Reliability and sensitivity analysis of an axially moving beam

The reliability and sensitivity analysis of an axially moving beam with simply supported boundary conditions are carried out. The equation of motion of the axially moving beam is established by applying the assumed mode method and Hamilton’s principle. The critical divergence moving velocity is obtained from analyzing the stability of the kinetic equation of the beam. The uncertainties of the moving velocity, and the structural and material parameters of the beam are taken into account. The probability distribution function of the state function indicating the stability of the beam is approximated by the Edgeworth series, from which the reliability and sensitivity of the beam are obtained. The effects of the mean values and standard variances of the moving velocity, and the structural and the material parameters of the beam on the reliability and sensitivity are conducted. From the results, it can be seen that the reliability decreases with the moving velocity increasing. The reliability of the system decreases with increasing length, and increases with increasing thickness of the beam. The reliability is more sensitive to the thickness than to the length of the beam. The reliability of the beam decreases with increasing mass density, and increases with increasing elastic modulus, showing that the beam with higher specific rigidity and less weight exhibits more stable.