A Boundary Control Scheme for Vibration Suppression of a Flexible Beam Transported under Water

This paper presents a boundary control scheme for suppressing the vibrations of a flexible beam that is transported under water. Whenever an object is moved in water, hydrodynamic forces like drag force, added mass force, buoyancy force, viscous damping force, vortex-induced force, etc., are generated due to the fluid-structure interaction. Such forces not only oppose the motion of the object but also cause the structure to vibrate. In this paper, Hamilton's principle is utilized in formulating the equations of motion of the system. Then, a boundary control scheme is developed to suppress the vibrations of the beam in water. Lyapunov function-based analyses are performed to prove that the closed loop system is uniformly ultimately bounded under the action of nonlinear hydrodynamic forces. Simulations are performed to demonstrate the effectiveness of the proposed control scheme.