引用本文: 孙秀荣, 张立娟, 赵洁妤, 宋杨. 考虑分布轴向力的细长杆横向振动与失稳分析1)[J]. 力学与实践, 2021, 43(1): 74-83.
SUN Xiurong, ZHANG Lijuan, ZHAO Jieyu, SONG Yang. TRANSVERSE VIBRATION AND INSTABILITY OF SLENDER ROD WITH CONSIDERATION OF DISTRIBUTED AXIAL FORCE1)[J]. MECHANICS IN ENGINEERING, 2021, 43(1): 74-83.
 Citation: SUN Xiurong, ZHANG Lijuan, ZHAO Jieyu, SONG Yang. TRANSVERSE VIBRATION AND INSTABILITY OF SLENDER ROD WITH CONSIDERATION OF DISTRIBUTED AXIAL FORCE1)[J]. MECHANICS IN ENGINEERING, 2021, 43(1): 74-83.

## TRANSVERSE VIBRATION AND INSTABILITY OF SLENDER ROD WITH CONSIDERATION OF DISTRIBUTED AXIAL FORCE1)

• 摘要: 为量化梁、杆、柱的自重(下称分布轴向力)对静力失稳和动力横向振动的影响,在《材料力学》和《机械系统动力学》教材的基础上,建立了分布轴向力下的杆柱失稳和横向振动的力学、数学模型。采用有限差分法、伽辽金法和数值积分法获取计算结果。结果表明：考虑分布轴向力的杆柱横向振动固有频率随杆长增加而减小,杆柱失稳时一阶固有频率为0;分布轴向力对较短杆柱的临界载荷影响较小,对较长杆柱影响较大;伽辽金法不适用计算超长杆柱的失稳临界载荷。

Abstract: In order to quantify the effect of the dead weight (hereinafter called the distributed axial force) of the beam, the rod and the column on the static instability and the transverse vibration, the mechanical and mathematical models of the instability and the transverse vibration are established with consideration of the distributed axial force. The finite difference method, the Galerkin method and the numerical integration method are used to obtain the numerical results. The results show that: the natural frequency of the rod with the axial distributed force decreases with the increase of the rod length, and the first order natural frequency is zero when the rod is unstable; the axial distributed force has a small impact on the critical load of the shorter rod, but has a greater impact for a longer rod; the Galerkin method is not suitable for calculating the buckling critical load of the super long rod.

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