Bending edge wave on a thin functionally graded cylindrical shell

A qualitative analysis of the localised wave on a thin isotropic elastic shell is carried out, in which the kinematics of the semi-infinite shell is governed by the Kirchhoff–Love assumptions of the Donnell–Mushtari thin shell theory. Non-homogeneity in the material properties of the shell is considered and characterised by a continuously varying grading function along the transverse coordinate of the shell. The model incorporates the Gurtin and Murdoch surface elasticity theory to ascertain the influence of surface mechanical parameters on the properties of the bending wave at the free edge of a cylindrical shell. The implementation of the asymptotic integration technique on the equations of motion and free edge boundary conditions of a circular cylindrical shell enables the extraction of the dispersion of bending wave within a small range of the half-thickness-to-curvature ratio. The effects of grading index and elastic parameters of the shell on the propagating frequency are established through the asymptotic dispersion relation, equivalent to a plate dispersion equation within the framework of the Kirchhoff–Love thin plate theory.