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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。
The spectral finite element method is proposed to study the dispersion and wave structure of guided waves in layered anisotropic composite plates. Based on the three-dimensional elastic dynamics equations, the waveguide cross section is separated by finite element method, and the displacement in the wave propagation direction is expressed by simple harmonic wave. The characteristic equation of guided wave dispersion is obtained. The dispersion characteristics and wave structure of guided waves propagating in different directions in single-layer and double-layer composite plates are analyzed. The influence of layer thickness ratio on phase velocity in double-layer composite plates is discussed. Numerical results show that the symmetric modes of the guided wave remain weakly dispersed over a wide frequency range when propagating in the fiber direction. The phase velocity of the guided wave basic mode in the double-layer composite plate is more affected by the layer thickness ratio at low frequency, and tends to the material with lower phase velocity as the frequency increases. The numerical simulation results provide a theoretical basis for the guided waves to be used in quantitative nondestructive testing and performance evaluation of composite materials.