Research on One-to-Two Internal Resonance of Sling and Beam of Suspension Sling–Beam System

An approach is presented to investigate the 1:2 internal resonance of sling and beam a suspension sling–beam system. The was taken as geometrically linear Euler beam, considered be nonlinear. dynamic equilibrium equation structures derived using modal superposition method, D’Alembert principle Hamilton principle. nonlinear equations free vibration forced oscillation were solved by multiple-scales method. We first approximation solutions for single-modal motion Numerical examples are provided verify correctness formula derivation obtain amplitude–time response vibration, primary response, amplitude–frequency amplitude–force oscillation. According analysis, it evident that combination system exhibits robust coupling properties due presence resonance, which useful engineering design.