Dynamic analysis of monopile OWTs with viscoelastic dampers based on pole-residue method

Abstract

The dynamic behaviour of monopile offshore wind turbines (OWTs) equipped with viscoelastic dampers (VE dampers) modelled by a fractional Kelvin–Voigt model is governed by a fractional differential equation. Most available methods to solve this kind of equation are limited to single-degree-of-freedom systems or simple deterministic loadings. Considering an OWT under either complex deterministic or random loadings, this work develops an efficient pole-residue method to evaluate its vibration. The key of the proposed method is to express the impulse response function with fractional derivatives into a pole-residue form. Then, the dynamic response time history and the response evolutionary power spectrum (EPS) are transformed into explicit solutions. In numerical studies, a monopile OWT with a VE damper subjected to irregular wind-wave loadings and nonstationary random earthquakes is investigated. Direct Duhamel integral and Monte Carlo simulations are utilized to verify their accuracy. After adding the VE damper, the deterministic response and the random EPS are significantly reduced. By conducting sensitivity analysis, we find that the growth of the fractional order of VE dampers leads to larger damping ratios of the OWT. Increasing the damping coefficient of the VE damper results in larger natural frequencies.