Numerical simulation of an elastic tube containing a flowing fluid

The finite element method is applied to analyze natural vibrations and stability of cylindrical tubes interacting with inviscid compressible fluid. The motion of bodies of revolution is described in the framework of the linear theory of elasticity. The compressible media is considered in accordance with potential theory. The corresponding differential equation for the potential velocity perturbation is reduced to a system of equations using the Galerkin method. For pipe used variational principle of virtual displacements, which includes the linearized Bernoulli equation to calculate the hydrodynamic pressure exerted by the fluid on the elastic structure. Numerical simulation is based on the semianalytic finite-element method. The solution of the problem reduces to evaluation and analysis of the complex eigenvalues of the connected system of equations. The results are compared with known theoretical and experimental data for pipes containing stationary or flowing medium. The limits of applicability of different types of finite elements including the shell element have been determined.