干摩擦悬臂梁一阶等效固有频率研究

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振动与冲击 ›› 2015, Vol. 34 ›› Issue (10) : 46-49.

论文

干摩擦悬臂梁一阶等效固有频率研究

赵峰1,2,3，曹树谦1,2,3，冯文周1,2,3

作者信息 +

The study of the first order equivalent natural frequency for a cantilever beam with dry friction

ZHAO Feng1,2,3，CAO Shu-qian1,2,3，FENG Wen-zhou1,2,3

Author information +

文章历史 +

摘要

采用牛顿第二定律及拉格朗日方程，分别对干摩擦悬臂梁及等效模型建立振动控制方程，获得两种模型的激励力与频率关系式，基于能量相等建立等效方程进行一阶等效固有频率研究，获得干摩擦悬臂梁等效固有频率解析表达式。采用数值方法计算干摩擦悬臂梁模型一阶固有频率。结果表明，数值与解析结果一致性较好，即悬臂梁等效固有频率随干摩擦增大而减小。所得解析表达式能更直接获得干摩擦力对悬臂梁固有频率影响规律。

Abstract

The aim of this paper is to address the study of the natural frequency of a cantilever beam with dry friction using an equivalent method. The motion equation of the studied model and the equivalent model (a cantilever beam) is established using the Newton’s second law and the second kind of the Lagrange equation, respectively. Then the relationship between excitation force and frequency of the two models can be obtained, base on the idea of inputting same energy, thus the equivalent method can be carried out to obtain an analytical expression for the first order natural frequency of the studied model. The numerical method for the first order natural frequency is used to verify the effectiveness of this equivalent method. The results show that the first order natural frequencies obtained by numerical and analytical method are better unanimous under different dry friction, that is, the equivalent natural frequencies decrease as increasing dry friction. Furthermore, the analytical expression of the equivalent natural frequency can directly reflect a relationship between the frequency and dry friction.

导出引用

赵峰1,2,3，曹树谦1,2,3，冯文周1,2,3. 干摩擦悬臂梁一阶等效固有频率研究[J]. 振动与冲击, 2015, 34(10): 46-49

ZHAO Feng1,2,3，CAO Shu-qian1,2,3，FENG Wen-zhou1,2,3. The study of the first order equivalent natural frequency for a cantilever beam with dry friction[J]. Journal of Vibration and Shock, 2015, 34(10): 46-49

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