The objective of this paper is to provide an analytical framework based on Wagner’s unsteady flow model, to study the nonlinear dynamic of pitch and plunge DOFs in airfoils. To this end, the nonlinear equations of motion of an airfoil section model with pitch and plunge DOFs are derived. The 2-DOF model of the system is converted to a 3-DOF model by adding augmented states related to the dynamic of the correction coefficient of the Wagner’s flow model. The resulting 3-DOF system is then normalized and re-expressed around the equilibrium state. As the mass and stiffness matrices of the resulting system are not symmetric, special techniques are used to diagonalize them and facilitate the later nonlinear analysis. Multiple timescales perturbation method is then used to provide analytical solution for the nonlinear self-excited 3-DOF model. The analytical and numerical results are compared at three different situations related to the subcritical, critical and supercritical values of the wind speed. It is observed that the qualitative and quantitative results of the numerical and analytical models are in excellent agreement with each other. To study the effect of nonlinearity on the system’s response, a linear eigenvalue analysis is carried out using a root locus plot of the homogenous linearized system. By comparing the analytical results of the linear and perturbed system with nonlinear numerical simulations, it is shown that the linear model provides a rough over-estimation for the instability speed and the use of a nonlinear model is inevitable for achieving sufficiently accurate findings. The approach and results presented in this paper can be used to provide better prediction for the dynamic behavior of flexible blades with pitch and plunge DOFs.

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