Modelling, simulation and control of nonlinear flexural-flexural-inextensional rotating beam

Abstract

A continuous rotating beam that undergoes flexure about two principal axes is modelled. The beam is characterized by gyroscopic type nonlinearities. The beam is of significant importance for applications such as large space structures, helicopter rotor blades, robot manipulators and long-span structures. Hamilton’s principle is used in deriving the Partial Differential Equations of motion (PDEs). An Ordinary Differential Equation (ODEs) solver based on the conventional Runge-Kutta method and a Differential Algebraic Equation (DAEs) solver based on Average Acceleration Formulation (AAF) have both been applied to simulate the system and the results are compared. Spectral analysis is carried out using EFT. In the second p art of this work, vibration suppression strategy based on Internal Resonance (IR) state is developed. By setting up different IR ratios, the modal coupling is greatly strengthened. Establishing IR state involves tuning the stiffness of the nonlinear beam by applying piezo-electric actuators to the system. A conceptual controller design is also presented. After the IR state is established, damping (velocity feedback) is introduced into the system and the vibration is thus successfully suppressed through two IR based PD controllers.