含裂纹悬臂输流管道颤振分析

Flutter of cracked cantilever pipes conveying fluid

基于适用于含非材料体(non-material volumes)系统的Lagrange方程,采用由无裂纹悬臂梁的模态函数加入分段立方多项式构造的裂纹梁的模态函数,推导出了含裂纹的悬臂输流管道的线性运动方程,最后用Matlab编程进行了数值计算,研究裂纹参数对悬臂输流管道动力特性和颤振特性的影响。结果表明:当固支端附近出现裂纹时,输流管道的颤振临界流速将减小,越靠近固支端,颤振临界流速减小的越多。且随着裂纹深度增加颤振临界流速降低的更加明显。但裂纹离固支端一定位置后时,裂纹的出现将会增大管道的临界流速。另外,裂纹的出现还将导致悬臂输流管道颤振阶数的改变。

Based on the extended Lagrange equations for systems containing non-material volumes,the equations of motion of cracked cantilever pipe conveying fluid were set up with the help of using supposed mode functions composed of modal functions of uncracked beam and additional polynomial functions to satisfy the boundary conditions and geometrical discontinuity conditions.A numerical example was taken to analyze the dynamical performance and flutter characteristics.The calculated results show the critical flow velocity in pipe conveying fluid descends when the crack emerges near the clamped end and will reduce more and more with the increase of crack depth.But when crack locates far from the clamped end beyond certain distance,the critical flow velocity will ascend with the appearance of crack.In addition,the flutter modes of system will be changed when the crack occurs.