  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.
