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| The solutions of primary resonance responses of suspended cables via the multiple scales method and homotopy analysis method |
| Received:May 30, 2013 Revised:August 08, 2013 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx201405005 |
| KeyWord:suspended cable primary resonance multiple scales method homotopy analysis method Runge-Kutta method |
| Author | Institution |
| 赵珧冰 |
湖南大学 土木工程学院, 长沙 |
| 孙测世 |
湖南大学 土木工程学院, 长沙 |
| 王志搴 |
湖南大学 机械与运载工程学院, 长沙 |
| 王连华 |
湖南大学 土木工程学院, 长沙 |
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| Abstract: |
| By applying the Hamilton's principle and quasi-static assumption,the equation of motion of the suspended cable was obtained by using the Galerkin procedure.Then,the multiple scales method and homotopy analysis method were applied to obtain the approximate series solutions of the primary resonance response of the suspended cable for the cases of the first two modes.Moreover,in order to verify the accuracy of the approximations,the Runge-Kutta method was also introduced.The numerical results show that:as the increasing of the sag-to-span ratio and the response amplitudes of the suspended cable,there are significant qualitative and quantitative differences in the frequency amplitude curves obtained by the multiple scales method and homotopy analysis method,and the results obtained by the homotopy analysis method are in good agreement with the numerical results.Finally,the displacement fields and the time response curves of the axial tension force are compared and analyzed. |
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