Multiple scales analysis of out-of-plane and in-plane vibrations of a wind turbine blade

TL;DR

This study analyzes the steady-state vibrations of wind turbine blades in both out-of-plane and in-plane directions, incorporating nonlinearities and large deformations to understand superharmonic resonances using multiple scales and harmonic balance methods.

Contribution

It introduces a detailed nonlinear dynamic model of wind turbine blades considering rotation effects and large deformations, applying multiple scales analysis for frequency response prediction.

Findings

Identification of superharmonic resonances in blade vibrations

Comparison of multiple scales and harmonic balance methods

Frequency response characteristics under various nonlinear conditions

Abstract

Steady-state response of an isolated horizontal axis wind turbine blade undergoing out-of-plane and in-plane vibrations are studied considering the two cases separately. Equations of motion for both cases are sought by modeling the blade as cantilevered Euler-Bernoulli beam and applying the Lagrangian formulation. Taking into account the effects of blade rotation on gravitational and aerodynamic forces and allowing the blade to undergo large deformations, various nonlinearities arise in the system resulting in superharmonic resonances. Taking practically relevant numerical values of parameters, we suitably order the parameters for their smallness. We then obtain the frequency responses corresponding to primary and superharmonic resonances by applying the method of multiple scales up to fourth and third orders for out-of-plane and in-plane cases respectively. Comparisons are drawn with the results obtained using the method of harmonic balance.