The horizontal-axis wind turbine blades have a low modal damping factor in the edgewise direction whether they are in operation or idle. To address this issue, the mathematical formulations of three viscoelastic dynamic vibration absorbers (VDVAs) coupled within a single-degree-of-freedom (SDOF) blade for damping edgewise vibrations are proposed. The dynamic integer-order models are obtained through the Euler-Lagrange formulation. After, the fractional order modeling is performed through the Caputo-Fabrizio fractional derivative, including a dimensional parameter Formula: see text to maintain the physical consistency of the models. Through an optimization problem based on the Formula: see text norm to minimize the variance of the squared frequency response of the SDOF blade, the VDVA parameters are optimized including the derivative order Formula: see text. Thus, parametric optimization was carried out when Formula: see text, finding that VDVAs perform at an acceptable level. Nevertheless, a high performance was observed in the interval Formula: see text, where the optimal order of each VDVA is included. Numerical simulations in the frequency domain are presented, demonstrating that VDVAs reduce vibration levels of the blade modal mass over a wider frequency bandwidth than that obtained using the tuned mass damper (TMD). Percentual reductions of the variance of the SDOF blade response of 0.714, 2.53%, 13.277, 13.389%, and 12.898, 13.36% were found for each VDVA concerning the TMD in all parametric scenarios investigated. In addition, analytical solutions were determined to compute the parameters of the viscoelastic tuned mass damper (VTMD) when the blade is parked. Finally, to support the findings in the frequency domain, time-domain numerical simulations are conducted of the modal mass response of the coupled and uncoupled blades to the VDVAs and TMD.
Maldonado-Bravo et al. (Fri,) studied this question.