离心场中纵向悬臂梁的大范围分岔分析

采用打靶法研究了离心场中纵向悬臂梁的大范围失稳与分岔问题。分析结果证实：随着参数a（离心臂长与梁长之比）的变化，梁平衡解可能发生三种分岔现象。文中给出了平衡解的分岔形态，并发现了梁分岔解的单向跳跃现象，即突变现象。

GLOBAL BIFURCATION ANALYSISOF A CANTILEVER BEAM VERTICALLY FIXED IN CENTRIFUGAL FIELD

Using the general Hamilton variation principle, anonlinear dynamic model of a cantilever beam vertically fixed incentrifugal field is established in the present work. The global bifurcation and instabilityof the system are studied by the shooting method. The analysis reveals that the equilibrium solution mayhave three sorts of bifurcation phenomena according to the parameter a(the length ratio of the centrifuge arm to the beam). 1) When a=0, thebifurcation is of the pitchfork type, since the system and thecentrifugal force are symmetrical. 2) When 00.5, the initial equilibrium state of the beam is also stable.The saddle-node bifurcation takes place owing to the twist ofthe beam. Both the second and the third bifurcation exhibit theunidirectional snap-through phenomenon (i.e. catastrophe phenomenon).These bifurcation properties are different from those of the beamhorizontally fixed in centrifugal field. The equilibrium solution of thehorizontal beam may only have the pitchfork bifurcation because the beamhorizontally fixed in centrifugal field has only the trivial solutionand the centrifugal force is symmetrical to the beam. For the beamvertically fixed in centrifugal field, the centrifugal force isunsymmetrical to its initial equilibrium state when the length of thecentrifugal arm is not zero. In the paper, the shapes of the bifurcationsolution are given as well.