Flow-induced vibration of a y-shaped tube conveying fluid

This work investigates out of plane vibration of a Y-shaped tube conveying fluid with clamed ends conditions. The mathematical model is based on the equation of motion of each tube coupled with matched boundary conditions at the junction of the three segments. The resulting equations are then resolved using Galerkin approach. The resulting eigen-values, eigen-function and shape modes are found numerically. A stability analysis of the solution is then performed. The effect of geometrical and flow parameters on the vibration of the Y-shaped tube conveying fluid is investigated. Results show that for small length of branching side compared to the supplying tube and for zero branching angle then the first three non-dimensional frequency is close to those of straight single tube with clamped-clamped conditions. Moreover, neutral stability regions were observed in firs, second, and third modes for large range of dimensionless flow velocity. Results further demonstrate that an increase in dimensionless flow velocity results in decreasing of the non-dimensional frequency for the first three modes. Effect of branching angle and geometrical configuration of the mode shape and frequency is also investigated.