Nonlinear response analysis of a cable-beam coupled system
LIU Hai-tao1，WEI Ming-hai 2，XIAO Yi-qing1，LIN Kun1
1. Harbin Institute of Technology Shenzhen Graduate School, Shenzhen 518055, China；
2. Department of Construction and Engineering Management, Shenyang Jianzhu University, Shenyang 110168, China
Abstract：Combined with quantitative analysis of the nonlinear vibration method, the nonlinear response of cable and beam as a coupled structure under the combined effects of internal and external resonance is investigated. Applied the method of multiple scales to the cable-beam coupled structure, analyzing the possible resonances between the mode of the beam and cable, and pointing out its forms. Considering the resonance 1:2 between the beam and cable, the nonlinear response of the cable-beam coupled structure under the primary resonance of the beam (auto-parametric resonance of the cable) and the principal parametric resonance of cable (sub-harmonic resonance of the beam) are respectively investigated. The effects of the cable sag to span ratio, mass ratio and stiffness ratio on the nonlinear responses are investigated follow. Last, in order to validate the correctness of the approximate solution, the displacement of the first order approximate analytical solution of the beam and cable are contrast to the numerical solution. The results show good agreement between the analytical and numerical solutions especially near the external resonance frequency.
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