NONLINEAR DYNAMICAL BIFURCATION AND CHAOTIC MOTION OF SHALLOW CONICAL LATTICE SHELL  

作　　者：王新志 韩明君 赵艳影 赵永刚 

机构地区：[1]School of Science,Lanzhou University of Technology,Lanzhou 730050,P. R. China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2006年第5期661-666,共6页应用数学和力学（英文版）

基　　金：Project supported by the Natural Science Foundation of Gansu Province of China (No.ZS021-A25-007-Z)

摘　　要：The nonlinear dynamical equations of axle symmetry are established by the method of quasi-shells for three-dimensional shallow conical single-layer lattice shells. The compatible equations are given in geometrical nonlinear range. A nonlinear differential equation containing the second and the third order nonlinear items is derived under the boundary conditions of fixed and clamped edges by the method of Galerkin. The problem of bifurcation is discussed by solving the Floquet exponent. In order to study chaotic motion, the equations of free oscillation of a kind of nonlinear dynamics system are solved. Then an exact solution to nonlinear free oscillation of the shallow conical single-layer lattice shell is found as well. The critical conditions of chaotic motion are obtained by solving Melnikov functions, some phase planes are drawn by using digital simulation proving the existence of chaotic motion.The nonlinear dynamical equations of axle symmetry are established by the method of quasi-shells for three-dimensional shallow conical single-layer lattice shells. The compatible equations are given in geometrical nonlinear range. A nonlinear differential equation containing the second and the third order nonlinear items is derived under the boundary conditions of fixed and clamped edges by the method of Galerkin. The problem of bifurcation is discussed by solving the Floquet exponent. In order to study chaotic motion, the equations of free oscillation of a kind of nonlinear dynamics system are solved. Then an exact solution to nonlinear free oscillation of the shallow conical single-layer lattice shell is found as well. The critical conditions of chaotic motion are obtained by solving Melnikov functions, some phase planes are drawn by using digital simulation proving the existence of chaotic motion.

关 键 词：lattice shell the method of quasi-shell BIFURCATION chaotic motion 

分 类 号：O343.5[理学—固体力学]