Vibration suppression in a traversing mass-cantilever beam system

Abstract

A cantilever beam carrying a traversing spring-mass system is modeled. Applications of the system include robot traversing on space trusses, loads moving along stacker cranes carrying moving loads in a large warehouse, and other such systems. The equations of motion are derived using Hamilton’s principle. The obtained nonlinear partial differential equations are reduced to the nonlinear ordinary differential equations using Galerkin method. A novel method to control the vibration caused by the coupling between the beam and the moving subsystem is developed, which involves tuning the system to achieve internal resonance and then adding damping to the mass through a simple PD controller. Internal resonance’s condition for the system is discussed through parametric analysis. Spectral analysis is carried out using FFT and a time-frequency analysis method.