Reflection of Waves at the Free Edge of a Laminated Circular Cylinder

Abstract

A wave function expansion method is employed to solve the reflection problem of time-harmonic elastic waves incident upon the free edge of a semi-infinite laminated circular cylinder. Wave functions are obtained using a propagator matrix approach for laminated isotropic cylinders and by a Rayleigh-Ritz type approximation for laminated composite cylinders. The least-square technique as well as the variational method are employed to evaluate the complex amplitudes and the energy flux associated with the reflected waves. To validate the solutions and present algorithm, results are compared with analytical solutions whenever available. Examples include free-end reflection of waves in an isotropic solid rod, a two-layered isotropic cylinder, and a four-ply [ + 15/ −15/ +15/ −15] graphite/epoxy cylinder. Numerical experimentation shows that the least-square method provides poor results for the laminated anisotropic cylinder compared to those obtained through the variational technique.