Quantitative Aeroelastic Stability Prediction of Wings Exhibiting Nonlinear Restoring Forces

In engineering practice, eigen-solution is used to assess the stability of linear dynamical systems. However, linearity assumption in systems sometimes implies simplifications, particularly when strong nonlinearities exist. this case, eigen-analysis requires linerisation problem and hence fails provide a direct estimation. For reason, more reliable tool should be implemented predict nonlinear phenomena such as chaos or limit cycle oscillations. One method overcome difficulty Lyapunov Characteristic Exponents (LCEs), which quantitative indications characteristics governed by time-dependent differential equations. Stability prediction using compatible with linear. Moreover, LCE estimations do not need steady equilibrium solution they can calculated system response evolves time. Hence, generalization traditional analysis eigenvalues. These properties are very useful aeroelastic problems possessing characteristics, may significantly alter result chaotic behaviour. A common nonlinearity flexible restoring force cubic stiffness, would substantially benefit from LCEs assessment. This work presents evaluation indicators presence force. The demonstrated on two-dimensional comparing behaviour estimated Exponents.