轴向受载的Bernoulli-Euler薄壁梁固有振动和稳定性的理论研究

Theoretical Research on Natural Vibration and Stability of Axially-Loaded Bernoulli-Euler Thin-Walled Beam

通过直接求解轴向受载的单对称均匀Bernoulli-Euler薄壁梁单元弯扭耦合振动的运动微分方程,推导了其动态传递矩阵。讨论了轴向载荷的变化对薄壁梁弯扭耦合振动固有频率的影响,并由此得到零频率振动(弹性屈曲)发生时相应的轴向载荷。数值结果表明本文方法在其适用范围内是精确有效的。

The dynamic transfer matrix of axially-loaded uniform Bernoulli-Euler thin-walled beam element was derived by solving the governing motion differential equation of beam. The effect of axial force on the natural frequency of thin-walled beam with bending-torsional vibration is discussed. The critical axial load corresponding to the zero frequency vibration (elastic buckling) was also obtained. The numerical example demonstrates that the accuracy and effectiveness of the present method are available in the adaptable range.