Longitudinal and Transverse Oscillations of an Elastically Fixed Wall of a Wedge-Shaped Channel Installed on a Vibrating Foundation

Аннотация

The problem of mathematical modeling of longitudinal and transverse oscillations of an elastically fixed wall of a narrow wedge-shaped channel filled with a viscous incompressible liquid and installed on vibrating foundation was stated and solved analytically. The problem was considered in a flat definition for the mode of steady-state forced harmonic oscillations. The mathematical model developed includes the Navier-Stokes equations and the equation of continuity for a thin layer of viscous incompressible liquid and the equations of dynamics of an elastically fixed channel wall. The conditions of adhesion of the liquid to the channel walls and the conditions of a free outflow of liquid at the ends were chosen as the boundary conditions. For the stated problem, the system of dimensionless variables was proposed. Analytical expressions for the wall displacements and the hydrodynamic parameter of the layer of liquid were obtained. The calculations, which made it possible to estimate the influence of inclination of the channel wall and the viscosity of the liquid to damping of oscillations of the elastically fixed wall, were performed.