A note on the state space representation of aeroelastic systems for time domain analysis

The time domain state space model for describing an aeroelastic system has usually been obtained by using rational function approximations to write unsteady aerodynamics in the time domain. This strategy has been employed by many researchers because the standard form of unsteady aerodynamics is typically computed in the reduced frequency domain with explicit or implied transcendental functions, which do not readily admit to applying frequency to time domain transforms. However, this article demonstrates that the unsteady aerodynamics do not need to be explicitly written in the time domain when the purpose is to obtain a state space model for aeroelastic analysis. A basic and classical result from the linear algebra is employed for constructing a constant dynamic matrix by using the pair of eigenvalues and eigenvectors obtained iteratively from the pk method. The results show that the new approach provides accurate results for linear dynamic aeroelastic models described in either physical or generalized coordinates.