Comparison of beam theories for characterisation of a NREL wind turbine blade flap-wise vibration

Abstract

Offshore wind turbine blades significantly differ from their onshore counterparts. With the increasing sizes, the hostile weather operational conditions, and the need to protect them against damage and breakdown, structural dynamics analysis is an essential and popular approach. An accurate and computationally simple model is desirable in the application of online structural health monitoring. For example using a digital twin of such structure. Free vibration investigation is a fundamental step for the analysis of structural dynamics. When a rotating blade deflects either in the plane of rotation or perpendicular to it, the centrifugal force on each blade exerts inertia force along the blade span, which has the effect of stiffening the blade and, as a result increasing the natural frequencies compared with the stationary ones. However, the influence of different blade parameters on the flap-wise vibrations is not very well understood. In this paper, the blade of horizontal axis wind turbines (HAWT) is modelled using different beam theories to pursue the effect of adding the different parameters on the dynamic modal characteristics. The examined models have been used to determine the natural frequencies and mode shapes of the National Renewable Energy Laboratory (NREL) 5-MW wind turbine. Results demonstrate that increasing angular velocity has a significant impact on the natural frequencies and mode shapes. The rotary inertia is found to impact the free vibration responses of the studied blades. Moreover, increasing hub radius, pre-cone and pitch angles are found to have less influence on the natural frequencies. Compared to the other investigated methods, Bernoulli’s based algorithms are found to produce less accurate results

Dynamic Responses Analysis of A 5MW NREL Wind Turbine Blade under Flap-Wise and Edge-Wise Vibrations

“…The blade undergoes flexural bending vibration in the flap-wise and edgewise directions, and the governing equation can be obtained by using the variational principle. For a HAWT blade, the Lagrangian function is given by [16]:…”

“…The study in [15] adopted the geometrically exact beam theory to find the natural frequencies and corresponding mode shapes in the flap-wise and edgewise directions to find the deflection response in both directions. The influence of different blade parameters on the flap-wise vibrations was studied in [16], where the effects of such parameters on dynamic characteristics of National Renewable Energy Laboratory (NREL) 5-MW wind turbine blades were investigated using different beam theories. In [16] the mode shape comparisons were carried out using MSF (modal scale factor) and MAC (modal assurance criteria) to study the correlation between the different theories used.…”

“…The influence of different blade parameters on the flap-wise vibrations was studied in [16], where the effects of such parameters on dynamic characteristics of National Renewable Energy Laboratory (NREL) 5-MW wind turbine blades were investigated using different beam theories. In [16] the mode shape comparisons were carried out using MSF (modal scale factor) and MAC (modal assurance criteria) to study the correlation between the different theories used. The study found that Bernoulli's algorithms produce less accurate results than Rayleigh and Timoshenko beam theories.…”

“…Each theory has its structural details and considers different stress deformations. The work in [16] found that Bernoulli's algorithms produce less accurate free vibration results than Rayleigh and Timoshenko beam theories. This study is based on structural modelling that adopted [16] for free vibration analysis and used the results to find the difference in dynamic deflection between the adopted theories.…”

“…The work in [16] found that Bernoulli's algorithms produce less accurate free vibration results than Rayleigh and Timoshenko beam theories. This study is based on structural modelling that adopted [16] for free vibration analysis and used the results to find the difference in dynamic deflection between the adopted theories. This study employs various beam theoies to analyse the structural dynamics of the blade.…”