无粘流中非线性板梁结构的分叉

研究了立方非线性板状梁叠层结构在无粘流体作用下的分叉问题．假设各板在同一时刻有相同的变形，建立了流体作用下简支板状梁的立方非线性模型，并利用Hopf分叉代数判据分析了简支板状梁流固耦合结构的分叉，结果表明该结构无Hopf分叉现象．最后，讨论了该结构平衡点的静态分叉和局部稳定性，数值仿真表明，该结构为非线性保守系统。

Bifurcation of Nonlinear Plate-Type Beams in Inviscid Fluids

The bifurcation of parallel plate-type beams with cubic nonlinear stiffness in inviscid fluids was investigated. A nonlinear model for a simply supported plate-type beam in inviscid fluids, a solid-liquid coupling system, was established on the basis of the hypothesis that all the plates have the same deflections at any instant. An algebraic criterion of Hopf bifurcation was used to analyze the bifurcation of the structure. The result shows that there is no Hopf bifurcation for the structure in inviscid fluids. Finally, the static bifurcation of equilibrium positions and local stability of the structure were discussed. The numerical simulation shows that the coupling system is a nonlinear conservative system.