An improved modal tracking algorithm for dispersion analysis of arbitrary prestressed plates

Abstract

Determining the dispersion characteristics of prestressed plates is essential for guided wave-based structural health monitoring, which can provide theoretical guidance for optimizing excitation mode and frequency. However, the multi-mode nature of guided waves brings huge challenges for modal tracking. Conventional methods require sufficiently small frequency steps and may encounter tracking errors during mode crossing and overlap. To address these issues, this paper established a multi-step superposition model to obtain the dispersion relation of arbitrary prestressed plates and proposed a novel modal tracking method based on structural similarity (SSIM) image registration for identifying all guided wave modes. Drawing inspiration from the image quality assessment technique, a novel index was introduced to evaluate the consistency between modal eigenvectors quantitatively. Furthermore, an improved algorithm using eigenvector operations was developed to further enhance the efficiency and applicability of the modal tracking process. Subsequently, application examples were conducted to thoroughly evaluate the performance of the proposed methods through comparison with conventional modal tracking methods. The results indicated that the proposed methods have accurate and reliable tracking performance even with larger wavenumber steps, which is unattainable with conventional methods. Notably, the computational efficiency of the improved algorithm is nearly 13 times faster than the SSIM-based image registration method. Finally, an investigation into the dispersion characteristics of aluminum plates under tensile, bending, and shear stress demonstrated the versatility of the improved modal tracking algorithm. This study provides valuable insights into the dispersion behavior of guided waves in prestressed plates.