The theoretical determination of the damping coefficients of the surrounding medium by means of the aerodynamical boundary-layer theory

In problems involving the occurrence of mechanical vibrations, it is generally assumed that the damping coefficients related to the surrounding medium, gas or liquid, are constant. The present investigation aims to demonstrate that the assumption of a constancy of the damping coefficients is incorrect. The case of a rigid orthogonal parallelepiped is considered. This case involves a vibratory system with six degrees of freedom. The vibration can take place in a compressible or incompressible liquid. The damping coefficients are determined on the basis of the aerodynamical theory of the boundary layer and the mechanical principle of the energetic equilibrium. It is found that the damping coefficients depend on the density and the kinematic viscosity of the surrounding medium. The values of the two medium parameters are a function of pressure and temperature. In addition, the damping coefficients depend also on the volume of the vibrating body, and the frequency and the maximum amplitude of the vibrations.