Dispersion and characteristic surfaces of waves in laminated composite circular cylindrical shells

Abstract

The dispersion behaviors and characteristic surfaces of waves in a laminated composite circular cylindrical shell are investigated using a semianalytical method based on the theory of three-dimensional elasticity. The radial displacement of the shell is modeled by finite elements, while the axial and circumferential displacements are expanded as the complex exponentials. The associated characteristic equation is developed by means of the Hamilton's principle. The eigenvalues are established in terms of the Rayleigh quotient. Six characteristic wave surfaces, viz., the phase velocity, phase slowness, and phase wave surfaces, as well as the group velocity, group slowness, and group wave surfaces, are introduced to visualize the effects of anisotropy on wave propagation. Numerical examples demonstrate that the ratio of the inner radius to the thickness of the shell has a stronger influence on the frequency spectra in the circumferential wave than on that in the axial wave; that negative group velocity appears at a range of smaller wave numbers and the range varies as the wave normal and the ratio of the inner radius to the thickness of the shell; and that the characteristic wave surfaces vary with the propagation modes of waves, the ratio of the inner radius to the thickness of the shell, and the lay-ups of the laminated shells.