Cubic static stall model for nonlinear aeroelastic behavior of high-aspect-ratio flexible composite wings

Abstract

In this paper, by defining a new paradigm for nonlinear aerodynamic equations of flow separation and static stall, a new form of nonlinear aeroelastic equations for a highly flexible composite wing with torsional and bending movement is presented. Structural modeling is carried out using nonlinear general flexible Euler–Bernoulli beam equations in the third-order. Combining the unsteady Wagner model and the nonlinear lift coefficient-angle of attack lead to the aerodynamic equations for simulating stall using a cubic approximation. The aeroelastic equations are obtained utilizing Hamilton’s principle and Lagrange equations. A time-history integration method is used to solve the integro-differential nonlinear aeroelastic equations. The obtained results are compared with previous studies for validation, and there is good agreement between the results. The results show that the use of the cubic curve instead of the piecewise linear curves which is commonly used in other references, although, causes an apparent complication of the equations but reduces the errors. It is also observed that the limit cycle oscillations speed changes by changing the angle of fibers, and the maximum of this instability speed occurs at an angle of about twenty degree.