Abstract:Cable structures, characterized by their low mass, low stiffness, and low damping, are prone to lateral vibrations under various excitations, which can significantly affect the safety, usability, and lifespan of the structure. To investigate the combined effects of mid-span and end excitations on the primary resonance of suspended cables, and the geometric nonlinearity is considered, the dimensionless differential governing equations are derived. The Galerkin method is employed to obtain discrete ordinary differential equations, which are then solved using the multiple scales method. The study explores the influence of different ratios of mid-span to end excitation amplitudes, different phase differences between mid-span and end excitations, and different positions of mid-span excitations on the primary resonance of suspended cables. It is found that these parameters do not alter the characteristic of the primary response-frequency curves. However, the amplitude ratio and phase difference result in shifts in the branches of the curves, and the smaller the amplitude or the closer the phase difference to π, the weaker the primary resonance of the cable. Changes in the position of mid-span excitation cause simultaneous translation and rotation of the phase-frequency curve, and the closer it is to the end excitation, the larger the system response.