A continuous frequency domain method with roots on the classic Hill's determinant analysis is presented to approximate the time-varying characteristics of a linear periodic system. The method is particularly useful to derive a time-invariant equivalent form of the time-varying aeroelastic problem of a rotor blade in forward flight. The proposed technique allows methodology usually employed in fixed wing aircraft to obtain closed-loop control laws be extended to rotary wings. The method is first validated solving Mathieu's equation. Next, the two-degree-of-freedom (flap bending and torsion) problem of rotating beam subject to unsteady and incompressible aerodynamics in forward flight is solved in the laplace domain. As a demonstration of the proposed method, the transfer functions in the 's' plane between a sudden and uniformly distributed input pressure perturbation applied along the beam and the output response of the two elastic degrees of freedom considered are obtained at a set of local sections.

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Nitzsche, F. (2001). Laplace-domain approximation to the transfer functions of a rotor blade in forward flight.