Dynamic Stability Analysis and Vibration Control of A Rotating Elastic Beam Connected With an End Mass

In this paper, dynamic stability analysis and vibration control for a rotating elastic beam connected with an end mass driven by a direct current (DC) motor is considered. A complete strategy including mathematical modeling, dynamic analysis, vibration controller design and simulation for linear and nonlinear systems are presented. Once the rotating flexible physical system has been described by a set of governing partial differential equations, they are manipulated to achieve an appropriate mathematical format for vibration control system design and computer simulation, respectively. Hamilton principle, Lagrange's equation, assumed-modes and the fourth-order Runge–Kutta methods are applied in the system modeling derivation, descretization, and numerical analysis. The correctness of the numerical results and the characteristic property between mathematics and dynamics are demonstrated as well. Also, a realizable vibration control scheme is developed which not only can stabilize all the vibration modes but also make this rotating elastic beam system efficient for good transient response.