Parametric Vibration Model and Response Analysis of Cable-Beam Coupling Under Random Excitation

Objective Considering the influence of cable geometric nonlinearity, inclination angle, and the synergistic vibration of the bridge deck beam, the parametric vibration characteristics of stay cables under random excitation is investigated in this paper. Methods Based on the establishment of the cable-beam coupled parametric vibration model under random excitation, the coupled motion equations of stay cable and bridge deck beam are derived and transformed into a random system of state equations by phase space transformation. The Wong-Zakai correction term in the Stradonovich principle is introduced and the Milstein-Platen method is used to discretize the given Ito state equations of cable-beam coupled vibration under random excitation. In order to avoid the influence of the parametric diffusion coefficient on the numerical format, an iterative method for solving the time history of the random vibration of the cable-deck beam is proposed. Then the vibration amplitude, radom response power spectral density and probability density change of the cable are analyzed from the random track angle, and the results are compared with the Gauss truncation method. The effects of damping ratio, initial tension, initial disturbance of stiffening beam and random excitation intensity on the vibration of the cable are studied. Conclusions It is found that the the iterative calculation results of random vibration of stay cables are consistent with the traditional Gaussian truncation method, and the proposed method can solve the vibration time history of cables under random excitation. It is also observed that the greater the intensity of the random excitation, the maximum response of the cable presents a non-linear increase; compared with the ideal excitation, the response of the stay cable under the action of the random excitation is larger under the same conditions.