A general solution for dynamic stability of the fluttered mode of damped, fluttered systems subjected to parametric random excitations is presented in this paper. First, the system equations are pairwisely uncoupled by a modal analysis based on normal modes of the system at the onset of fluttering. The stochastic averaging method is then applied to obtain Ito's equation governing the amplitude of the fluttered mode. Finally, the Lyapunov exponent of the fluttered mode is derived, from which the criterion for asymptotic sample stability of the mode is determined. A cantilevered beam acted upon by a static follower force and a white noise parametric excitation at the free end, and a skew panel subjected to an aerodynamic force in the chordwise direction and a white noise excitation in the spanwise direction are demonstrated as examples. Numerical results show that, although the static follower force or the aerodynamic force exceeds the flutter load, the fluttered mode of the beam or the panel may remain stable in the sense of asymptotic sample stability due to the presence of the white noise excitation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.