正交各向异性板中非主轴方向的Lamb波

基于线性三维弹性理论，采用勒让德正交多项式展开法，推导了波沿正交各向异性材料非主轴方向传播时的Lamb波耦合波动方程，并对耦合波动方程进行了数值求解。为验证该方法的适用性和正确性，首先将此方法应用于各向同性材料，并与已知的数据结果进行了比较；然后以单向纤维增强复合材料为例，计算了耦合Lamb波沿不同的非主轴方向传播时的相速度频散曲线，并分别研究了传播方向改变时低阶模态Lamb波和高阶模态Lamb波频散特性的变化。最后，针对潜在用于各向异性复合材料结构健康监测的耦合Lamb波低阶模态，给出了其在不同传播方向时的相速度分布和群速度分布。同时，结合低阶模态Lamb波的位移分布特性和材料的各向异性特点，阐释了S0模态对波的传播方向变化最为敏感的原因。

LAMB WAVES PROPAGATION ALONG NON-PRINCIPAL DIRECTIONS IN ORTHOTROPIC PLATE

Based on linear three-dimensional elasticity, the equations of wave motion for coupled Lamb waves are derived by using a Legendre orthogonal polynomial approach when waves propagate along non-principal directions of the material, and the coupled equations of wave motion are also solved numerically. Firstly, for verifying the applicability and validity of this proposed method, this approach is applied to isotropic material and obtained results are compared to known results. Then, the phase dispersion curves of coupled Lamb waves along different non-principal directions are calculated, and the effects of the different propagation directions on fundamental modes and high-order modes are investigated. Finally, the distributions of phase and group velocities of fundamental modes are shown respectively, which have the great potential for structural health monitoring of anisotropic materials.Simultaneously, the reason that S0 mode is the most sensitive to the change of the propagation direction is illustrated with considering of both displacement distribution of fundamental modes and material’s anisotropy property.