Model for Vibration of Rotating Beams Supported by Flexible Foundation and Driven by DC Motor

This paper presents a mathematical dynamic model of a flexible arm-flexible-foundation manipulator driven by a DC motor. The mechanical system equations of motion are derived using the Lagrangian dynamics, the assumed modes method and the condition of inextensibility, the foundation flexiblility is represented by two linear springs in the vertical and the horizontal directions. The simple DC motor theory is borrowed and augemented to the mechanical model through the motor torque and hub angular velocity. The system produced is a nonlinear system that is electromechanically coupled and presented in state space. Simulation results showed the effects of root flexibility and the arm attachment angle on the system dynamics. The spectrums of the tip deflection and the armature current showed that the electrical current carries the arm vibration signature.