Parametric investigation of the stability of coaxial cylindrical shells containing flowing fluid

The dynamic behavior of elastic coaxial cylindrical shells interacting with two flows of a perfect compressible fluid is investigated by application of the finite element method. The fluid behavior is described by the potential theory, the equations of which are reduced to the integral expressions using the Bubnov-Galerkin method. The pressure exerted by the fluid on the deformable body is determined through the use of the Bernoulli equation. The treatment of elastic shells is accomplished in the framework of the classical shell theory. A mathematical formulation of the problem is based on the principle of virtual displacements. With all things considered, the stated problem reduces to simultaneous solution of 4 sets of equations. For shells with different boundary conditions the numerical investigations have been carried out to explore the effects of the annular gap, the flowing fluid density and physicomechanical properties of the shells on the stability boundary.