伸展运动悬臂梁的稳定性分析

The stability of deploying cantilever beam in the uniform speed case is studied. The governing equations are solved numerically to obtain the tip displacement of the deploying cantilever beam. Two types of methods to determine the stability of such a time-varying parameter system are proposed, namely, the instantaneous eigenvalue method and the stiffness matrix method. The eigenvalues are obtained to analyze the instability by means of studying the real and imaginary parts of the eigenvalues. The negative stiffness occurs while the beam in its unstable state and the features of instability also could be reflected by the changes of stiffness with time. Taking one order and five order truncation for the governing equations respectively, we compare the results of the two cases and find that their results have a good agreement.