不同温度下裂纹悬臂梁的模态和疲劳寿命分析

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振动与冲击 ›› 2017, Vol. 36 ›› Issue (8) : 132-137.

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马一江 1 ，陈国平 1

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Modal and fatigue life analysis of a cracked cantilever beam under different temperatures

MA Yijiang,CHEN Guoping

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摘要

基于扭转弹簧模型和修正Paris公式，提出了一种在不同外界温度下含初始裂纹悬臂梁的疲劳寿命估算方法。在模态分析过程中，通过弹性模量引入温度模块，利用扭转弹簧等效该裂纹，将悬臂梁转化为由扭转弹簧联接的两段弹性梁；推导出不同温度下含裂纹梁固有振型的特征方程，分析温度和裂纹几何参数对裂纹梁固有频率的影响。在疲劳寿命分析过程中，利用复弹性模量引入阻尼损耗因子，基于修正Paris方程和同步分析法，考虑裂纹梁振动与疲劳裂纹扩展的相互作用，分析温度、阻尼和悬臂梁根部区域裂纹几何参数对裂纹梁疲劳寿命的影响。结果表明：随着裂纹相对位置的减小以及裂纹相对深度的增大，裂纹悬臂梁的固有频率和疲劳寿命则逐渐降低；而外界温度的升高也会导致裂纹悬臂梁固有频率和疲劳寿命的降低；同时随着阻尼损耗因子的逐渐增大，裂纹悬臂梁的疲劳寿命也会逐渐增加。

Abstract

Based on the torsion spring model and the modified Paris formula,an analytical method was proposed to predict the fatigue life of a cantilever beam with an initial crack under different external temperatures.In the modal analysis process,the temperature module was introduced through the elastic modulus,and the cracked cantilever beam was transformed to two intact elastic beams by using a torsion spring to replace the crack segment; An inherent vibration characteristic equation of the cracked beam would be deduced under different temperatures,and effects of temperatures and crack geometric parameters on the frequency of the cracked beam would be analyzed.In the fatigue life analysis process,the damping loss factor was introduced through the complex elastic modulus.Considering the interaction of the cracked beam vibration and the fatigue crack growth,effects of temperatures,dampings and crack geometric parameters on the fatigue life of the cracked beam would be analyzed based on the modified Paris formula and the timing analysis method.Results indicate: the natural frequency and fatigue life of the cracked cantilever beam gradually decrease with the decreased relative position and the increased relative depth of the crack.And the increase of external temperature leads to the decrease of the natural frequency and fatigue life of the cracked cantilever beam.The fatigue life of the cracked beam gradually increases with the increased damping loss factor.

关键词

裂纹

/ 悬臂梁 / 扭转弹簧 / 温度 / 振动疲劳

Key words

crack

/ cantilever beam / torsion spring / temperature / vibration and fatigue

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马一江 1,陈国平 1. 不同温度下裂纹悬臂梁的模态和疲劳寿命分析[J]. 振动与冲击, 2017, 36(8): 132-137

MA Yijiang,CHEN Guoping. Modal and fatigue life analysis of a cracked cantilever beam under different temperatures[J]. Journal of Vibration and Shock, 2017, 36(8): 132-137

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