Chaotic Oscillation of Saddle Form Cable-Suspended Roofs under Vertical Excitation Action |
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Authors: | Fan Jiashen He Fusheng Liu Zhengrong |
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Institution: | (1) Department of Civil Engineering, Yunnan Polytechnic University, Kunming, 650051, China;(2) Department of Mathematics, Yunnan Normal University, c[Kunming, 650092, China;(3) Department of Mathematics, Yunnan University and Yunnan Institute of Applied Mathematics, Kunming, 650091, China |
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Abstract: | The purpose of this paper is to investigate the dynamic behaviour of saddle form cable-suspended roofs under vertical excitation action. The governing equations of this problem are system of nonlinear partial differential and integral equations. We first establish a spectral equation, and then consider a model with one coefficient, i.e., a perturbed Duffing equation. The analytical solution is derived for the Duffing equation. Successive approximation solutions can be obtained in likely way for each time to only one new unknown function of time. Numerical results are given for our analytical solution. By using the Melnikov method, it is shown that the spectral system has chaotic solutions and subharmonic solutions under determined parametric conditions. |
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Keywords: | Saddle form cable-suspended roofs truncated spectral model bifurcation chaos |
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