  The nonlinear forcing terms for the wave equation in general curvilinear
coordinates are derived based on a hyperelastic material. The expressions for
the nonlinear part of the first Piola-Kirchhoff stress are specialized for
axisymmetric torsional and longitudinal fundamental wave fields in a cylinder.
The matrix characteristics of the nonlinear forcing terms and secondary mode
wavestructures are manipulated to analyze the higher harmonic generation due to
the guided wave mode self interactions and mutual interactions. It is proven
that both torsional and longitudinal mode secondary fields can be cumulative by
specific type of guided wave mode interactions. A method for the selection of
preferred fundamental excitations that generate strongly cumulative higher
harmonics is formulated, and described in detail for second harmonic
generation. Hyperelastic finite element models are built to simulate second
harmonic generation by T(0,3) and L(0,4) modes. A linear increase of the modal
amplitude ratio A2/A1^2 over the propagation distance is observed for both
cases, which indicates mode L(0,5) is effectively generated as cumulative
second harmonics.
