Stability Of Cracked Cantilever Pipeline Conveying Fluid On Two-Parameter Elastic Foundation With Distributed Follower Force

With the development and progress of modern society industry, flow pipeline is widely used in petroleum, chemical and other important engineering field it as an important means of transportation. Safety and durability problem increasingly prominent.It will bring us casualties and property losses if these problems cannot be handled very well. In recent years,accidents happened that caused by the stability of the flow pipeline frequently,therefore the study of flow pipeline stability is a very necessary and great practical significance in the aspect of engineering design and operation.The thesis mainly studies the stability of the cantilever pipes with the distributed follower force on two-parameter foundation by using the complex mode method, the matrix transfer method and Galerkin method when the foundation stiffness varies and effects by the crack location and depth. Main contents and results are as follows:1. Through the stress analysis of cantilever pipes system, we get the movement differential of the cantilever pipes with the distributed follower force equation on two-parameter foundation, and then make it dimensionless.2. By solving the differential equations of dimensionless motion with the complex mode method,we can get the corresponding modal function. The relationship between the flow velocity and the first and second order natural frequency can be calculated without crack, while taking into account the stability of the entire cantilever pipe system when the foundation stiffness and mass ratio vary.3. The system frequency equation is calculated by using transfer matrix method without crack. The relationship between dimensionless critical velocity with flutter instability and dimensionless distributed force is got when the foundation stiffness takes different values. It is concluded that the complex frequency of the cantilever pipe system when dimensionless velocity,dimensionless distributed force, foundation stiffness and mass ratio vary,analyses the stability of the pipeline.4. Transfer matrix of crack is got through simplifying the crack part processing and combining with the boundary conditions of crack, and then made it into the overall transfer matrix of the cantilever flow pipeline with crack. Natural frequency and modal function of the cantilever flow pipeline are obtained by computing and also calculate system characteristic frequency of the first order with crack location and depth vary.5. The relationship between critical dimensionless velocity with instability and dimensionless distributed force can be got when position of crack is different by solving the characteristic frequency. We can get the complex frequency when the foundation stiffness, mass ratio, distributed force and dimensionless velocity distribution, the crack location and depth vary. The stability of the pipeline system is analyzed.