转动惯量和弹性支承对非保守杆稳定性的影响

研究了具有多个弹性支承的弹性简支杆在切向均布随从力作用下的动力特性和稳定性问题。对于杆内出现的弹性支承情形,采用了以分段表示的运动微分方程、弹性支承处的连续性条件和边界条件来描述。在数值求解时,以含有两个弹性支承简支杆为例,采用有限差分法,导出了差分方程的递推格式以及边界条件和连续条件的离散形式,具体分析了弹性支承的弹性系数和支承位置以及转动惯量对非保守杆的振动频率和稳定性的影响。此外,该方法还能求解复杂边界条件下具有多个弹性支承的非保守弹性杆的复特征值问题。

EFFECTS OF MOMENT OF INERTIA AND INTERNAL ELASTIC SUPPORTS ON THE STABILITY OF NON-CONSERVATIVE RODS

The dynamic behavior and the stability of simply supported elastic rods with internal elastic supports under the action of uniformly distributed tangential follower force are investigated. For rods with internal elastic supports, the governing differential equations at each section and continuous conditions at internal elastic supports as well as boundary conditions are given. Simply supported elastic rods with internal elastic supports are studied using the finite difference method. Recurrence formulas for governing differential equations and discrete formulas for continuous conditions at internal elastic supports as well as boundary conditions are derived respectively. Graphical results are presented to show the effects of elastic constants of the internal elastic supports, locations of the elastic supports and moment of inertia on vibration frequencies and stability of simply supported rods. The present method is applicable to complex eigenvalue problems of non-conservative rods with internal elastic supports and complicated boundary conditions.