Coupled Parametric Vibration Model and Response Analysis of Single Beam and Double Cable Under Deterministic Harmonic and Random Excitation

In order to reveal the coupling parametric vibration characteristics of stay cables under combined excitation, considering the effects of cable geometric nonlinearity, inclination and the cooperative vibration of adjacent cables and bridge deck beams, a single-beam–double-cable coupled parametric vibration model excited by Gaussian white noise and deterministic harmonic excitation is established, and the coupled motion equations are derived. The Milstein–Platen method is used to directly obtain the coupled random vibration time history of the single-beam–double-cable structure, and an iterative method is proposed to counter the influence of the parametric diffusion coefficient on the numerical format. By comparing with the finite element method and the Monte Carlo numerical simulation method, the accuracy of the Milstein–Platen method in solving the vibration time history of cable–beam coupling parameters under combined excitation is first verified. Then the random displacement, power spectral density and probability density variation of the cable and beam under the combined excitation of different intensities are analyzed from the angle of random orbit. The results show that under the joint action of deterministic harmonics and random excitation, the time–domain, frequency, and probability characteristics of the single-beam–double-cable coupling system are greatly affected by the Gaussian white noise excitation proportion coefficient, and the degree of influence is different. In addition, compared with the single cable model, the vibration analysis results of the coupling model considering multiple stay cables are more reasonable.