Energy transfer between components of a cable stayed beam model under the concentrated excitation: 1:2 modal resonance

The present study aims to investigate the dynamic behaviors and energy transfer between components of a cable stayed beam structure subjected to a concentrated load, in which the primary resonance of the beam and one-to-two internal resonance between modes of the beam and the cable occur. Galerkin discretization and multiple time scales method are applied to derive the modulation equations of the system governing the amplitude and phase. Two sags of span ratios are defined to modulate the internal resonance. Frequency response, amplitude response, phase diagram, Poincare map, and time history curves are calculated and used to investigate the modal resonance dynamics. The results demonstrate that the beam and the cable have two resonant peaks in frequency responses, where the beam always shows hardening spring property and the cable may present hardening and softening spring properties affected by sag to span ratio. The system is prone to complex dynamic behavior with the small amplitude excitation in the primary resonance region.