A Krylov-Bogoliubov-type approximation for continuous-oscillation systems with damping non-linearities

Abstract

NASA experiments have indicated the need of non-linear damping models to describe the motion of large flexible space structures. In this work, energy-type non-linear damping models in an infinite-dimensional setting are studied. According to the geometry of the structures considered, energy-type non-linear damping models are divided into two types. The existence and uniqueness result of the non-linear damping models is based upon the work of Lunardi. Then, a Krylov-Bogoliubov-type approximation is established for the non-linear damping models in the case where the linear damping part is neglected. In general, the generalization of the Krylov-Bogoliubov approximation method, which applies only to a single-degree-of-freedom (DOF) model, to a multi-DOF model has been a formidable task. A numerical example is provided to demonstrate the efficiency of the Krylov-Bogoliubov approximation for our continuous systems.