Nonlinear vibrations of axially moving viscoelastic Timoshenko beams under strong external excitation

Nonlinear vibrations of axially moving viscoelastic Timoshenko beams under strong external excitations were investigated. The governing partial-differential equations were derived according to the extended Hamilton's principle. The effects of shear deformation and rotary inertia were taken into account. The beam material obeys the Kelvin model in which the material derivative was taken part in the viscoelastic constitution relation instead of the simple partial time derivative. The method of multiple scales was applied to obtain the steady state response and establish the solvability conditions. The stability boundaries were formulated analytically via Routh-Hurwitz criterion. Some numerical examples were presented to demonstrate the effects of related parameters on the response.