Critical velocity analysis of Fluid-containing Pipe with Non-Classical Boundary Conditions

calculating the critical velocity of fluid-containing pipes is an important issue in engineering. For this purpose, the critical velocity of fluid-containing pipes with Non-classical boundary conditions is investigated. The equation of motion is based on the Euler-Bernoulli beam model. Non-classical boundary conditions include conditions such as Translational springs, torsional springs, concentrated mass and dampers. In order to calculate the critical velocity the frequency equation is solved numerically. when real part of frequency equation reaches zero, the critical velocity in the pipe appears and the system becomes unstable.influence of various parameters including spring hardness and concentrated mass on critical velocity is investigated and comparative diagrams of different spring hardnesses and concentrated mass are drawn. The results show that the critical velocity in the Translational double-ended state is higher than the torsional spring-concentrated mass and torsional springconcentrated mass boundary condition . The results also indicate a significant decrease in the frequency in the non-classical boundary condition compare to classical boundary condition.