Coulomb Damping - Theory

Theory

Coulomb damping dissipates energy constantly because of sliding friction. The magnitude of sliding friction is a constant value; independent of surface area, displacement or position, and velocity. The system undergoing Coulomb damping is periodic or oscillating and restrained by the sliding friction. Essentially, the object in the system is vibrating back and forth around an equilibrium point. A system being acted upon by Coulomb damping is nonlinear because the frictional force always opposes the direction of motion of the system as stated earlier. And because there is friction present, the amplitude of the motion decreases or decays with time. Under the influence of Coulomb damping, the amplitude decays linearly with a slope of ±((2μmgω_n)/(πk)) where ω_n is the natural frequency. The natural frequency is the number of times the system oscillates between a fixed time interval in an undamped system. It should also be known that the frequency and the period of vibration do not change when the damping is constant, as in the case of Coulomb damping. The period τ is the amount of time between the repetition of phases during vibration. As time progresses, the object sliding slows and the distance it travels during these oscillations becomes smaller until it reaches zero, the equilibrium point. The position where the object stops, or its equilibrium position, could potentially be at a completely different position than when initially at rest because the system is nonlinear. Linear systems have only a single equilibrium point.