谱有限元数值分析各向异性复合板中导波色散特性

提出谱有限元方法研究层状各向异性复合板中导波的色散特性和波结构。基于三维弹性动力学方程,用有限元方法离散波导截面,波传播方向的位移用简谐波表示,得到了导波色散的特征方程。分析了单层和双层复合板中导波沿不同方向传播的色散特性和波结构,讨论了双层复合板中层厚比对相速度的影响。数值研究结果表明:导波的对称模态沿纤维方向传播时在较宽的频率范围内保持弱色散状态。双层复合板中导波基本模态的相速度在低频时受层厚比的影响较明显,随着频率的增加趋向于相速度较低的材料。数值模拟结果为导波用于复合材料定量无损检测和性能评价提供理论依据。

Spectral finite element method analysis of dispersion characteristics of guided wave in anisotropic composite plates

Spectral finite element method is introduced to study the dispersion and the mode shape of guided waves in layered anisotropic composite plates. Based on the three-dimensional elastodynamic equation, the dispersion equation is obtained by finite-element-discretization of the cross-section of the waveguide alone. The displacements along the wave propagation direction are also described in an analytical fashion as harmonic exponential functions. The dispersion curves and the mode shape of guided waves that propagate in different directions of single-layer and double-layer composite plates have been analyzed. The effect of the thickness ratio of the bi-layered composite plates to the phase velocity of the basic modes is discussed. The results showed that the symmetric mode is characterized by weak dispersion along the fiber direction in a wide frequency range. The phase velocity of basic modes is greatly influenced by the thickness ratio of bi-layered composite plates at low frequencies, and is closer to the lower phase velocity of the material with the increase of frequency. The study provides a theoretical basis of guided waves for quantitatively non-destructive testing and performance evaluation of composite materials.