Finite Element Bond Graph Model of Rotors

摘要

Lumped parameter models can not sufficiently describe dynamics of many distributed systems, such as a continuous rotating shaft with bending. The finite element method is employed to embed distributed dynamics of rotating shafts with bending into constitutive laws of bond graphs resulting a finite element bond graph model. Defining the nodal displacements, the finite element mass and stiffness matrices are obtained from energy equations, and represented as constitutive relations for multi-port I and C's. Centrifugal forces are included through multi-port C, and the Coriolis forces are embedded via gyrators. Finally, the FE bond graph is reconstructed in a simple vector bond graph form, which can be integrated into any bond graph model of rotating shafts.