ABSTRACT
The dynamics and control of interconnected rigid/flexible bodies such as robotic, aeronautic, and space structures is based on mathematical modeling and analysis and concurrent numerical solutions. This chapter discusses minimization of vibration (deformation) of elastic beams and shafts. At first, a movable support (or mass block) is used to model a flexible beam type robotic manipulator arm to minimize the lateral deformation of the beam. The rotating inertia force is considered as an external applied force. The function of the motion of the movable support is obtained through a step by step approach using calculus of variations. Then the same procedure can be applied to shaft-gear systems. The model and the governing equations of the shaft-gear systems are also presented. The chapter presents few approaches to minimize the vibration in elastic beam/shaft models with adjustable support and mass. Time variant boundary conditions are shown to have a distinctive influence on maintaining the elastic deformation minimum.
