Theoretical and experimental research of thin-walled structures interacting with viscous fluid

Abstract

The results of studying thin-walled plates and cylindrical shells interacting with the stationary or flowing viscous compressible fluid are presented. The numerical solution of the problem has been carried out using the finite element method. The motion of liquid medium is described by the system of linearized Navier-Stokes equations, the solution of which is sought for in the form of the acoustic approximation in terms of velocity perturbation potential. The relations obtained for liquid and the corresponding boundary conditions are transformed by the Bubnov-Galerkin method. The behavior of a thin-walled structure is described in the framework of the classical theory of thin plates. The mathematical formulation of the dynamic problem of an elastic body is based on the variational principle of virtual displacements. Stability estimation is based on the calculation and analysis of complex eigenvalues of a coupled system of equations. The influence of fluid viscosity and other parameters on the natural vibration frequencies and critical velocities responsible for the loss of structural stability has been analyzed. The natural frequencies and the corresponding decrements of harmonic vibrations of rectangular plates located in the air and on the free liquid surface have been studied with the help of developed experimental setup. It has been found out that the damping coefficient corresponding to one vibration mode (bending or torsional) grows with an increase in the number of nodal lines. It has been demonstrated that this relation can be violated during the interaction of the plates with the liquid.