Solutions of dynamic problems for incompressible and slightly compressible helically orthotropic non-uniform thick-walled cylinders ☆

Exact analytic solutions are obtained of the one-dimensional dynamic problem for an incompressible elastic radially non-uniform helically orthotropic thick-walled cylinder under plane-strain conditions, loaded with a time-dependent pressure from inside and/or outside. The necessary and sufficient conditions for solutions to exist and to be unique are established. The convergence of the wave solutions for slightly compressible cylinders to the analytic relations obtained for incompressible cylinders is investigated.