A z-Transform Discrete-Time State-Space Formulation for Aeroelastic Stability Analysis

In many complex aerospace applications, it is common to use numerical tools to evaluate the unsteady aerodynamic behavior. The present work presents an alternate formulation for the state-space representation of aeroelastic systems based on digital control theory that is shown to be more effective and accurate for the coupling of numerical solutions with such systems. The application of the z transform allows for direct frequency domain representations of the aerodynamic solutions without the need for approximating models, as generally occurs in other state-space formulations. This fact also makes this new methodology a more straightforward procedure for aeroelastic analyses. A typical section model of a NACA 0012 airfoil at transonic flow conditions is used as a test case to assess the correctness and accuracy of the proposed formulation. The present results are compared with data obtained from continuous-time state-space formulations and through the direct integration of the aerodynamic and structural dynamic equations. (AU)