Nonlinear coupled dynamics of suspended cables due to crossover points shifting and symmetry breaking

Abstract

This work deals with the nonlinear coupled dynamics of suspended cables considering two unavoidable factors: temperature changes and damaged situations. Particularly, the thermal-induced crossover shifting and damage-induced symmetry-breaking are considered and investigated. A kinematically condensed mathematical model with thermal and damage effects simultaneously is employed for the transverse displacements. A weighted-residual technique based on the Galerkin method is adopted to reduce the continuous model from the partial differential equations to ordinary ones. Following the multiple scales procedure for a weakly nonlinear system, both the polar and Cartesian forms of modulation equations are achieved. Based on the eigenvalue analyses, natural frequencies and mode shapes with thermal and damage effects are presented, and the crossover and veering points between natural frequencies are observed. Resonant behaviors of suspended cables after crossover points shifting and symmetry-breaking are revealed by using the numerical continuation and bifurcation analysis. Quantitative and qualitative differences in dynamic behaviors induced by temperature and damage factors are exhibited and illustrated through some parametric studies. Direct numerical integration solutions are adopted to confirm the perturbation ones, and a good agreement is observed.