A collocation method for bending, torsional and axial vibrations of offshore wind turbines on monopile foundations. (1st December 2020) - Chaves Júnior, Cícero Vitor; Araújo, Rafael Campos de Alencar; de Souza, Camilla Mahon Campello; Ferreira, Augusto César Albuquerque; Ribeiro, Paulo Marcelo Vieira
Abstract: The design of monopile offshore wind turbines requires consideration of the most diverse excitation spectra, such as sea currents, waves, wind, and earthquakes, and it is often concerned with resonance aspects. The structural system resembles an inverted pendulum, where a variable cross-section tower is coupled to a support structure that is embedded in the seabed. This work presents original mathematical developments based on the collocation method for evaluation of bending, torsional, and longitudinal vibrations of these structures. The proposed expressions consider a polynomial approximation of the mode shapes and collocation points on the tower, and monopile, which satisfy the differential equation of free vibrations. Effects of elastic supports, rotary and torsional inertia, geometric nonlinearity produced by the nacelle and water added mass are evaluated in different model approximations, which are compared to results from 04 reference wind turbines. The formulations are also analyzed using benchmarks for classical structural dynamics solutions proposed for vibrations of beams and shafts with variable cross-section. The results demonstrate the efficiency of this method, which produces solutions with the same quality as those obtained with finite element models. At the same time, they indicate the possibility of a useful and straightforward procedure for the solution of natural modes using basic mathematics that allows generalization to other boundary conditions and differential equations. Highlights: The practical solution of variable coefficient differential equations in OWTs. Evaluation of natural frequencies and mode shapes (bending, torsional and axial). Allows polynomial approximations of any order, in the tower and monopile. Easily programmable and has no geometric constraints for cross-sectional variation. Practical studies assessing the influence of SSI and FSI in five OWTs.