含裂纹梁的模态与振动疲劳寿命分析

Modal and vibration fatigue life analysis of a cracked beam

基于传递矩阵法和Paris公式,提出一种对含初始横向裂纹悬臂梁进行模态和振动疲劳寿命分析的理论方法.采用无质量弯曲弹簧来等效横向裂纹,弹簧刚度通过裂纹引起悬臂梁的局部柔度来表述,则整条悬臂梁被离散成弯曲弹簧连接的两段完整梁.根据Euler-Bernoulli梁理论,采用更精简方法推导出悬臂梁的特征传递矩阵,分析裂纹参数对悬臂梁前五阶模态的影响.通过同步分析法使得裂纹梁模态和疲劳裂纹扩展分析同时进行,采用Paris公式模拟疲劳裂纹的扩展速率,研究悬臂梁根部区域裂纹参数对悬臂梁振动疲劳寿命的影响.结果表明,疲劳裂纹对悬臂梁的各阶模态和振动疲劳寿命的影响很大,且悬臂梁根部区域的任意位置都可能发生疲劳断裂.

Based on the transfer matrix method and Paris equation,an analytical method is proposed to conduct the modal and vibration fatigue life analysis of the cantilever beam with an initial transverse crack.The bending spring without mass is used to replace the transverse crack,and the spring stiffness is obtained by the caused local flexibility of the cantilever beam.Then,the whole cantilever beam is dispersed into two complete beams connected by the bending spring.According to the Euler-Bernoulli beam theory,the characteristics transfer matrix of the cantilever beam is derived by a simpler method,and the influence of the crack parameters on the first five modes is analyzed.The simultaneous analysis of the cracked beam modal and fatigue crack growth is conducted by the timing analysis method,and fatigue crack growth velocity is simulated by Paris equation,then the effect of the crack parameters on the vibration fatigue life is investigated.Results indicate that the fatigue crack has an important effect on the modal and vibration fatigue life of the cantilever beam,and the fatigue damage may occur at any position in the root zone.