The Effect of Initial Stresses on Dispersion Relations of Guided Waves in Functionally Graded Fan-Shaped Cylindrical Structures

Because of mechanical loads, thermal fields, or the limitation of the manufacturing technology, initial stresses in functionally graded (FGM) structures are inevitable in various engineering applications. In the context of “Mechanics of Incremental Deformations”, the effect of the initial stresses in the axial direction on dispersion relations of guided waves in FGM fan-shaped cylindrical structures is investigated by exploiting the double orthogonal polynomial series method. The influence of the variation in the graded function and cross-section size on the effect of initial stresses is analyzed. Results indicate that the effect of the initial stretch and compressive stresses on dispersion curves is usually (but not always) opposite. The variation in graded function and cross-section size significantly influences the effect of initial stresses on the dispersion curves, and its influence on different modes is also distinct. The obtained results provide theoretical guidance on guided wave non-destructive testing for FGM fan-shaped cylindrical structures.