含多条裂纹梁的模态与振动疲劳寿命分析
Analysis of Mode and Vibration Fatigue Life of Beam with Multiple Cracks

基于Paris公式，提出了一种含多条裂纹梁疲劳寿命预估的方法。在模态分析中，基于传递矩阵方法，利用质量的弯曲弹簧等效裂纹，提出一种求解含有多条裂纹梁固有振型的方法,分析裂纹数目、裂纹位置、裂纹深度对裂纹梁固有频率的影响。在振动疲劳分析中，研究了在简谐激励作用下裂纹数目对裂纹尖端应力强度因子的影响。通过Paris疲劳裂纹扩展方程和同步分析法，考虑裂纹梁振动与裂纹扩展的相互作用，分析了裂纹数目和裂纹位置对裂纹梁疲劳寿命的影响。结果表明,裂纹数量、裂纹位置和深度对梁的模态参数和疲劳寿命有重要影响。
An analytical method is proposed to predict the fatigue life of the beam with multiple cracks based on the Paris equation.In the modal analysis process, the segment of cracks is replaced with bending springs, a new method for solving natural modes of the beam with multiple cracks is proposed based on the transfer matrix method, and the effect of the number, locations and depths of cracks on the natural frequency of the cracked beam is analyzed. In the vibration fatigue analysis, the effect of the number of cracks on the crack-tip stress intensity factor under harmonic excitation is analyzed. Considering the interaction of cracked beam vibration and fatigue crack growth, the effect of the number and the location of the cracks on the cracked beam fatigue life is analyzed based on timing analysis and Paris equation. The results indicate that the number, locations and depths of cracks have important effects on the modal parameters and the fatigue life of the structure.