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Steady-state response of an isolated horizontal axis wind turbine bladeundergoing out-of-plane and in-plane vibrations are studied considering the twocases separately. Equations of motion for both cases are sought by modeling theblade as cantilevered Euler-Bernoulli beam and applying the Lagrangianformulation. Taking into account the effects of blade rotation on gravitationaland aerodynamic forces and allowing the blade to undergo large deformations,various nonlinearities arise in the system resulting in superharmonicresonances. Taking practically relevant numerical values of parameters, wesuitably order the parameters for their smallness. We then obtain the frequencyresponses corresponding to primary and superharmonic resonances by applying themethod of multiple scales up to fourth and third orders for out-of-plane andin-plane cases respectively. Comparisons are drawn with the results obtainedusing the method of harmonic balance.

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