Nonlinear vibrations and stability of an axially moving Timoshenko beam with an intermediate spring support

In this paper, the nonlinear forced vibrations and stability of an axially moving Timoshenko beam with an intra-span spring-support are investigated numerically. Taking into account the shear deformation and rotary inertia, three coupled nonlinear partial differential equations of motion are obtained using Hamiltonʹs principle along with stress–strain relations. These equations are discretized into a set of coupled nonlinear ordinary differential equations via the Galerkin method. The pseudo-arclength continuation technique is used to solve the governing set of equations. The frequency–response curves of the system in the subcritical regime are obtained and examined. In addition, direct time integration is employed to investigate the global dynamics of the system through constructing the bifurcation diagrams of Poincaré maps.