Geometrically nonlinear aeroelastic behavior of pretwisted composite wings modeled as thin walled beams

Abstract

Geometrically nonlinear aeroelastic behavior of pretwisted composite high aspect ratio wings, structurally modeled as thin walled beams (TWB) is studied. The structural equations of motion are obtained for the circumferentially asymmetric stiffness (CAS) configuration TWB based on the kinematic relations governing the thin walled beams, including the nonlinear strain–displacement relations and utilizing the principles of analytical dynamics. Unsteady aerodynamic loads in the incompressible flow regime are expressed using Wagner’s function in time-domain. The aeroelastic system of equations is augmented by the differential equations governing the aerodynamics lag states to come up with the final coupled fluid–structure equations of motion. The governing equations of the aeroelastic system is solved, for the TWB with CAS composite layup, by means of a Ritz based solution methodology utilizing the mode shapes of the linear structural system to approximate the spatial variation of degrees of freedom in the thin walled beam. Time response of the nonlinear aeroelastic system is obtained via the Runge–Kutta direct integration algorithm. Effects of the fiber angle and pretwist angle of the CAS layup configuration on the nonlinear aeroelastic stability margins and limit cycle oscillation behavior are studied in depth.