并从数值计算的角度分析了产生影响的原因。最后,针对碳纤维缠绕的复合材料空心圆柱体,分别求解纵向、扭转和弯曲三种不同模态纵向导波的相速度频散曲线。计算了不同径厚比下的弯曲模态相速度频散曲线,分析径厚比的变化对频散曲线的影响。

Based on linear three-dimensional elasticity, the wave motion equations for coupled longitudinal guided waves are derived by using a Legendre orthogonal polynomial approach, and the coupled equations of wave motion are solved numerically. Firstly, to determine the applicability and accuracy of this method, the dispersion curves of longitudinal guided waves in isotropic hollow cylinders were solved by using Disperse software. The results obtained by Disperse calculation are compared with those by Legendre orthogonal polynomial approach method. The calculation results of the two methods are consistent. Then, the influence of the Legendre polynomial cutoff value on the convergence of the axisymmetric guided wave dispersion curves is discussed. The reason of the influence is analyzed by the numerical calculation. Finally, for the composite hollow cylinder wound by carbon fiber, the dispersion curves of three different modes of longitudinal guided waves are calculated separately. The phase velocity dispersion curves for different ratios of outer radius to thickness are calculated to analyze the influence of the ratio on the dispersion curves.