Elastic Support And Stability Cracked Pipes Conveying Fluid Force Distribution Under Entourage

Fluid-structure interactions of elastic support pipes and crackedpipes conveying fluid under the coaction of distributed follower forceand flowing fluid are respectively analyzed theoretically, numerically aswell as dynamical property under various factors and abundantmanifestation of stability. Finite element software ABAQUS is utilizedto evaluate simulation results and invested theoretical yields ofcantilevered pipes conveying fluid loaded with distributed follower force.Following are the main contents and results of this study:1. The dynamic differential equation for pipes under co-action ofdistributed follower force and flowing fluid is established and thendiscretized with Galerkin method by choosing modal functions ofelastically supported beam and cracked beam as trial functions. Generalmodal function expression and frequency eigenvalue of elasticallysupported pipes are worked out combined with boundary conditions.General expression and frequency eigenvalue of cracked pipes areworked out by transfer matrix method combined boundary conditions.2. Relationships between dimensionless critical flow velocity anddistributed follower force and changes of the first two eigenvalues ofpipes supported with various elastically supported stiffness are gainedvia solving eigenvalue problem. Relationships between critical flowvelocity and dimensionless distributed follower force changing with crack, location, depths and eigenvalues of cracked pipes are gained.3. Complex frequencies of pipes are gained changing with supportstiffness, distributed follower force, flow velocity,mass ratio as well ascritical flow velocity. Influences on critical flow velocity and instabilityforms under various crack depths and locations of simply supportedpipes are gained.4. ABAQUS finite element model of cantilevered pipes withdistributed follower force is established. Stability of pipes under theco-action of follower force and flowing fluid is studied resorting tofluid-structure interaction contact face. Numerical simulation results areassessed referring invested theoretical conclusions.