Energy-Flow Approach Identifying Dynamic Characteristics of Aeroelastic–Electromagnetic Coupling Flutter System in Aircraft Designs

An energy-flow approach (EFA) is developed to reveal the critical flutter speed (CFS) of an air–structure electromagnetic interactive flutter system. To illustrate the theory and method, a two-DOF integrated linear/nonlinear coupling system is investigated, in which the electromagnetic isolator adds damping, increasing CFS and collecting vibration energy. Following a summary of EFA applicable to the system, numerical simulations on a simplified aeroelastic system of natural frequencies 3 and 0.6 are completed. The results reveal that (a) EFA can effectively identify CFSs of linear/nonlinear systems, at which the systems show non-damping periodical motions with periodical phase space diagrams and time histories of generalised potential energy (GPE)/kinetic energy (GKE) and zero time-averaged energy flows; (b) under and over CFSs, the systems respectively show damped and convergence motions; and (c) the electromagnetic isolator clearly increases CFSs and enables the collection of vibration energy. To check possible chaotic motions for a non-damping flutter system of two natural frequencies without their common rational period, a system with two frequencies 1 and 3 is examined. At zero wind speed, its free vibrations under the initial conditions are chaotic. For cases of air excitation, given the inertia, stiffness, and damping coupling mechanism contributed by wind flows, the original two frequencies with no common period gradually close in on each other until they reach the corresponding flutter speeds, producing periodical motions of single frequency. The results under/over CFS for linear systems show similar damped/convergence oscillations. However, for nonlinear systems, the under-flutter speed gives damped oscillation, while the over-flutter one still shows periodical motion consisting of two mixed frequencies with their common period. The results confirm that the proposed EFA is an effective general means to tackle any complex linear/nonlinear integrated flutter-control system for aircraft designs as well as green energy collection.