Elastodynamic Green’s Function for Laminated Anisotropic Circular Cylinders

Abstract

The construction of a steady-state Green’s function for a laminated anisotropic circular cylinder is presented herein. The cylinder’s profile through its depth consists of any number of perfectly bonded, uniform thickness concentric cylindrical layers, with each able of having its own distinct elastic cylindrically anisotropic properties. Green’s function is predicated on the superposition of numerically generated modal solutions from a system of equations based on a semi-analytical finite element formulation. Two methods are proposed for its construction, both relying on the same set of eigendata. One is by means of an integral transform. The other may be viewed as the forced vibration of a cylinder with cylindrically monotropic properties under symmetry/antisymmetry conditions on the cross section containing the source load. The second method, being more restrictive with respect to material properties, was intended primarily as a cross-check of the integral transform version of Green’s function. Numerical implementation details are discussed in terms of two example thickness profiles to show the essential keys for the convergence and accuracy of Green’s function.