Guided waves are generally considered as a powerful approach for crack detection in structures, which are commonly investigated using the finite element method (FEM). However, the traditional FEM has many disadvantages in solving wave propagation due to the strict requirement of mesh density. To tackle this issue, this paper proposes an efficient time-domain spectral finite element method (SFEM) to analyze wave propagation in cracked structures, in which the breathing crack is modeled by defining the spectral gap element. Moreover, novel orthogonal polynomials and Gauss–Lobatto–Legendre quadrature rules are adopted to construct the spectral element. Meanwhile, a separable hard contact is utilized to simulate the breathing behavior. Finally, a comparison of the numerical results between the FEM and the SFEM is conducted to demonstrate the high efficiency and accuracy of the proposed method. Based on the developed SFEM, the nonlinear features of waves and influence of the incident mode are also studied in detail, which provides a helpful guide for a physical understanding of the wave propagation behavior in structures with breathing cracks.

导波通常被认为是一种有效的结构裂缝检测方法，通常使用有限元方法（FEM）对其进行研究。然而，由于对网格密度的严格要求，传统的有限元法在解决波传播方面有许多缺点。为了解决这个问题，本文提出了一种有效的时域频谱有限元方法（SFEM）来分析裂纹结构中的波传播，其中通过定义谱隙元素来模拟呼吸裂纹。此外，采用新颖的正交多项式和高斯-洛巴托-莱根特式正交规则构造光谱元素。同时，采用可分离的硬接触来模拟呼吸行为。最后，有限元和SFEM之间的数值结果进行了比较，以证明该方法的高效率和准确性。在已开发的SFEM的基础上，还详细研究了波浪的非线性特征和入射模式的影响，这为物理理解具有呼吸裂纹的结构中的波浪传播行为提供了有用的指导。