The dynamic response of the host structure to a high-frequency actuation is usually used for the detection of tiny damage in structures in the form of breathing crack. The simulation of the microcrack’s effect on the response is essential for several damage identification targets. The conventional finite element method suffers from very small mesh size requirements to address the high-frequency problems, resulting in very large mass and stiffness matrices. In this study, the scaled boundary finite element method was applied to model different schemes of structural health monitoring of a structure with breathing cracks based on high-frequency vibration. The scaled boundary finite element method discretizes only the boundary of the model and thus substantially reduces the size of structural matrices. The node-to-node contact strategy was introduced to the scaled boundary finite element method to capture the contact problem that occurs during the vibration of the breathing crack. As breathing crack vibration results in some nonlinear effects, the simulation of three phenomena was of interest: higher harmonic generation, frequency shift, and vibro-acoustic modulation. A shooting method was used for efficient time integration and description of the frequency response function in the nonlinear regime. According to the results, the scaled boundary finite element method is of great power, efficiency, and accuracy to treat the contact problems, especially in high-frequency regimes. Moreover, the nonlinear methods provide certain advantages over the linear techniques in the early detection of incipient damage.

主机结构对高频驱动的动态响应通常用于检测呼吸裂纹形式的结构中的细微损坏。模拟微裂纹对响应的影响对于几个损伤识别目标至关重要。常规的有限元方法的网格尺寸要求非常小，无法解决高频问题，从而导致质量和刚度矩阵非常大。在这项研究中，采用比例边界有限元方法对基于高频振动的带有呼吸裂纹的结构的结构健康监测的不同方案进行建模。比例边界有限元方法仅离散化模型的边界，从而大大减少了结构矩阵的大小。将节点到节点的接触策略引入到比例边界有限元方法中，以捕获在呼吸裂纹的振动过程中发生的接触问题。由于呼吸裂纹的振动会导致一些非线性影响，因此需要对以下三种现象进行仿真：高次谐波产生，频移和振动声调制。一种射击方法被用于有效的时间积分和非线性状态下频率响应函数的描述。根据结果​​，比例边界有限元方法具有很大的功效，效率和准确性，可以解决接触问题，尤其是在高频条件下。此外，在早期检测早期损坏方面，非线性方法相对于线性技术具有某些优势。