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| The dynamic stability analysis of shallow arches with geometrical imperfections |
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| DOI：10.7511/jslx20086173 |
| KeyWord:shallow arches,geometrical imperfection,dynamic stability,viscoelastic,general displacement control method |
| YI Zhuang-peng1 ZHAO Yue-yu2 ZHU Ke-zhao2 |
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| Abstract: |
| This paper is concerned with the effects of geometrical imperfections on the dynamic stability of viscoelastic hinged shallow arches.The dynamic equation of shallow arch subjected to sinusoidal impulsive load is derived from the d'Alembert principle and the Euler-Bernoulli assumption.Then with the application of the Galerkin method the nondimensional nonlinear differential equations,which can be solved by the Rungle-Kulta method,are determined.On the other hand the general displacement control method,which can effectively trace the dynamic post-buckling path of structure,is introduced to obtain the response curve of shallow arch with geometrical imperfection in the geometrical and material finite element analysis.These two methods are used to investigate the effects of the first three harmonic geometrical imperfections on the dynamic stabilities of shallow arches,where the critical loads are both determined by the B-R criterion.The main results are firstly that the dynamic critical load of shallow arch is larger when the material is viscoelastic and the differences in the structural response curves are great between viscoelastic and elastic shallow arch,and secondly that the second-order harmonic geometrical imperfection decreases the dynamic critical load remarkably,furthermore the dynamic critical load of viscoelastic shallow arch may be smaller than that of elastic shallow arch. |
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