A comprehensive study on guided wave dispersion in complex structures

Guided waves play a crucial role in non-destructive testing, offering a reliable and efficient means for inspecting structures and materials. In this paper, we present the implementation of a wave finite element method for extracting dispersion curves, providing a feasible approach for analysing guided wave propagation in structures characterized by complex geometries and diverse material properties. Various numerical examples are investigated, including layered composites, functionally graded materials, rail sections, and metastructures, showcasing the versatility of the method. Mode sorting is a serious problem associated with this method crucial for distinguishing different guided wave modes. A mode sorting algorithm based on modal assurance criteria is implemented which can effectively trace different guided wave modes. To enhance accuracy, dispersion calculations are assisted by incorporating micro-modelling techniques for composite materials. Furthermore, the influence of initial stress on dispersion curves is examined, revealing that the effects of tensile and compressive stresses can vary at different frequencies and for different modes. Attenuation or damping is inherent in every structure and material, significantly influencing wave propagation. The article also investigates viscoelasticity and damping, expanding the method's applicability by introducing a novel approach to calculate attenuation using the frequency domain modulus for computing complex angular frequencies. The present method offers a fast, accurate, and feasible solution for extracting dispersion curves in structures with intricate geometries and material properties.