A semi-analytical spectral element model for guided wave propagation in composite laminated conical shells

Abstract

The conical shell is a typical non-uniform waveguide with its circumferential radius varies linearly. This work aims to provide physical insights for the composite laminated conical shell in terms of waves. A semi-analytical spectral element model is presented, which adopts the Fourier series in the circumferential direction and the higher-order shape functions in the axial direction. The first-order shear deformation theory and Hamilton principle are employed to derive the energy functions of the conical shell, and they are discretized using the spectral elements to achieve a weak-form variational problem. The dispersion equation and the group velocity expression are derived via the piecewise approximation concept and Bloch's periodic theorem. The accuracy of the developed spectral element is verified by comparison with published results. The deformation evolution mechanisms of the composite conical shell are revealed, and the wave propagation characteristics of uniform and ply drop-off composite conical shells are investigated. The results demonstrated that wavenumber distribution at 0-5kHz is spatially dependent, and wavenumber becomes cut off and bifurcate near the cone vertex. When the frequency exceeds 2kHz, the deformation of conical shell changes from rigid to flexible, and the structure tends to be a uniform waveguide. Compared to the geometric curvature effect, the asymmetric lay-up leads to more significant mode coupling.