Nonlinear vibrations of axially moving viscoelastic Timoshenko beams under strong external excitation
Li Biao 1, Tang You-Qi 1, Ding Hu 1, Chen Li-Qun 1, 2
1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China;2. Department of Mechanics, Shanghai University, Shanghai 200444, China
Abstract：Abstract: This paper investigated nonlinear vibrations under strong external excitations of axially moving viscoelastic Timoshenko beams. The governing partial-differential equations are derived from extended Hamilton’s principle. The effects of shear deformation and rotary inertia are taken into account by the Timoshenko beam theory. The beam material obeys the Kelvin model in which the viscoelastic constitution relation use material derivative, not simple the partial time derivative. The method of multiple scales is applied to obtain the steady state response and establish the solvability conditions. The stability boundaries are formulated analytically via Routh-Hurwitz criterion. Some numerical examples are presented to demonstrate the effects of related parameters on the response.
2012, Vol. 31 
