Stress distribution and fatigue life of nonlinear vibration of an axially moving beam

In this paper, the effects of the nonlinear vibration on stress distribution and fatigue life of the axially moving beam are studied. The parametric excitation of the flexible material is created by the pulsating moving speed. Three-to-one internal resonance condition is satisfied. The three-parameter model is adopted in the viscoelastic constitutive relation. The nonlinear vibration of the axially moving beam with parametric and internal resonance are studied by using the direct multiple scales method (MSM) with numerical simulation confirmation. Based on the approximate analytical solution, the distribution of tensile stress and bending stress on the axially moving beam is presented by adopting a V-belt as the prototype. Based on the maximum stable cyclic stress, the limit cycle response of the V-belt is utilized to evaluate the effect of the resonance on the fatigue life. Also, the influences of the internal resonance on the steady-state responses and the fatigue life of the V-belt are revealed. Numerical examples illustrate that large unwanted resonances occur and the second-order mode receives vibration energy from to the first-order mode. The numerical results demonstrate that the nonlinear vibration significantly reduces the fatigue life of the V-belt. The fatigue life analysis method in this paper can be applied to the excited vibration of other axially moving systems and even static continuum.