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Abstract

This is an introduction and overview of the work that has been done in nonlinear aeroelasticity prior to the last decade. many of the issues discussed here are still under active investigation. of particular interest are the limit cycle oscillations that may occur once the dynamic stability (flutter) boundary has been exceeded.

Semi-Analytical Reduced-Order Models for the Aeroelastic Behavior of Subsonic Flexible Wings via Generalised Plate and Beam Formulations

“…By substituting the modal expansions in the PVW, the aeroelastic equilibrium PDE eventually becomes a linear system of ODEs for the generalised coordinates regardless the aerostructural model, namely [94]: depend on the wing shape; t is the vector of all unknown generalised coordinates (including added aerodynamic states) and drives the aeroelastic dynamic response. Note that a change of variables is always possible as long as a proper transformation matrix can be defined and all aero-structural matrices are then consistently projected onto the new modal base [10,19].…”

“…respectively, or their equivalent first-order forms [94]: are the generalised aeroelastic mass, damping and stiffness matrices, which depend parametrically on the flow speed. In particular, flutter occurs at the lowest flow speed F U which makes the real part of at least one of the complex eigenvalues i become positive (i.e., the dynamic behaviour becomes unstable thru a Hopf bifurcation [35], where a couple of complex conjugates eigenvalues crosses the imaginary axis and leaves the response undamped), two or even more generalised aeroelastic modes coupling at the flutter frequency F f .…”

CFD simulation of flow-induced vibration of an elastically supported airfoil

“…The classical example is the flutter instability of airfoils, which occurs for systems with two degrees of freedom when the critical flow velocity is surpassed [1]. Flutter is a dynamic instability of an elastic structure coupled to airflow, caused by the interaction between elastic, inertial and aerodynamic forces.…”

Parallel numerical simulation of oscillating airfoil NACA0015 in the channel due to flutter instability

“…The airfoil can be approximated as a two-degree-of-freedom system, with vertical translation and rotation modes. During flutter instability, this movement is harmonic with constant (or increasing) amplitude, and the energy dissipated by the internal damping is compensated by energy transfer from the airflow [1][2][3].…”