Aeroelastic response of a swept wing with cubic structural non-linearities

Abstract

Linear and non-linear aeroelastic analyses of swept cantilever wings containing a cubic non-linearity in an incompressible flow are investigated. Expressions of aerodynamic forces and moments for an element of the swept wing are derived in the time domain using a relation between Theodorsen and Wagner's functions. Consequently, the governing aeroelastic equations of two degrees of freedom wings are derived for both swept backward and forward wings. Linear analysis is carried out via solving the governing equations with the standard fourth-order Runge—Kutta method. For the sake of verification of the derived formulas, the results of the numerical solution for a linear flutter boundary are compared with the experimental data in several cases. Considering softening and hardening cubic structural non-linearities, non-linear analysis of the swept wing is studied. For the wings containing hardening cubic non-linearities, the first- and third-order harmonic balance (HB) methods are employed to find the amplitude and frequency of limit cycle oscillations (LCOs). Comparison between results of the HB method and those of the numerical solution of the governing equations indicates a close agreement. Finally, few parameters on the linear and non-linear flutter boundaries and also the amplitude and frequency of the LCO are studied.