Guided waves in layered cylindrical structures with sectorial cross-section under axial initial stress

Due to mechanical loads, thermal fields and the limitation of the manufacturing technology, initial stresses in layered cylindrical structures are ineluctable. Accordingly, for the purpose of the guided wave nondestructive testing for the layered cylindrical structure with a sectorial cross-section, an analytical approach, the double-orthogonal polynomial method is utilized to investigate the influence of axial initial stress on wave characteristics. Based on Biot's Mechanics of Incremental Deformations, the dynamic equations for the sectorial cylindrical structures in terms of displacements and axial initial stress are deduced. By virtual of the Heaviside function, the boundary conditions are automatically incorporated into constitutive equations and then into wave equations. The corresponding dispersion curves and displacement distributions of various sectorial cylindrical structures are calculated. Numerical results indicate that the influence of the initial stress applied on the outer layer is much significant at low frequencies, and the influence of the initial stress applied on the inner layer is much significant at high frequencies; the cut-off frequencies have negative relation with the area of the cross-section; the displacements at high frequencies are mainly distributed in the layer with smaller elasticity modulus, especially the layer simultaneously with bigger initial stress.

Automated summary

In this study, the influence of axial initial stress on wave characteristics of sectorial cylindrical structures was analyzed using the double-orthogonal polynomial method. It was found that the initial stress applied on the outer layer has a significant impact at low frequencies, while the inner layer's initial stress has a significant impact at high frequencies. Cut-off frequencies are negatively related to the cross-section area.