Added mass and damping coefficient calculation for the rigid cylinder vibrating in cylindrical channel based on viscous fluid motion equation numerical integration

The one-dimensional NavierStokes equations solution has been considered to perform the added mass and damping coefficient calculation during vibration of the rigid cylinder in the cylindrical channel. A harmonic type of oscillations and the cylindrical channel geometry allow to eliminate two independent variables, which leads to the fourthorder ordinary differential equation. Low liquid viscosity generates thin boundary layers, and consequently the derived resolving equation becomes stiff. This numerical problem can be solved by means of precision increasing (60–80 decimal digits in Mathematica software numbers representation) and appropriate integration step selection. The relations of added mass and damping coefficients on liquid viscosity have been plotted.