Stability of moving viscoelastic panels interacting with surrounding fluid

Abstract

We study a model describing the out-of-plane vibrations of an axially moving viscoelastic panel submerged in flowing fluid. The panel is assumed to travel at a constant velocity between two fixed supports, and it is modeled as a flat panel made of viscoelastic Kelvin-Voigt material. The fluid flow is modeled with the help of the added mass coefficients. The resulting dynamic equation is a partial differential equation of fifth order in space. Five boundary conditions are set for the studied problem. The behavior of the panel is analyzed with the help of its eigenvalues (eigenfrequencies). These characteristics are studied with respect to the velocity of the panel. In our study, we have included the material (total) derivative in the viscoelastic relations. We study the effects of the surrounding flowing fluid on the behavior of the moving viscoelastic panel. It was found that, in presence of flowing fluid, the critical panel velocity was significantly lower than in the vacuum case. Secondly, for high enough values of viscosity, the panel did not experience instability detected at low values of viscosity in the form of divergence. The flowing fluid was found to diminish the stabilizing effects brought about by material viscosity.