Innovative approach with harmonic modes and finite element modeling for the nonlinear dynamic analysis of a suspension bridge

Abstract The non-linear characteristics of a general multiple degrees-of-freedom suspension bridge under harmonic excitation are studied with an innovative approach consisting of the harmonic modes, the finite element modeling and the Incremental Harmonic Balance method. The geometric non-linearity induced by large amplitude vibration is considered. The harmonic mode and mean kinetic energy of the system are proposed to describe the non-linear responses. The harmonic mode can be expressed as a linear combination of different linearized system modes. The resonance responses of the structure are characterized with the participation ratio of these system modes. Its composition under harmonic excitations can easily be described in terms of the different harmonic mode shapes and then the system modes. The proposed method is further applied to analyze, in detail, the properties of the harmonic modes and the evolution of the steady state non-linear responses with variations in the excitation frequency.