摘要
建立了轴对称转动粘弹性不可移简支梁的几何非线性动力学模型。应用Laplace变换和摄动法分析了超静定粘弹性杆的平衡解,得到了转动粘弹性梁的预应力平凡平衡态。应用Galerkin和摄动法得到了粘弹性梁平凡解的失稳临界值,分析了梁轴向伸长对失稳临界值的影响;通过极限分析获得了系统的后屈曲稳态近似解,讨论了平凡解二次分岔后的近似稳定吸引域,并数值仿真了系统平凡解失稳后初始挠动向稳态解的演变。本文的大范围稳定性分析发现了粘弹性系统叉式分岔失稳后的平凡态又经二次鞍结点分岔而稳定以及单向跳跃(突变)等不同于弹性系统的现象。
A nonlinear dynamic model of a simply supported viscoelastic beam undergoing overall axially symmetrical rotation was established. The trivial equilibrium of the system was investigated by employing perturbation and Laplace transformation methods. The critical value of the trivial equilibrium loses its stability was studied by Galerkin and perturbation methods. The effect on the critical value by axial elongation was discussed. The post buckling steady state equilibriums were obtained by limit analysis method and the stable region of the trivial equilibrium through second bifurcation was analyzed approximately. The initial perturbation evolves to the steady-state equilibriums when the trivial equilibrium loses its stability was calculated numerically. By this global stable studying of the visco-elastic system, some phenomena such as the unstable trivial equilibrium turns to stable again through the second saddle-node bifurcation and the unidirectional snap-through phenomenon （i. e. catastrophe phenomenon） and so on, which are different from the elastic system, are discovered.
出处
《力学季刊》
CSCD
北大核心
2010年第1期64-70,共7页
Chinese Quarterly of Mechanics
基金
国家自然科学基金委员会-中国工程物理研究院联合基金资助项目(NSAF10876100)
中国工程物理研究院双百人才基金(ZX04002)
