An inertia-capacitance beam substructure formulation based on bond graph terminology with applications to rotating beam and wind turbine rotor blades

Abstract

In this thesis, an Inertia-Capacitance (IC) beam substructure formulation based on bond graph terminology is developed. The IC beam is formulated in the centre of mass body fixed coordinate system which allows for easy interfacing of the IC beam in a multibody system setting. This multibody floating frame approach is also computationally cheaper than nonlinear finite element methods. Elastic deformations in the IC beam are assumed to be small and described by modal superposition. The formulation couples rigid body motions and elastic deformations in a nonlinear fashion. Detailed derivations for a two-dimensional planar IC beam with bending modes are presented. Brief derivations are also presented for the two-dimensional IC beam with both bending and axial modes and for the three-dimensional IC beam with bending modes. A modal acceleration method via the decoupling of modes is developed for use in the IC beam. The Karnopp-Margolis method is used in the model set-ups to ensure complete integral causality. This results in an efficient numerical system.

The large deflection cantilevered beam and the rotating beam spin-up maneuver problems are solved. Convergence studies of various model parameters are performed. The effects of axial modes in the spin-up maneuver problem are also investigated. Investigations are also made on the hinges used for the substructure interconnections. The IC beam is shown to be capable of solving these problems accurately and efficiently. Lastly, the methodology to apply the IC beam formulation to the wind turbine rotor blades is presented.