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| DOI：10.7511/jslx20075127 |
| KeyWord:discretization,suspended cables,onevs.three internal resonance,the method of multiple scales |
| WANG Lian-hua ZHAO Yue-yu JIN Yi-xin HU Jian-hua |
| School of Civil Engineering,Hunan University,Changsha 410082,China |
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| Abstract: |
| The two-mode nonlinear response of the suspended cable subjected to the external excitation with onevs.three internal resonance is investigated.Taking into account the geometric non-linearity of the suspended cable and the assumption of quasi-static stretching due to the fact that the transverse wave speed is much lower than the longitudinal one,the non-linear governing in-plane equation of the suspended cable is derived by means of Hamilton principle.And it is shown that onevs.three internal resonances between the first and third symmetric modes may be activated for a range of elasto-geometric parameters.First,the Galerkin method is used to discretize the nonlinear equation of planar motion.Then the method of multiple scales is applied to perturb the discretized equations of motion.And it shows,except the amplitudes of the first and third symmetric mode,other amplitudes will die out due to the presence of damping.Thus,the solvability conditions reduce to a two-dimensional system.At last,the averaged equations under two cases of primary resonances are obtained. |
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