Bifurcation analysis of an arch structure with parametric and forced excitation |
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| Authors: | Fangqi Chen Jianshu Liang Yushu Chen Xijun Liu Hongcheng Ma |
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| Institution: | aDepartment of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China;bDepartment of Mechanics, Tianjin University, Tianjin 300072, PR China;cLiuhui Center for Applied Mathematics, Nankai University and Tianjin University, Tianjin 300072, PR China;dCollege of Mechanical and Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang 050054, PR China |
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| Abstract: | The  subharmonic bifurcation and universal unfolding problems are discussed for an arch structure with parametric and forced excitation in this paper. The amplitude–frequency curve and some dynamical behavior have been shown for this class of problems by Liu et al. Here, by means of singularity theory, in the case of strict 1:2 internal resonance, the bifurcation behavior of the amplitude with respect to a parameter (which is related to the amplitude of the live load imposed on the arch structures) is studied. The results indicate that it is a high codimensional bifurcation problem with codimension 5, and the universal unfolding is given. From the mechanical background, 20 forms of two parameter unfoldings with some constraints are studied. The transition sets in the parameter plane and the bifurcation diagrams are plotted. The results obtained in this paper present some new dynamic buckling patterns and abundant bifurcation phenomena. |
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| Keywords: | Arch structures    sciencedirect subharmonic resonance" target="_blank">com/cache/MiamiImageURL/B6V48-4HC6J36-1-W/0?wchp=dGLbVlb-zSkWz" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=20 width="9"/> subharmonic resonance Bifurcation Universal unfolding |
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