The non-linear oscillations of a rod with close values of the cross-section axial moments of inertia

An analytical solution of the problem of the forced flexural oscillations of a rod with fixed hinged supports is presented. The rod has close natural frequencies of flexural oscillations in two mutually perpendicular planes due to the close values of the principal axial moments of inertia of the cross-section. The geometrical non-linearity, due to the change in the length of the middle line of the rod when it undergoes three-dimensional motion, is taken into account. The oscillations of the rod in the neighbourhood of the principal and first superharmonic resonances are investigated.