轴力对自由边界Timoshenko梁横向动特性影响研究

Effect of Axial Force on the Lateral Vibration Characteristics of Timoshenko Beam Under Free Boundary Condition

从Timoshenko梁平衡方程出发,结合梁的内力和位移参数的关系,建立了轴力作用下Timoshenko梁自由振动偏微分方程;采用分离变量法求解自由边界轴力作用下Timoshenko梁自由振动方程;给出了求解Timoshenko梁固有频率的方程。在自由边界无轴力作用条件下,将固有频率计算结果与Euler梁计算结果对比,验证了给出的梁运动方程求解方法的正确性;为了估算轴力对导弹横向动特性的影响,建立了截面为环形的Timoshenko梁模型,不同轴向压力下横向固有频率计算结果表明,轴向压力对最低阶频率的影响最大,阶次越高影响越小。

The partial differential equation of Timoshenko beam’s free vibration with axial force is established based on equilibrium equations and the relationship between internal forces and displacements.The partial differential equation is solved by variable separation approach,the equation of Timoshenko beam’s frequencies is provided.The method of deduction is validated by the results of Euler beam without axial force.The Timoshenko beam model with annular cross section is built to estimate the effects of axial force on the lateral vibration characteristics of the missile,the results show that the effect on natural frequencies decreases with the increase of orders.