Vibration control of a coupled nonlinear string system in transverse and longitudinal directions

Abstract

In this paper, vibration control is considered in both transverse and longitudinal directions for a coupled nonlinear flexible string system. The vibrating string is nonlinear due to the consideration of the coupling between transverse and longitudinal displacements. By using Hamilton's principle, the dynamics of the nonlinear string are presented by two partial differential equations (PDEs) and four ordinary differential equations (ODEs). Based on Lyapunov's direct method, boundary control is constructed to regulate the string's vibration and stabilize the system. Numerical simulations are provided to demonstrate the effectiveness of the proposed control. © 2011 IEEE.