# Viscous Damping Coefficient

Dampers have been widely used to reduce the amplitude of vibration by absorbing or dissipating energy. In general, damping can be divided into three types: viscous damping, column or friction damping, and solid (internal) or structural damping. We will focus on viscous damping in this blog. The principal of viscous damping is to convert kinetic energy due to vibration to heat. Viscous damper designs are adaptable to many applications such as shock absorber in vehicle, viscous torsional damper in engine.

The damping force is produced when a rigid body is in contact with a viscous fluid. It is usually proportional to the velocity of the body Ʋ,

F = cƲ

Where c is called the damping coefficient.

A simple dashpot configuration shown in the Figure. The plate slides over a fixed reservoir of viscous liquid dynamic viscosity µ. The area of the plate in contact with the liquid is A. The shear stress developed between the fluid and the plate creates a resultant friction force acting on the plate. Assume the reservoir is stationary and the upper plate slides over the liquid with a constant velocity Ʋ. The reservoir depth h is small enough that the velocity profile in the liquid can be approximated as linear. If y is coordinate measured upward from the bottom of the reservoir, the velocity profile can be written as:

u(y) = Ʋ y
h

The shear stress developed on the plate is determined from Newton’s viscosity law:

† = µ du = µ Ʋ
dy        h

The viscous force acting on the plate is:

F = †A = µA  Ʋ
h

By comparing the equations, it can be concluded that the damping coefficient for the dashpot is:

c =  µA
h

Note the large damping force can be accomplished by a very viscous fluid, small h, and a large A.