An Intrinsic Description of the Nonlinear Aeroelasticity of Very Flexible Wings

Abstract

A modal solution is presented to the aeroelastic equations of very flexible wings in intrinsic form, that is written using inertial velocities and strains as primary variables. After assuming 2-D thin-airfoil aerodynamics on the wing sections, it is shown that the equations of motion can be written in canonical state-space form on the intrinsic modal coordinates without any matrix inversion and including only quadratic nonlinearities. Flutter characteristics are readily obtained from a linearized description of the dynamics equations, and the approach provides an efficient way of computing the nonlinear response with large wing displacements. Both situations are exemplified numerically on the Golang wing. The use of modal coordinates will serve to highlight some of the particular characteristics of the use of intrinsic beam solutions in aeroelastic problems with geometrical nonlinearities.

Flutter analysis of fixed and rotary wings through a one-dimensional unified formulation

“…Moreover, Patil et al developed a non-linear 1D formulation for laminated box beams by adopting an asymptotic technique to compute the cross-sectional mechanical properties [13,14]. Later, Palacios et al used the same formulation to evaluate the aeroelastic behavior of highly flexible wings [15]. Nowadays, the rapid increase of the computational power has motivated the development in the area of computational fluid dynamics (CFD).…”

Nonlinear Model Reduction for Aeroelastic Control of Flexible Aircraft Described by Large Finite-Element Models

“…The resulting model will then be tightly coupled with unsteady aerodynamics obtained from thin-strip approximations, as it was done by Palacios and Epureanu. 13 More complex aerodynamics based on the linearized unsteady vortex-lattice formulation of Murua et al, 7 which accounts for large-deformations in the equilibrium conditions, could be considered, but a 2-D description was selected for simplicity in a first demonstration of the approach. This will provide a compact description of the problem suitable for both modelling and control design.…”

Robust Aeroelastic Control of Very Flexible Wings using Intrinsic Models

“…The current study uses 11 bending modes and 1 axial mode which produced results that match well with previous studies using 2D aerodynamic approximations (see Table 3), whereas 3D aerodynamic methods such as UVLM more accurately reflect tip effect which have a noticeable impact on the computed flutter speed. 18 Time-domain simulation shows that structural nonlinearities do not give rise to any limit-cycle oscillations on the Goland wing at post-flutter speeds. Patil et al 26 also confirmed that structural nonlinearities in themselves are unable to create limit-cycle oscillations post-flutter.…”

“…The exact form of the aerodynamic forces in the modal description, derived using Wagner's function, is described by Palacios and Epureanu. 18 These forces can be approximated by a quadratic coupling between the velocity modes augmenting the modal ODE. The aeroelastic modal dynamics can then be written as:…”

“…The framework will be the intrinsic formulation of the problem, introduced for geometriccally-exact beam dynamics by Hodges 16 and expanded to nonlinear aeroelastic problems by Sotoudeh et al 7 Our description will use the modal projection of the intrinsic beam equations of Palacios, 17 with aerodynamics given by the strip theory, as in Palacios and Epureanu. 18 This provides a compact description of the problem suitable for control design. The paper thus describes the development of a H ∞ control system on wings described by a intrinsic modal formulation, with the aim of providing gust alleviation and disturbance rejection using conventional flap actuation.…”