Vibration analysis aims to reduce equipment maintenance costs and downtime by detecting faults. There are two types of vibrations: free vibrations where the energy stays constant and forced vibrations caused by periodic force input. Damping reduces oscillations by dissipating the stored energy. The most common type is viscous damping where resistance from a fluid dissipates energy depending on parameters like relative velocity. Viscous damping uses fluid films between surfaces, with damping resistance proportional to relative velocity. Fluid dashpots use viscous friction to proportionally relate force to velocity in the opposite direction to slow motion. Eddy current damping uses a magnet and non-ferrous metal where motion induces eddy currents providing resistance.

1. Subject: Dynamics of Machinery
Topic:Damped Free Vibration

2. Vibration Analysis
• Vibration Analysis, applied in an industrial or
maintenance environment aims to reduce maintenance
costs and equipment downtime by detecting equipment
faults. Vibration Analysis is a key component of a
Condition Monitoring (CM) program.
• Free vibrations are oscillations where the total energy
stays the same over time. This means that the amplitude
of the vibration stays the same. Forced vibrations occur
when the object is forced to vibrate at a particular
frequency by a periodic input of force.

3. Damping
• Damping is an influence within or upon an
oscillatory system that has the effect of reducing,
restricting or preventing its oscillations.
• In physical systems, damping is produced by
processes that dissipate the energy stored in the
oscillation.

4. Damping
Types of
Damping
Viscous
Damping
Coulomb or Dry
friction
Damping
Material or solid
or structural
Damping

5. Viscous Damping
• This is the most commonly used damping mechanism
to reduce the amplitude of vibrations.
• When system vibrates in a fluid medium like: air, gas,
water or oil, the resistance is offered by the fluid to
the vibrating body which dissipate the energy.
• Depends upon:
– Relative velocity of vibrating body
– Parameters of the damper

6. Viscous Damping
• In viscous damping, the two surfaces having relative
motion are separated by a viscous fluid film.
• This fluid film offers resistance to motion of one surface
with respect to another surface. This resistance is known
as damping resistance.
𝐹 = µ
𝐴𝑉
𝑦
𝐹 = 𝑐 𝑥
F=damping resistance, N
𝑥=relative velocity between two surfaces, m/s
c=damping coefficient, N-s/m

7. Fluid Dashpot Damping
• A dashpot is a mechanical device,
a damper which resists motion via
viscous friction.
• The resulting force is proportional to the velocity,
but acts in the opposite direction, slowing the
motion and absorbing energy. It is commonly used
in conjunction with a spring (which acts to resist
displacement).

8. Applications
• Door closer.
• Dampers and shock absorbers.
• Automobile shock absorber.
• Carburetors to reduce emissions.
• Large forces and high speeds can be controlled by
dashpots. For example, aircraft carrier decks.
• Electrical switchgear.
• Anti stall mechanism in internal combustion engines.

9. Fluid Dashpot Damping

10. Eddy Current Damping
• It is based on the principle of magnetic flux.
• It consist of a magnet and non-ferrous metal.
• Due to movement of non-ferrous plate an eddy
current is generated and there is resistance to the
motion of the plate in a magnetic field which results
in damping.

11. Applications
• It is used in,
– Vibrometers
– Vibration control devices
– Vehicle braking
– Roller coaster braking
– Elevators

12. Eddy Current Damping

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