One-To-One-To-One Internal Resonance Analysis of a Double-Cable-Stayed Flexible Beam-Structure Mounted with a Manipulator System

Abstract

This paper deals with the theoretical studies to investigate the in-plane eigenvalue problems and the one-to-one-to-one internal resonance behaviors of a double-cable-stayed flexible beam-structure mounted with a manipulator system (DCFBMS) under constant rotational speed. A more precise and rigorous dynamic model with proper boundary conditions has been developed in which geometric nonlinearity and coupling nonlinearity of cables and beam are considered while the manipulator has been modeled as a rigid link. The in-plane eigenvalue problem of the model considering the boundary and continuous conditions has been evaluated and graphically demonstrated. Then, the ordinary differential equations (ODEs) are obtained by Galerkin’s method and multiple scales method has been employed to further analyze the vibration attributes of steady-state responses and their stability under internal resonance condition. The nonlinear response, stability and bifurcations for one-to-one-to-one internal resonance have also been investigated by varying system parameters. Analytically obtained results have been verified by Runge–Kutta method and found to be in good agreement. The present theoretical results deliver a useful insight into the nonlinear dynamic behavior and operational stability of DCFBMS.