Response Analysis of Vortex-Induced Random Vibration of Multi-Degree-of-Freedom Nonlinear Structure

Many wake oscillator (or lift oscillator) models are limited to studying the vortex-induced vibration (VIV) of linear structures excited by a constant-speed fluid flow. However, in wind engineering, real wind is typically a combination of mean wind and fluctuating wind. This paper introduces a multi-degree-of-freedom (MDOF) nonlinear structural system and fluctuating wind into the wake oscillator models, forming the nonlinear vortex-induced random vibration (VIRV) systems. By transforming the VIRV systems into stochastically excited and dissipated Hamiltonian systems, the stochastic averaging methods of quasi-Hamiltonian systems are applied. Based on the integrability and resonance, four types of VIRV quasi-Hamiltonian systems can be identified. After stochastic averaging, lower dimensional and equivalent Itô stochastic differential equations (SDE) are obtained. The VIRV response are predicted by solving the averaged Fokker-Planck-Kolmogorov (FPK) equations. For the four types of VIRV systems, four detailed examples are provided to illustrate the technical procedures. The obtained analytical results are compared with Monte Carlo (MC) simulation results, demonstrating good agreement and verifying the efficacy of the proposed methods.