NONLINEAR QUADRATIC INTERACTIONS IN CABLE-STAYED BEAMS

Abstract eng:
An analytical model is proposed to study the nonlinear interactions between deck and cable motions in cable-stayed bridges. The integro-differential problem, describing the in-plane motion of a simple cable-stayed beam, presents quadratic and cubic nonlinearities in the cable equation and at the boundary cable-beam connection. System modal properties analytically derived evidence the occurrence of 1:2 and 1:3 internal resonances in the parameter range of technical interest. Quadratic interactions appearing at lower oscillation amplitude than cubic are the primary object of the study. Two cases of 1:2 resonance, namely, global-local and local-global interactions are analyzed by a 2dof analytical model. In the first case, the cable undergoes large oscillations due to an energy-transfer from lower-frequency (global mode) to higher-frequency (local mode) which are amplified for cable of light weight. In the second case, cable oscillations are induced by global motion at a double frequency of the first local mode through the well-known parametric excitation phenomenon.

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