06-09-2016, 10:42 AM
1453176564-coulombdamping.docx (Size: 1.64 MB / Downloads: 5)
Coulomb damping: It states that for two dry solid surfaces sliding against one another, the magnitude of the kinetic friction exerted through the surface is independent of the magnitude of the velocity (i.e., the speed) of the slipping of the surfaces against each other. The damping force is constant in magnitude but opposite in direction to that of the motion of the vibrating body. It is caused by friction between rubbing surfaces that are either dry or have insufficient lubrication.
In this figure there are two cases:
Case 1 : x andx ̇ positive or x is positive and is negative.
using Newton’s second law:
and the solution of the equation will be
Where
Case 2:
x is positive and is negative or both are negative.
and using Newton’s second law:
and the solution of the equation will be
Motion of the mass with coulomb damping:
The motion in the first half cycle
at initial condition :
and
the constants will be :
and the Eq. becomes :
This means that the vibration amplitude is reduced about 2δ in half cycle.
The motion in the second half cycle
At the initial conditions, the constants will be :
And the Eq. becomes: